Liquid heating apparatus
BACKGROUND OF THE INVENTION 
     The present invention relates to a liquid heating apparatus for use in a boiler and the like utilizing an up/down flow process with respect to the heated gas. 
     The so-called `up/down flow process` herein means a method wherein a heated gas is made to flow in an inverted U-shaped gas passage so as to effect heat exchange between the flowing heated gas and a liquid surrounding said gas passage, whereby the temperature of the heated gas is gradually lowered with its progress and the downward movement of the gas in the falling portion of the gas passage is facilitated to enhance the draft power of the passage, smooth the discharge of carbon dioxide as well as the supply of air and raise the combustion efficiency. This process will first be explained. 
     Referring to FIG. 1 in the appended drawings, when the pressure acting upon the point A (the heat source) and the point B (the flue gas exit) on the datum level L and the point C of the height H of an inverted U-shaped gas passage X is expressed by P A , P B  and P C , respectively, the relations of these points are expressed by the following equations. ##EQU1## 
     γ A  AND γ B  HEREIN REPRESENT THE SPECIFIC WEIGHT OF THE LIQUID WITHIN THE GAS PASSAGE X at an optional height (0&lt;H) above A and B, respectively. When the pressure P B  acting upon the point B is equivalent to atmospheric pressure P O , since P B=P   O , from the equation (2), ##EQU2## 
     When the equation (1) is substituted by the equation (3), ##EQU3## AND THE PRESSURE ACTING UPON THE POINT A is lower than the atmospheric pressure by an equivalent of ##EQU4## 
     When the draft power Pch on this occasion is expressed by the following equation ##EQU5## in the case of Pch&gt;0, the pressure acting upon the point A can be expressed by P A  &lt;P C  (negative pressure), and a flow in the direction of A → C → B takes place. In the case where radiation occurs in the portion ACB of the gas passage X to give rise to a thermal gradient along the direction of the gas passage, γ a  and γ b  take the value that 
     
         γ.sub.a = f(h) γ.sub.b = f(h) . . . (6), 
    
     and the equation (5) can be expressed as follows. ##EQU6## Accordingly, in order to realize the state of Pch&gt;0, the relation between γ a  and γ b  in the equation (7) should be as follows. 
     
         γ.sub.b - γ.sub.a &gt;0 γ.sub.b &gt; γ.sub.a . . . (8) 
    
     Consequently, the greater is the value of (γ b  -γ a ) as well as the value of H, the greater becomes the flow. 
     Next, from the following equations expressing the state of a perfect gas 
     
         PV = RT, V = (1/γ), 
    
     
         (p/γ) = rt, γ= (p/rt) ... (9) 
    
     wherein, 
     P: gas pressure, kg/m 2  ; 
     V: volume of gas, m 3  ; 
     R: constant for fluid gas, kgm/kg°K ; 
     t: absolute temperature, °K : 
     γ: specific weight of gas, kg/m 3 . 
     Accordingly, ##EQU7## 
     From this equation, it is clear that the smaller is the ratio of Tb to Ta, the greater becomes the value of γ b  - γ a  and consequently the value of Pch becomes greater (Ta and Tb herein represent the absolute temperature of the gas within the supply pipe at an optional height above the point A and point B). 
     It will be understood from the above description that the draft power is closely related to the difference of density between the rising gas passage and the falling gas passage, and the greater is the difference of density between the two passages, to wit, the greater is the difference of temperature between the rising heated gas chamber and the falling heated gas space, the greater is the draft power that is generated. 
     To cite an instance of the liquid heating apparatus utilizing the above described up/down flow process developed hitherto, there has been proposed an apparatus such as shown in FIG. 2 by the present inventor. This previously proposed apparatus is of a structure such that an inner body portion 41 is installed within an outer body portion 40 by leaving a required space between the two so as to form an outside water jacket 45, an inside water jacket 46 defined by a double wall consisting of flat plate-shaped members, said inside water jacket communicating with said outside water jacket at the upper and lower parts thereof, is installed within said inner body portion 41, a rising heated gas chamber 42 is formed along one side of said inside water jacket 46 while a falling heated gas space 43 is formed along the other side of the same, a flue communicating with said falling heated gas space 43 is provided at the upper part of said rising heated gas chamber 42, and a flue gas exit 44 is provided at the lower part of said falling heated gas space 43. 
     However, a liquid heating apparatus of such a structure is defective in that, inasmuch as the heated gas heats the upper part c of the inner body portion 41 intensely, the temperature of the upper part a of the outside water jacket 45 rises rapidly compared with the lower part b thereof, while the heating of the liquid within the lower part b of said water jacket 45 is insufficient and, therefore, the thus insufficiently heated liquid stagnates in the upper part a of the outside water jacket 45, natural convection of the liquid is hampered thereby making it difficult to raise the combustion efficiency as well as the thermal efficiency, to wit, as for the thermal efficiency in particular, achievement of more than 70% is infeasible, and moreover NOx which is very harmful to the environmental sanitation as well as the durability of the apparatus is generated. 
     However, development of a liquid heating apparatus capable of achieving thermal efficiency of more than 70% has recently been hoped for. Accordingly, the present inventor has examined the foregoing drawbacks of the existing apparatuses in every way and has come to the finding that those drawbacks are related to the ratio of the width Wd of gas passage of the falling heated gas space 43 to the width Wu of the gas passage of the rising heated gas chamber 42 as well as the ratio of the width Bi of the passage of the inside water jacket to the width Bo of the passage of the outside water jacket, to wit, in the case where Wd/Wu and Bi/Bo are respectively about 0.8 or more, there occurs such a phenomenon as seen in conventional apparatuses, while in the case where said ratios are respectively 0.8 or less than 0.8, said phenomenon disappears and a thermal efficiency of more than 70% can be achieved. 
     And, this effect is considered attributable to the fact that, by virtue of setting the value of said Wd/Wu at 0.8 or less than 0.8, heat exchange between the heated gas and the liquid surrounding the gas passage is performed efficiently, and as a result, the temperature of the heated gas is lowered remarkably and the downward movement of the gas in the falling portion of the gas passage is facilitated thereby to enhance the draft power, smooth the discharge of carbon dioxide as well as the supply of air and raise the combustion efficiency, and also by virtue of the value of said Bi/Bo being 0.8 or less than 0.8, the heat capacity of the liquid within the inside water jacket 46 is less than that of the outside water jacket 45 and the inside water jacket 46 is heated with the heated gas by way of both sides thereof, and as a result, the temperature of the liquid within the inside water jacket 46 is raised rapidly while the temperature of the liquid within the outside water jacket 45 is not so rapidly raised compared with the liquid within the inside water jacket 46; consequently, there occurs rising current of liquid within the outside water jacket 45 due to the sudden rising flow as in boiling, and by virtue of this rising current, these occurs an increase of pressure in the upper part of both the outside and the inside water jacket 45, 46, and this increase of pressure, coupled with the difference of the temperature of liquid within the foregoing water jackets 45, 46, gives rise to a downward movement of the liquid within the outside water jacket 45, whereby there is generated a remarkable convective movement of the liquid within a closed passage including the both water jackets 45, 46. 
     SUMMARY OF THE INVENTION 
     The present invention has been achieved on the basis of the foregoing finding, and it is intended for providing a liquid heating apparatus which not only eliminates the drawbacks of the conventional liquid heating apparatuses and achieves a thermal efficiency of more than 70% but also is free from generating NOx which is very harmful to the environmental sanitation as well as the durability of apparatus per se. 
     The object of the present invention is to provide a liquid heating apparatus which comprises an inner body portion disposed within a vertical hexahedral outer body portion and spaced therefrom so as to form an outside water jacket, two vertically oriented plate members disposed within said inner body portion with there being a space between the two plate members forming on inside water jacket and spaces between the plate members and the walls of inner body portion forming a rising heated gas chamber along one side and a falling heated gas space along the other side of the latter space, said rising heated gas chamber communicating with said falling heated gas space at their upper ends and the ratio ξf of the width Wd of said falling heated gas space to the width Wu  of said rising heated gas chamber being set at 0.8 or less than 0.8, whereby the drop of the gas temperature while it flows can be accelerated to enhance the draft power, the discharge of carbon dioxide as well as the supply of air can be smoothed, the combustion efficiency can be improved and the generation of harmful NOx can be controlled. 
     Another object of the present invention is to provide a liquid heating apparatus comprising a vertical cylinder-shaped first outer body portion, a first inner body portion which has a shape practically the same as that of said first outer body portion and is disposed within the latter so as to leave a first space defining an outside water jacket, a second outer body portion which has a shape practically the same as that of the first inner body portion and is disposed within the latter and is spaced therefrom to define a second space for falling heated gas, and a second inner body portion which has a shape practically the same as that of said second outer body portion and is disposed within the latter and is spaced therefrom so as to form a third space which defines an inside water jacket and also forms a rising heated gas chamber within said second inner body portion, wherein said inside and outside water jackets intercommunicate at their upper and lower ends and said rising heated gas chamber and falling heated gas space intercommunicate at their upper ends, the ratio of the radius R of said falling heated gas space to the radius r of said rising heated gas chamber (in the case where the inside and outside water jackets are of truncated cone shape, R and r represent the mean radius respectively) is set at a value satisfying the inequality 0&lt;(R/r) - 1≦0.8, whereby the falling of the temperature of the heated gas while flowing can be accelerated to enhance the draft power, the discharge of carbon dioxide as well as the supply of air can be smoothed, the combustion efficiency can be improved and the generation of harmful NOx can be controlled. 
     A further object of the present invention is to provide a liquid heating apparatus which is so designed that the heated gas having its combustion efficiency improved as stated above heats the inside water jacket on both sides thereof within the rising heated gas chamber and the falling heated gas space and, as a result, the temperature of the liquid within the inside water jacket rises rapidly while the temperature of the liquid within the outside water jacket rises relatively slowly, thereby giving rise to a rising current of the liquid within the inside water jacket, and by virtue of this rising current, there occurs an increase of pressure in the upper part of both water jackets which causes a falling current of the liquid within the outside water jacket in concert with the difference of temperature of the liquid within both water jackets, whereby a smooth convective movement of the liquid can be achieved within the closed passage including both water jackets, a rapid rise of the temperature of the upper part of the outside water jacket corresponding to the top of the gas passage relative to the lower part of said water jacket such as seen in conventional apparatuses can be prevented and the entire liquid can be heated uniformly and quickly, and accordingly, the apparatus minimizes combustion noise, and can be manufactured at moderate cost as the structure thereof is simple. 
     A still further object of the present invention is to provide a liquid heating apparatus which is so devised that by virtue of setting the ratio of the width of the passage of the inside water jacket to the width of passage of the outside water jacket at 0.8 or less than 0.8 thereby making the heat capacity of the liquid within the inside water jacket smaller than that within the outside water jacket, coupled with heating the inside water jacket by the heated gas on both sides thereof as stated above, the temperature of the liquid within the inside water jacket rises rapidly while the temperature of the liquid within the outside water jacket does not rise so rapidly compared with the temperature of the liquid within the inside water jacket, and consequently, there occurs a rising current of liquid within the inside water jacket due to the sudden rising flow as in boiling thereby causing an increase of the pressure in the upper part of both the outside and inside water jackets, and by the synergy of this increase of pressure and the difference of pressure within both water jackets, a falling current of liquid within the outside water jacket occurs, whereby a remarkable convective movement of the liquid can be brought about within the closed passage including both water jackets. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     In the appended drawings: 
     FIG. 1 is a diagram illustrative of the up/down flow process with respect to the heated gas; 
     FIG. 2 is a schematic representation of a longitudinal sectional view of a conventional liquid heating apparatus; 
     FIG. 3 is a front view of the first embodiment of the liquid heating apparatus according to the present invention; 
     FIG. 4 is a cross-sectional view taken along the line IV--IV in FIG. 3; 
     FIG. 5 is a cross-sectional view taken along the line V--V in FIG. 4; 
     FIG. 6 is a longitudinal sectional view of the second embodiment of the liquid heating aparatus according to the present invention; 
     FIG. 7 is a cross-sectional view taken along the line VII--VII in FIG. 6; 
     FIG. 8 is a schematic representation of a device for the purpose of testing the liquid heating apparatus according to the present invention; 
     FIG. 9A is a front view of a part of the foregoing first embodiment for the purpose of illustrating the dimension of the respective part thereof; 
     FIG. 9B is a plane figure of the same part as in FIG. 9A; 
     FIG. 10A is a front view of a part of the foregoing second embodiment for the purpose of illustrating the dimension of the respective part thereof; 
     FIG. 10B is a plane figure of the same part as in FIG. 10A; 
     FIGS. 11 and 12 are respectively graphs illustrating the results of tests conducted by varying the width of the gas passage in the first and second embodiments; and 
     FIGS. 13 and 14 are respectively graphs illustrating the results of tests conducted by varying the width of the water passage in the first and second embodiments. 
     DETAILED DESCRIPTION OF THE INVENTION 
     In FIGS. 3 through 5 illustrating the first embodiment of the present invention, the reference numeral 1 denotes a vertical hexahedral outer body portion. Within this outer body portion is disposed a vertical hexahedral inner body portion 2 with there being a space therebetween so as to form an outside water jacket 3 between the outer and inner body portions. Within this inner body portion 2 is disposed a flat board-shaped inside water jacket 8 composed of two vertically oriented plate members, said inside water jacket 8 communicating with the foregoing outside water jacket 3 through an upper convection coupling member 4 and a lower convection coupling member 5. Along one side of the inside water jacket 8 is formed a rising heated gas chamber 9 while along the other side of the same is formed a falling heated gas space 10 so as to make the ratio Sf of the width Bfi of liquid passage of the inside water jacket 8 to the width Bfo of liquid passage of the outside water jacket 3 satisfy the inequality 0≦Sf≦0.8 and also make the ratio ξf of the width Wd of gas passage of the falling heated gas space 10 to the width Wu of gas passage of the rising heated gas chamber 9 satisfy the inequality 0&lt;ξf≦0.8. The upper part of the rising heated gas chamber 9 is provided with a flue 11 communicating with the falling heated gas space 10, while the lower part of the falling heated gas space 10 is provided with a flue gas exit 12 leading to the outside of the apparatus. 13 denotes a water entrance, 14 denotes a hot water faucet, and 15 denotes a combustor such as a gas burner and the like. 
     As for the operation of this apparatus, when combustion is effected by means of an appropriate combustor 15, e.g., a gas burner and the like disposed beneath the rising heated gas chamber 9 upon falling the liquid in the outside water jacket 3 defined by the outer body portion 1 and the inner body portion 2 as well as the flat board-shaped inside water jacket 8 through the water entrance 13, the heated gas rises within the rising heated gas chamber 9 defined by the inner wall of the inner body portion 2 and the inner wall of the inside water jacket 8, runs against the inner wall of the upper part of the rising heated gas chamber 9, has its direction of flow rectified thereat, passes the flue 11, falls within the falling heated gas space 10 defined by the inner wall of the inner body portion 2 and the outer wall of the inside water jacket 8 and is discharged to the outside of the apparatus through the flue gas exit 12 provided at the lower part of said falling heated gas space 10. The heated gas performs the heat exchange efficiently on the surface of the plate members 6, 7 of the inside water jacket 8 during its movement, heats the liquid within the inside water jacket 8 as well as the liquid within the outside water jacket 3 defined by the outer body portion 1 and the inner body portion 2, brings about a natural convection of the liquid within the inside water jacket 8 and the outside water jacket 3 by utilizing the inside water jacket 8 for convective rising of the liquid due to the sudden rising flow as in boiling and the outside water jacket 3 for convective falling of the liquid, respectively whereby the liquid within the apparatus is uniformly heated and hot water can be obtained quickly. 
     Moreover, the heated gas is supposed to pass the flue gas exit 12, enter the exhaust pipe 31, run against the inner wall of the funnel 32 attached to the fore end of said exhaust pipe 31, change its direction of flow and go outside through an opening of said funnel 32. The space between the fore end of the exhaust pipe 31 and the inner wall of the funnel 32 is designed to be narrower than the width of the opening of the funnel 32, and therefore, on the occasion of discharging the heated gas through the exhaust pipe 31, by virtue of a suction force working therein, the speed of current of the gas to be discharged is accelerated to improve the fluidity thereof and ensure the supply of air sufficient for combustion through the air supply tube 33, whereby a complete combustion is effected. 34 denotes a drain tube. 
     In FIGS. 6 and 7 illustrating the second embodiment of the present invention, the reference numeral 16 denotes a first outer body portion of cylindrical shape. Within this outer body portion 16 is disposed a cylindrical first inner body portion 17 with there being a space therebetween forming an outside water jacket 18. Within this inner body portion 17 is vertically disposed a cylindrical inside water jacket 23 which is defined by a cylindrical second outer body portion 22 and a cylindrical second inner body portion 21 and communicates with said outside water jacket 18 by way of the upper and lower convection coupling members 19 and 20. Along the inside of said inside water jacket 23 is formed a rising heated gas chamber 24, while along the outside of the same water jacket is formed a falling heated gas space 25 so as to make the ratio Sc of the width Bci of liquid passage of the inside water jacket 23 to the width Bco of liquid passage of the outside water jacket 18 satisfy the inequality 0&lt;Sc≦0.8 and also make the ratio of a radius r of said rising heated gas chamber 24 to a radius R of said falling heated gas space 25 satisfy the inequality 0&lt;(R/r) - 1≦0.8. The upper part of the rising heated gas chamber 24 is provided with a flue 26 communicating with the falling heated gas space 25, while the lower part of the falling heated gas space 25 is provided with a flue gas exit 27 leading to the outside of the apparatus. 28 denotes a water entrance, 29 denotes a hot water faucet, 30 denotes a combustor such as a gas burner and the like, and 34 denotes an enlarged portion of the falling heated gas space. 
     As for the operation of this apparatus, when combustion is effected by means of an appropriate combustor 30, e.g., a gas burner and the like disposed beneath the rising heated gas chamber 24 upon filling a liquid, to wit, water, in the outside water jacket 18 defined by the first outer body portion 16 and the first inner body portion 17 as well as the inside water jacket 23 defined by the second outer body portion 22 and the second inner body portion 21, the heated gas rises within the rising heated gas chamber 24 defined by the inner body portion of the inside water jacket 23, runs against the inner wall of the upper part of the rising heated gas chamber 24, changes its direction of flow thereat, passes the flue 26, falls within the falling heated gas space 25 defined by the inner wall of the inner body portion 17 and the outer wall of the outer body portion 22 and is discharged to the outside of the apparatus through the flue gas exit 27 provided at the lower part of said falling heated gas space 25. The heated gas performs the heat exchange efficiently on the surface of the inner wall of the inner boby portion 17 and the wall surfaces of the inner and outer body portions 21 and 22 during its circular movement, heats the water within the inside water jacket 23 as well as the water within the outside water jacket 18, brings about a natural convection of the water within the inside water jacket 23 and the outside water jacket 18 by effecting convective rising of water in the former jacket 23 while effecting convective falling of water in the latter jacket 18, whereby the water within the apparatus is uniformly heated. 
     Moreover, at the time when the heated gas fallen within the falling heated gas space 25 passes the enlarged falling heated gas space 34 below said space 25, which is wider than the width of the space 25, and is discharged to the outside from the flue gas exit 27, because the exit of the falling heated gas space 25 is narrower than the width of the enlarged falling heated gas space 34, by virtue of a suction force working therein, the speed of the current of the heated gas to be discharged is accelerated to improve the fluidity thereof and ensure a sufficient supply of air necessary for combustion from beneath. 
     Since an apparatus according to the present invention is of such construction as described above, it has a wide range of application such as a variety of water heaters as well as instantaneous water heaters for domestic use, boilers as well as waste heat recovering devices for industrial use, etc. and is very effective in economizing energies and resources. The liquid for use in the present invention can be water and other liquids. 
     In the following will be shown the results of tests conducted by the use of the respective liquid heating apparatuses illustrated by the foregoing embodiments of the invention. 
     To begin with, the testing device employed for testing the respective embodiments is as shown in FIG. 8, and particulars of this testing device as well as the method of measurement by means of this device will be explained with reference to the following Table-A through Table-H illustrative of the results of said measurement. 
     As the fluid to be subjected to heating with the liquid heating apparatus 50 according to the present invention, the underground water which will not be such influenced by the temperature of surrounding fluids is utilized. Referring to FIG. 8, the underground water is pumped up by the feed-water pump 51 and is adjusted to a prescribed pressure by means of the constant-pressure tank 52, introduced into the open tank 53, supplied to the liquid heating apparatus 50 via the water supply pipe 54 under a constant pressure, and its inlet temperature (105) is measured with the thermometer 69. 
     The city gas is introduced into a burner through a pipeline equipped with the pressure regulator 70 and the gas meter 55 to be burned therein. On this occasion, the gas pressure (109) is adjusted to a prescribed value by means of the pressure regulator 70, and the gas consumption (101) and gas temperature (102) are measured with said gas meter 55 and the thermometer 67. Moreover, an exhaust absorbing device (not shown) is equipped in the exhaust funnel 56, and analysis of the exhaust is conducted based on continuous recording by the infra-red CO/CO 2  analyzer 57 and the Orzert gas analyzer 57, whereby CO concentration (108) is calculated. 
     The measurement of the exhaust gas temperature (106) is conducted through the procedure comprising setting 12 units of C.A. thermocouples perpendicularly to the passage within the exhaust funnel 56 and reading the value indicated with the digital thermometer 59 by operating the thermocouple switch 58, thereby measuring the mean temperature at the cross section of said exhaust funnel while confirming unevenness of the value by means of the pen recorder 60. 
     In the case of constant pouring-out of hot water, by leaving the adjusting valve open, the water is supplied to the liquid heating apparatus 50 for heating, and the resulting hot water is supplied to the mixing chamber 61 through a supply pipe connected to a hot water faucet after adjusting its flow to a prescribed flow by means of the adjusting valve 73 provided at said supply pipe. After stirring within the mixing chamber 61 into a uniform temperature and measuring the outlet temperature (104) with the thermometer 68, the hot water is passed through the pipe 62 and stored in the hot-water reservoir 63. At this time, the weight of the hot water flowing per unit time is measured by means of a stop watch together with the weight gauge 64, and the flow quantity (103) is calculated based on the result of this measurement. 
     On the other hand, in the case of storing hot water, the valve 74 is first closed thereby filling up the liquid heating apparatus 50 with water. Then, the valve 72 is closed, the combustor is ignited, and upon attaining a temperature of 50° C as set with a thermostat not shown herein, said thermostat is actuated to extinguish fire. Immediately thereafter, the valve 74 of the hot water exit is opened thereby storing the hot water in the heat insulating tank 65, and the volume (111) of the thus stored hot water is measured with a weight gauge not shown herein while the temperature (110) thereof is measured with the thermometer 71. The surface temperature (107) of the heating apparatus 50 in motion is measured with the autographic recorder 66. 
     Experiment 1. 
     The liquid heating apparatus employed for the present experiment was of the same structure as that of the first embodiment and the radio Sf of the width of liquid passages was fixed while the ratio ξf of the width of gas passages was set at various values. Referring to FIGS. 9A and 9B, the dimension of the respective parts was as shown in the following Table-1. 
     
                                           Table-1                                 
__________________________________________________________________________
             No.     1     2     3     4     5     6     7                
__________________________________________________________________________
height       H.sub.1 (mm)                                                 
                     1120  1120  1120  1120  1120  1120  1120             
             H.sub.2 (mm)                                                 
                     1000  1000  1000  1000  1000  1000  1000             
longer latus L.sub.1 (mm)                                                 
                     500   500   500   500   500   500   500              
             L.sub.2 (mm)                                                 
                     400   400   400   400   400   400   400              
shorter latus                                                             
             E (mm)  194.2 198.2 210.2 218.2 242.2 266.2 418.2            
width of rising                                                           
             Wu (mm) 80    80    80    80    80    80    80               
heated gas chamber                                                        
width of falling                                                          
             Wd (mm) 16    20    32    40    64    88    240              
heated gas space                                                          
ratio of width                                                            
             ξ f = Wd/Wu                                               
                     0.20  0.25  0.40  0.50  0.80  1.10  3.00             
of gas passages                                                           
width of inside                                                           
             Bfi (mm)                                                     
                     7.4   7.4   7.4   7.4   7.4   7.4   7.4              
water jacket                                                              
width of outside                                                          
             Bfo (mm)                                                     
                     45.4  45.4  45.4  45.4  45.4  45.4  45.4             
water jacket                                                              
ratio of width of                                                         
             Sf = Bfi/Bfo                                                 
                     0.163 0.163 0.163 0.163 0.163 0.163 0.163            
heat transfer area                                                        
             A (m.sup.2)                                                  
                     1.990 2.001 2.035 2.055 2.120 2.186 2.597            
__________________________________________________________________________
 
    
     When a variety of liquid heating apparatuses according to the above design were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of constant pouring-out of hot water, the result was as shown in the following Table-A, respectively. 
     
                                           Table-A                                 
__________________________________________________________________________
             No.     1     2     3     4     5     6     7                
__________________________________________________________________________
room temperature                                                          
             ° C                                                   
                     17.5  20.5  25.5  28.0  27.0  24.0  21.5             
   unit calorific                                                         
             Kcal/Nm.sup.3                                                
                     3062  3065  3091  3165  3102  3073  3065             
   value                                                                  
   fuel consumption                                                       
             Nm.sup.3 /h                                                  
                     6.82  6.81  7.27  8.45  9.34  10.41 12.40            
   (101)                                                                  
in-                                                                       
put                                                                       
   fuel temperature                                                       
             ° C                                                   
                     16.8  19.7  26.0  27.2  26.3  22.8  20.5             
   (102)                                                                  
   atmospheric                                                            
             mm Hg   754.3 761.3 758.4 762.5 759.0 754.0 759.2            
   pressure                                                               
   input (I.P)                                                            
             Kcal/h  20900 20897 22492 26776 29000 32000 38024            
   flow quantity                                                          
             kg/h    400   400   400   500   500   500   500              
   (103)                                                                  
   outlet temperature                                                     
             ° C                                                   
                     64.5  65.0  67.2  63.0  62.3  61.7  60.9             
   (104)                                                                  
   inlet temperature                                                      
             ° C                                                   
                     13.8  13.7  13.8  14.0  14.0  13.5  13.5             
out-                                                                      
   difference between                                                     
put                                                                       
   outlet &amp; inlet                                                         
             deg     50.7  51.3  53.4  49.0  48.3  48.2  47.4             
   temperatures                                                           
   specific heat                                                          
             Kcal/kg ° C                                           
                     1.0   1.0   1.0   1.0   1.0   1.0   1.0              
   specific weight                                                        
             kg/m.sup.3                                                   
                     1000  1000  1000  1000  1000  1000  1000             
   output (O.P)                                                           
             Kcal/h  20273 20500 21368 24500 24128 24096 23689            
thermal      %       97.0  98.1  95.0  91.5  83.2  75.3  62.3             
efficiency (η)                                                        
exhaust gas  ° C                                                   
                     97.2  85.5  130.4 189.0 392.8 470.3 512              
temperature (106)                                                         
surface temperature                                                       
of heating   ° C                                                   
                     32.3  32.5  33.2  36.3  45.2  48.3  50.2             
apparatus 50 (107)                                                        
exhaust gas  %       3.5   3.1   4.9   7.3   15.6  18.8  20.5             
heat loss                                                                 
com-                                                                      
bus-                                                                      
    CO concentration                                                      
             CO/CO.sub.2 %                                                
                     0.0125                                               
                           0.0003                                         
                                 0.0003                                   
                                       0.0003                             
                                             0.0004                       
                                                   0.0004                 
                                                         0.0006           
tion                                                                      
    (108)                                                                 
condi-                                                                    
    NOx              un-   un-   un-   un-   un-   un-   un-              
tion         PPM     detect-                                              
                           detect-                                        
                                 detect-                                  
                                       detect-                            
                                             detect-                      
                                                   detect-                
                                                         detect-          
                     able  able  able  able  able  able  able             
    type of burner                                                        
             BR-type BR-100                                               
                           BR-100                                         
                                 BR-100                                   
                                       BR-100                             
                                             BR-100                       
                                                   BR-100                 
                                                         BR-100           
burn-                                                                     
    diameter of nozzle                                                    
             mm φ                                                     
                     5.1φ ×2                                    
                           5.1φ ×2                              
                                 5.3φ ×2                        
                                       5.6φ ×2                  
                                             6.0φ ×2            
                                                   6.0φ ×2      
                                                         6.2φ         
                                                         ×2         
er                                                                        
    regulated pressure                                                    
             mm Aq   60    60    60    65    60    75    90               
    (109)                                                                 
remark       compen- 0.832 0.833 0.840 0.860 0.843 0.835 0.833            
             sation                                                       
             coeffi-                                                      
             cient                                                        
__________________________________________________________________________
 
    
     Further, when various liquid heating apparatus according to the design shown in Table-1 above were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of storing hot water, the result was as shown in the following Table-B. 
     
                                           Table-B                                 
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                     No.     2     5    7                                 
__________________________________________________________________________
room temperature     ° C                                           
                             20.5  27.0 21.5                              
   unit calorific value                                                   
                     Kcal/Nm.sup.3                                        
                             3065  3102 3065                              
in-                                                                       
   fuel consumption (101)                                                 
                     Nm.sup.3 /h                                          
                             1.08  1.69 3.4                               
put                                                                       
   fuel temperature (102)                                                 
                     ° C                                           
                             19.7  26.3 20.5                              
   atmospheric pressure                                                   
                     mm Hg   761.3 759.0                                  
                                        759.2                             
   input (I.P)       Kcal/h  3313  5254 10433                             
   mean temperature of hot water (110)                                    
                     ° C                                           
                             62.3  64.8 65.5                              
   inlet temperature (105)                                                
                     ° C                                           
                             14.8  15.5 15.0                              
   difference between outlet &amp; inlet                                      
out-                                                                      
   temperatures      deg     47.5  49.3 50.5                              
put                                                                       
   specific heat     Kcal/kg ° C                                   
                             1.0   1.0  1.0                               
   specific weight   kg/m.sup.3                                           
                             1000  1000 1000                              
   volume of hot water in reservoir (111)                                 
                     kg      65    73   113                               
   output (O.P)      Kcal/h  3088  3599 5707                              
thermal efficiency (η)                                                
                     %       93.2  68.5 54.7                              
exhaust gas temperature (106)                                             
                     ° C                                           
                             135.5 429  498                               
surface temperature of heating                                            
                     ° C                                           
                             33.5  40.9 53.2                              
apparatus 50 (107)                                                        
exhaust gas heat loss                                                     
                     %       5.3   17.3 20.0                              
com-                                                                      
    CO concentration (108)                                                
                     CO/CO.sub. 2 %                                       
                             0.0003                                       
                                   0.0006                                 
                                        0.0007                            
bus-                                                                      
tion                                                                      
    NOx                      undetect-                                    
                                   undetect-                              
                                        undetect-                         
condi-               PPM     able  able able                              
tion                                                                      
burn-                                                                     
    type of burner   BR-type BR-100                                       
                                   BR-100                                 
                                        BR-100                            
er  diameter of nozzle                                                    
                     mm φ                                             
                             5.1φ ×2                            
                                   6.0φ ×2                      
                                        6.2φ ×2                 
    regulated pressure (109)                                              
                     mm Aq   60    60   90                                
__________________________________________________________________________
 
    
     Shown in FIG. 11 is a graph prepared on the basis of the above data. As a result of the foregoing test, it was verified that, when the ratio ξf of width of gas passages was set at 0.8 or less than 0.8, the thermal efficiency could be increased to more than 70%. 
     Experiment 2. 
     The liquid heating apparatus employed for the present experiment was of the same structure as that of the second embodiment and the ratio So of width of liquid passages was fixed while the ratio ξc of width of gas passages was set at various values. Referring to FIGS. 10A and 10B, the dimension of the respective parts was as shown in the following Table-2. 
     
                                           Table-2                                 
__________________________________________________________________________
                No.     1    2    3    4                                  
__________________________________________________________________________
height          H.sub.1 (mm)                                              
                        1095 1095 1095 1095                               
                H.sub.2 (mm)                                              
                        1000 1000 1000 1000                               
width           E&#39; (mm) 385.2                                             
                             399.8                                        
                                  512.6                                   
                                       831.6                              
radius of heating gas space                                               
                R (mm)  127.6                                             
                             134.9                                        
                                  191.3                                   
                                       350.8                              
radius of heating gas chamber                                             
                r (mm)  106.3                                             
                             106.3                                        
                                  106.3                                   
                                       106.3                              
                ξc = R/r - 1                                           
                        0.200                                             
                             0.269                                        
                                  0.800                                   
                                       2.300                              
width of inside water jacket                                              
                Bci (mm)                                                  
                        13   13   13   13                                 
width of outside water jacket                                             
                Bco (mm)                                                  
                        65   65   65   65                                 
ratio of width of liquid passages                                         
                Sc = Bci/Bco                                              
                        0.20 0.20 0.20 0.20                               
heat transfer area                                                        
                A (m.sup.2)                                               
                        1.849                                             
                             1.986                                        
                                  2.345                                   
                                       3.445                              
__________________________________________________________________________
 
    
     When various liquid heating apparatuses according to the above design were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of constant pouring-out of hot water, the result was as shown in the following Table-C respectively. 
     
                                           Table-C                                 
__________________________________________________________________________
                No.    1      2      3      4                             
__________________________________________________________________________
room temperature                                                          
                ° C                                                
                       4.0    4.5    28.0   8.0                           
   unit calorific value                                                   
                Kcal/Nm.sup.3                                             
                       3043   3032   3076   3054                          
in-                                                                       
   fuel consumption (101)                                                 
                Nm.sup.3 /h                                               
                       8.46   8.33   13.06  16.77                         
put                                                                       
   fuel temperature (102)                                                 
                ° C                                                
                       6.2    6.8    27.1   26.8                          
   atmospheric pressure                                                   
                mm Hg  748.2  736.6  739.5  751.7                         
   input (I.P)  Kcal/h 25751  25257  40200  51230                         
   flow quantity (103)                                                    
                kg/h   500    500    500    500                           
   outlet temperature (104)                                               
                ° C                                                
                       60.4   61.0   60.0   57.5                          
out-                                                                      
   inlet temperature (105)                                                
                ° C                                                
                       12.8   12.8   13.8   13.5                          
put                                                                       
   difference between outlet &amp;                                            
                deg    47.6   48.2   46.2   44.0                          
   inlet temperatures                                                     
   specific heat                                                          
                Kcal/kg ° C                                        
                       1.0    1.0    1.0    1.0                           
   specific weight                                                        
                kg/m.sup.3                                                
                       1000   1000   1000   1000                          
   output (O.P) Kcal/h 23820  24120  32361  30789                         
thermal efficiency (η)                                                
                %      92.5   95.5   80.5   60.1                          
exhaust gas temperature (106)                                             
                ° C                                                
                       154.8  118.0  397.7  552.0                         
surface temperature of heating                                            
apparatus 50 (107)                                                        
                ° C                                                
                       29.2   28.7   39.6   45.5                          
exhaust gas heat loss                                                     
                %      5.9    4.4    15.8   22.2                          
com-                                                                      
bus-                                                                      
    CO concentration (108)                                                
                CO/CO.sub.2 %                                             
                       0.0015 0.0002 0.0003 0.0002                        
tion                                                                      
    NOx                undetect-                                          
                              undetect-                                   
                                     undetect-                            
                                            undetect-                     
condi-          PPM    able   able   able   able                          
tion                                                                      
    type of burner                                                        
                BR-type                                                   
                       BR-100 BR-100 BR-115 × 2                     
                                            BR-115 × 2              
burn-                                                                     
    diameter of nozzle                                                    
                mm φ                                                  
                       5.6φ × 2                                 
                              5.6φ × 2                          
                                     5.0φ × 4                   
                                            5.4φ × 4            
er  regulated                                                             
    pressure (109)                                                        
                mm Aq  60     60     60     70                            
remark          compen-                                                   
                       0.827  0.824  0.836  0.830                         
                sation                                                    
                coeffi-                                                   
                cient                                                     
__________________________________________________________________________
 
    
     Moreover, when various liquid heating apparatuses according to the design shown in the foregoing Table-2 were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of storing hot water, the result was as shown in the following Table-D respectively. 
     
                                           Table-D                                 
__________________________________________________________________________
                     No.     2     3    4                                 
__________________________________________________________________________
room temperature     ° C                                           
                             4.5   28.0 8.0                               
   unit calorific value                                                   
                     Kcal/Nm.sup.3                                        
                             3032  3076 3054                              
in-                                                                       
   fuel consumption (101)                                                 
                     Nm.sup.3 /h                                          
                             1.53  2.45 3.31                              
put                                                                       
   fuel temperature (102)                                                 
                     ° C                                           
                             6.8   27.1 26.8                              
   atmospheric pressure                                                   
                     mm Hg   736.6 739.5                                  
                                        751.7                             
   input (I.P)       Kcal/h  4663  7545 10114                             
   mean temperature of hot water (110)                                    
                     ° C                                           
                             63.0  63.6 63.9                              
   inlet temperature (105)                                                
                     ° C                                           
                             12.8  13.8 13.5                              
   difference between outlet &amp; inlet                                      
                     deg     50.2  49.8 50.4                              
out-                                                                      
   temperatures                                                           
put                                                                       
   specific heat     Kcal/kg ° C                                   
                             1.0   1.0  1.0                               
   specific weight   kg/m.sup.3                                           
                             1000  1000 1000                              
   volume of hot water in reservoir (111)                                 
                     kg      85    105  120                               
   output (O.P)      Kcal/h  4267  5229 6048                              
thermal efficiency (η)                                                
                     %       91.5  69.3 59.8                              
exhausts gas temperature (106)                                            
                     ° C                                           
                             153.3 420.5                                  
                                        580.3                             
surface temperature of heating                                            
apparatus 50 (107)   ° C                                           
                             32.3  40.8 56.2                              
exhaust gas heat loss                                                     
                     %       5.8   16.4 24.2                              
com-                                                                      
bus-                                                                      
    CO concentration (108)                                                
                     CO/CO.sub.2 %                                        
                             0.0002                                       
                                   0.0003                                 
                                        0.0003                            
tion                                                                      
    NOx                      undetect-                                    
                                   undetect-                              
                                        undetect-                         
condi-               PPM     able  able able                              
tion                                                                      
burn-                                                                     
    type of burner   BR-type BR-100                                       
                                   BR-115 × 2                       
                                        BR-115 × 2                  
er  diameter of nozzle                                                    
                     mm φ                                             
                             5.6φ × 2                           
                                   5.0φ × 4                     
                                        5.4φ × 4                
    regulated pressure (109)                                              
                     mm Aq   60    60   70                                
__________________________________________________________________________
 
    
     Shown in FIG. 12 is a graph prepared on the basis of the above data. As a result of the foregoing test, it was verified that, when the ratio ξc of width of gas passages was set at 0.8 or less than 0.8, the thermal efficiency could be increased to more than 70%. 
     Experiment 3 
     The liquid heating apparatus employed for the present experiment was of the same structure as that of the first embodiment and the ratio ξf of width of gas passages was fixed while the ratio Sf of width of liquid passages was set at various values. Referring to FIGS. 9A and 9B, the dimension of the respective parts was as shown in the following Table-3. 
     
                                           Table-3                                 
__________________________________________________________________________
                  No.    1    2    3    4    5                            
__________________________________________________________________________
height            H.sub.1 (mm)                                            
                         1120 1120 1120 1120 1120                         
                  H.sub.2 (mm)                                            
                         1000 1000 1000 1000 1000                         
longer latus      L.sub.1 (mm)                                            
                         500  500  500  500  500                          
                  L.sub.2 (mm)                                            
                         400  400  400  400  400                          
shorter latus     E (mm) 198.20                                           
                              205.80                                      
                                   213.50                                 
                                        236.20                            
                                             251.20                       
width of inside water jacket                                              
                  Bfi (mm)                                                
                         7.4  15.0 22.7 45.4 60.4                         
width of outside water jacket                                             
                  Bfo (mm)                                                
                         45.4 45.4 45.4 45.4 45.4                         
ratio of width of liquid passages                                         
                  Sf = Bfi/Bfo                                            
                         0.163                                            
                              0.330                                       
                                   0.500                                  
                                        1.000                             
                                             1.33                         
width of rising heated gas chamber                                        
                  Wu (mm)                                                 
                         80   80   80   80   80                           
width of falling heated gas space                                         
                  Wd (mm)                                                 
                         20   20   20   20   20                           
ratio of width of gas passages                                            
                  ξf = Wd/Wu                                           
                         0.25 0.25 0.25 0.25 0.25                         
heat transfer area                                                        
                  A (m.sup.2)                                             
                         2.001                                            
                              2.019                                       
                                   2.046                                  
                                        2.105                             
                                             2.153                        
__________________________________________________________________________
 
    
     When a variety of liquid heating apparatuses according to the above design were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of constant pouring-out of hot water, the result was as shown in the following Table-E respectively. 
     
                                           Table-E                                 
__________________________________________________________________________
                No.     1    2    3    4    5                             
__________________________________________________________________________
room temperature                                                          
                ° C                                                
                        20.5 3.8  3.5  6.8  8.9                           
input                                                                     
     unit calorific value                                                 
                Kcal/Nm.sup.3                                             
                        3065 3021 3025 3040 3051                          
     fuel consumption                                                     
     (101)      Nm.sup.3 /h                                               
                        6.81 6.86 6.85 6.83 6.82                          
     fuel temperature                                                     
                ° C                                                
                        19.7 5.7  5.9  7.2  7.9                           
     (102)                                                                
     atmospheric                                                          
                mm Hg   761.3                                             
                             754.7                                        
                                  760.1                                   
                                       767.7                              
                                            759.8                         
     pressure                                                             
     input (I.P)                                                          
                Kcal/h  20897                                             
                             20724                                        
                                  20721                                   
                                       20763                              
                                            20808                         
output                                                                    
     flow quantity (103)                                                  
                kg/h    400  400  400  400  400                           
     outlet     ° C                                                
                        65.0 62.0 58.6 51.7 47.7                          
     temperature (104)                                                    
     inlet      ° C                                                
                        13.7 13.1 13.1 13.3 13.3                          
     temperature (105)                                                    
     difference                                                           
     between outlet &amp;                                                     
     inlet tempera-                                                       
                deg     51.3 48.9 45.5 38.4 34.2                          
     tures                                                                
     specific heat                                                        
                Kcal/kg ° C                                        
                        1.0  1.0  1.0  1.0  1.0                           
     specific weight                                                      
                kg/m.sup.3                                                
                        1000 1000 1000 1000 1000                          
     output (O.P)                                                         
                Kcal/h  20500                                             
                             19584                                        
                                  18193                                   
                                       15365                              
                                            13692                         
thermal efficiency (η)                                                
                %       98.1 94.5 87.8 74.0 65.8                          
exhaust gas temperature (106)                                             
                ° C                                                
                        85.5 119.0                                        
                                  201.2                                   
                                       292.8                              
                                            333.0                         
surface temperature of                                                    
heating apparatus 50 (107)                                                
                ° C                                                
                        32.5 33.0 33.5 36.0 36.0                          
exhaust gas heat loss                                                     
                %       3.1  4.4  7.8  11.5 13.2                          
combustion                                                                
      CO concentration                                                    
      (108)     CO/CO.sub.2 %                                             
                        0.0003                                            
                             0.0003                                       
                                  0.0003                                  
                                       0.0003                             
                                            0.0003                        
condition                                                                 
      NOx       PPM     undetect-                                         
                             undetect-                                    
                                  undetect-                               
                                       undetect-                          
                                            undetect-                     
                        able able able able able                          
burner                                                                    
     type of burner                                                       
                BR-type BR-100                                            
                            BR-100                                        
                                  BR-100                                  
                                       BR-100                             
                                            BR-100                        
     diameter of nozzle                                                   
                mm φ                                                  
                        5.1φ ×  2                               
                            5.1φ ×  2                           
                                  5.1φ ×  2                     
                                       5.1φ ×                   
                                            5.1φ ×  2           
     regulated pressure                                                   
                mm Aq   60  60    60   60   60                            
     (109)                                                                
remark          compen- 0.833                                             
                            0.821 0.822                                   
                                       0.826                              
                                            0.829                         
                sation                                                    
                coeffi-                                                   
                cient                                                     
__________________________________________________________________________
 Herein:                                                                  
 input (I.P) = unit calorific value × fuel consumption              
 output(O.P) = flow quantity × specific heat × difference     
 between inlet and outlet temperatures                                    
 thermal efficiency (η) = output/input                                
 exhaust gas heat loss (ρ) =  V(cgtg - coto) × Hu               
 wherein V: amount of exhaust at a temperature tg                         
 Hu: amount of exhaust at a low calorific value                           
 cg, co: specific heat of heated gas at tg, to                            
 tg, to: exhaust gas temperature, atmospheric temperature                 
 
    
     Next, when a variety of liquid heating apparatuses according to the above design were tested by the use of a testing device illustrated in FIG. 8 with respect to their efficiency in the case of storing hot water, the result was as shown in the following Table-F respectively. 
     
                                           Table-F                                 
__________________________________________________________________________
                       No.    1    3    4    5                            
__________________________________________________________________________
room temperature       ° C                                         
                              20.5 3.5  6.8  8.9                          
input                                                                     
    unit calorific value                                                  
                       Kcal/Nm.sup.3                                      
                              3065 3025 3040 3051                         
    fuel consumption (101)                                                
                       Nm.sup.3 /h                                        
                              1.11 1.41 2.05 2.46                         
    fuel temperature (102)                                                
                       ° C                                         
                              19.7 5.9  7.2  7.9                          
    atmospheric pressure                                                  
                       mm Hg  761.3                                       
                                   760.1                                  
                                        767.7                             
                                             759.8                        
    input (I.P)        Kcal/h 3413 4266 6262 7506                         
output                                                                    
    mean temperature of hot water (110)                                   
                       ° C                                         
                              63.0 63.3 62.2 62.5                         
    inlet temperature (105)                                               
                       ° C                                         
                              13.7 13.1 13.3 13.3                         
    difference between outlet &amp; inlet                                     
    temperatures       deg    49.3 50.2 48.9 49.2                         
    specific heat      Kcal/kg ° C                                 
                              1.0  1.0  1.0  1.0                          
    specific weight    kg/m.sup.3                                         
                              1000 1000 1000 1000                         
    volume of hot water in reservoir (111)                                
                       kg     65   69   84   92                           
    output (O.P)       Kcal/h 3205 3464 4108 4526                         
thermal efficiency (η)                                                
                       %      93.9 81.2 65.6 60.3                         
exhaust gas temperature (106)                                             
                       ° C                                         
                              112.5                                       
                                   273.3                                  
                                        408.3                             
                                             423.9                        
surface temperature of heating                                            
                       ° C                                         
                              34.5 35.1 42.3 48.6                         
apparatus 50 (107)                                                        
exhaust gas heat loss  %      4.3  12.0 16.0 17.2                         
combustion                                                                
      CO concentration (108)                                              
                       CO/CO.sub.2 %                                      
                              0.0003                                      
                                   0.0003                                 
                                        0.0025                            
                                             0.0040                       
condition                                                                 
      NOx              PPM    undetect-                                   
                                   undetect-                              
                                        undetect-                         
                                             undetect-                    
                              able able able able                         
burner                                                                    
      type of burner   BR-type                                            
                              BR-100                                      
                                   Br-100                                 
                                        BR-100                            
                                             BR-100                       
      diameter of nozzle                                                  
                       mm φ                                           
                              5.1φ × 2                          
                                   5.1φ × 2                     
                                        5.1φ × 2                
                                             5.1φ×2             
      regulated pressure (109)                                            
                       mm Aq  60   60   60   60                           
__________________________________________________________________________
 
    
     Shown in FIG. 13 is a graph prepared on the basis of the above data. As a result of the foregoing test, it was verified that, when the ratio Sf of width of liquid passages was set at 0.8 or less than 0.8, the thermal efficiency could be increased to more than 70%. 
     Experiment 4 
     The liquid heating apparatus employed for the present experiment was of the same structure as that of the second embodiment and the ratio ξc of width of gas passages was fixed while the ratio Sc of width of liquid passages was set at various values. Referring to FIGS. 11A and 11B, the dimension of the respective parts was as shown in the following Table-4. 
     
                                           Table-4                                 
__________________________________________________________________________
                 No.     1    2    3    4    5                            
__________________________________________________________________________
height           H.sub.1 (mm)                                             
                         1095 1095 1095 1095 1095                         
                 H.sub.2 (mm)                                             
                         1000 1000 1000 1000 1000                         
width            E&#39; (mm) 399.8                                            
                              399.8                                       
                                   399.8                                  
                                        399.8                             
                                             399.8                        
width of inside water jacket                                              
                 Bci (mm)                                                 
                         13   26   39   65   130                          
width of outside water jacket                                             
                 Bco (mm)                                                 
                         65   65   65   65   65                           
ratio of width of liquid passages                                         
                 Sc = Bci/Bco                                             
                         0.20 0.40 0.60 1.00 2.00                         
radius of heating gas space                                               
                 R (mm)  134.9                                            
                              134.9                                       
                                   134.9                                  
                                        134.9                             
                                             134.9                        
radius of heating gas chamber                                             
                 r (mm)  106.3                                            
                              106.3                                       
                                   106.3                                  
                                        106.3                             
                                             106.3                        
                 ξc = R/r - 1                                          
                         0.269                                            
                              0.269                                       
                                   0.269                                  
                                        0.269                             
                                             0.269                        
heat transfer area                                                        
                 A (m.sup.2)                                              
                         1.986                                            
                              2.106                                       
                                   2.183                                  
                                        2.550                             
                                             3.318                        
__________________________________________________________________________
 
    
     When a variety of liquid heating apparatuses according to the above design were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of constant pouring-out of hot water, the result was as shown in the following Table-G respectively. 
     
                                           Table-G                                 
__________________________________________________________________________
                  No.    1    2    3    4    5                            
__________________________________________________________________________
room temperature  ° C                                              
                         4.5  12.0 15.0 18.5 8.8                          
input                                                                     
     unit calorific value                                                 
                  Kcal/Nm.sup.3                                           
                         3032 3054 3058 3062 3054                         
     fuel consumption (101)                                               
                  Nm.sup.3 /h                                             
                         8.33 8.25 8.24 8.23 8.25                         
     fuel temperature (102)                                               
                  ° C                                              
                         6.8  12.5 13.8 17.1 7.9                          
     atmospheric pressure                                                 
                  mm Hg  736.6                                            
                              762.2                                       
                                   761.0                                  
                                        738.4                             
                                             759.8                        
     input (I.P)  Kcal/h 25257                                            
                              25210                                       
                                   25209                                  
                                        25188                             
                                             25199                        
output                                                                    
     flow quantity (103)                                                  
                  kg/h   500  500  500  500  500                          
     outlet temperature (104)                                             
                  ° C                                              
                         61.0 59.1 57.6 51.9 47.9                         
     inlet temperature (105)                                              
                  ° C                                              
                         12.8 13.5 13.5 13.8 13.0                         
     difference between                                                   
     outlet &amp; inlet tempera-                                              
                  deg    48.2 45.6 44.1 38.1 34.9                         
     tures                                                                
     specific heat                                                        
                  Kcal/kg ° C                                      
                         1.0  1.0  1.0  1.0  1.0                          
     specific weight                                                      
                  kg/m.sup.3                                              
                         1000 1000 1000 1000 1000                         
     output (O.P) Kcal/h 24120                                            
                              22815                                       
                                   22058                                  
                                        19067                             
                                             17438                        
thermal efficiency (η)                                                
                  %      95.5 90.5 87.5 75.7 69.2                         
exhaust gas temperature (106)                                             
                  ° C                                              
                         118.0                                            
                              178.5                                       
                                   209.3                                  
                                        298.5                             
                                             301.5                        
surface temperature of                                                    
heating apparatus 50 (107)                                                
                  ° C                                              
                         28.7 35.2 36.0 36.0 34.8                         
exhaust gas heat loss                                                     
                  %      4.4  6.9  8.1  11.8 11.9                         
combustion                                                                
      CO concentration (108)                                              
                  CO/CO.sub.2 %                                           
                         0.0002                                           
                              0.0003                                      
                                   0.0003                                 
                                        0.0003                            
                                             0.0002                       
condition                                                                 
      NOx         PPM    undetect-                                        
                              undetect-                                   
                                   undetect-                              
                                        undetect-                         
                                             undetect-                    
                         able able able able able                         
burner                                                                    
      type of burner                                                      
                  BR-type                                                 
                         BR-100                                           
                              BR-100                                      
                                   BR-100                                 
                                        BR-100                            
                                             BR-100                       
      diameter of nozzle                                                  
                  mm φ                                                
                         5.6φ×2                                 
                              5.6φ×2                            
                                   5.6φ×2                       
                                        5.6φ×2                  
                                             5.6φ×2             
      regulated pressure                                                  
                  mm Aq  60   60   60   60   60                           
      (109)                                                               
remark            compen-                                                 
                         0.824                                            
                              0.83 0.831                                  
                                        0.832                             
                                             0.830                        
                  sation                                                  
                  coeffi-                                                 
                  cient                                                   
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     Moreover, when a variety of liquid heating apparatuses according to the above design were tested by the use of the testing device illustrated in FIG. 8 with respect to their efficiency in the case of storing hot water, the result was as shown in the following Table-H respectively. 
     
                                           Table-H                                 
__________________________________________________________________________
                       No.    1    3    4    5                            
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room temperature       ° C                                         
                              4.5  15.0 18.5 8.8                          
input                                                                     
    unit calorific value                                                  
                       Kcal/Nm.sup.3                                      
                              3032 3058 3062 3054                         
    fuel consumption (101)                                                
                       Nm.sup.3 /h                                        
                              1.56 1.84 2.92 4.95                         
    fuel temperature (102)                                                
                       ° C                                         
                              6.8  13.8 17.1 7.9                          
    atmospheric pressure                                                  
                       mm Hg  736.6                                       
                                   761.0                                  
                                        738.4                             
                                             759.8                        
    input (I.P)        Kcal/h 4751 5636 8964 15129                        
output                                                                    
    mean temperature of hot water (110)                                   
                       ° C                                         
                              64.0 63.3 63.4 61.9                         
    inlet temperature (105)                                               
                       ° C                                         
                              12.8 13.5 13.8 13.0                         
    difference between outlet &amp; inlet                                     
                       deg    51.2 49.8 49.6 48.9                         
    temperatures                                                          
    specific heat      Kcal/kg ° C                                 
                              1.0  1.0  1.0  1.0                          
    specific weight    kg/m.sup.3                                         
                              1000 1000 1000 1000                         
    volume of hot water in reservoir (111)                                
                       kg     85   92   120  185                          
    output (O.P)       Kcal/h 4352 4582 5952 9047                         
thermal efficiency (η)                                                
                       %      91.6 81.3 66.4 59.8                         
exhaust gas temperature (106)                                             
                       ° C                                         
                              165.2                                       
                                   253.5                                  
                                        413.0                             
                                             579.3                        
surface temperature of heating                                            
                       ° C                                         
                              31.3 38.9 43.0 55.2                         
apparatus 50 (107)                                                        
exhaust gas heat loss  %      6.2  10.5 16.5 24.5                         
combustion                                                                
      CO concentration (108)                                              
                       CO/CO.sub.2 %                                      
                              0.0002                                      
                                   0.0003                                 
                                        0.0015                            
                                             0.0023                       
condition                                                                 
      NOx              PPM    undetect-                                   
                                   undetect-                              
                                        undetect-                         
                                             undetect-                    
                              able able able able                         
burner                                                                    
      type of burner   BR-type                                            
                              BR-100                                      
                                   BR-100                                 
                                        BR-100                            
                                             BR-100                       
      diameter of nozzle                                                  
                       mm φ                                           
                              5.6φ × 2                          
                                   5.6φ × 2                     
                                        5.6φ × 2                
                                             5.6φ × 2           
      regulated pressure (109)                                            
                       mm Aq  60   60   60   60                           
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     Shown in FIG. 14 is a graph prepared on the basis of the above data. As a result of the foregoing test, it was verified that, when the ratio Sc of width of liquid passages was set at 0.8 or less than 0.8, the thermal efficiency could be increased to more than 70%.