in fig1 the metal pipe line 1 is shown as consisting of the single pipe section 2 and the double pipe section 3 joined together in the horizontal direction . such construction is used to provide a thermal sleeve 6 for a nozzle 5 of a pressure vessel 4 of a nuclear power plant . the horizontal fluid passage through the single pipe 2 is reduced in diameter at a in fig1 and is joined to the thermal sleeve 6 and the cylindrical space 7 defined between the nozzle 5 and the thermal sleeve 6 is enlarged in diameter at b , whereby the enlarged diameter portion 8 is defined . cooling water is forced to flow in the direction indicated by the arrows in fig1 so that dead water fills the cylindrical space 7 and the so - called air pocket 9 where air is trapped is left at the enlarged - diameter portion 8 . according to the present invention , such air pocket 9 is eliminated when the residual - stress - improvement treatment is carried out . according to the present invention , an induction heating coil x is used to heat the single - wall pipe section 2 so that the temperature of the pipe walls adjacent to a welded joint 10 is raised as shown in fig4 from time t 0 to time t 1 . in this case , heat is transferred from the single - wall pipe section 2 to the double - wall pipe section 3 so that the latter is also heated . dead water remains in the cylindrical space 7 so that the temperature at the model or sampling point b becomes higher than that at the model or sampling point d . when the temperature at the model or sampling point b reaches at a level at which nucleate boiling occurs at the inner wall surface of the double - wall pipe section 3 , steam thus produced as well as air in the air pocket 9 are gradually discharged . while nucleate boiling continues , the temperature of the portion adjacent to the air pocket 9 becomes lower temporarily than the temperature at the other portions in the peripheral direction ( see fig3 ) because of heat of evaporation . as air is discharged , water intrudes into the air pocket 9 so that the whole peripheral inner wall surface of the enlarged - diameter portion 8 is made into contact with cooling water so that film boiling results . however , if the temperature at the model or sampling point b is less than a temperature ( for example , about 130 ° c . at 3 kgf / cm 2 ) at which nucleate boiling occurs , the auxililary heating is carried out by energizng an induction heating coil y shown in fig1 as described above . the temperature rise and drop at each model or sampling point a , b , c or d is indicated by the curve a , b , c or d in fig4 . when film boiling occurs in the enlarged - diameter portion 8 , the air pocket 9 is eliminated so that a temperature distribution becomes substantially uniform in the peripheral direction . therefore , a nucleate boiling temperature is used as a reference to produce a temperature difference between the outer and inner wall surfaces adjacent to the welded joint 10 ( that is , between the model or sampling points c and d ). ( in this case , in addition to the induction heating , the induction heating coil y may be used as an auxiliary means .) the temperature difference is within a range lower than a transformation temperature and within a range in which thermal stresses are caused in excess of yield points in various directions in the pipe wall . the heating time t 1 required for bringing a temperature into the steady state is obtained by the following equation : fig5 shows a temperature distribution of the metal pipe line 1 at t 1 . for instance , the temperatures at the model or sampling points c and d are 550 ° c . and 200 ° c ., respectively , so that their difference is higher than a temperature difference ( in excess of 200 ° c . in the case of an austenitic stainless steel ) which is sufficiently high enough to cause thermal stresses in excess of a yield point . whether or not the poriton adjacent to the model or sampling point b is in the film boiling state can be detected by the fact that there is no severe temperature variation due to the replacement of the remaining air and steam produced as indicated by the arrow x on the curve b in fig4 or by detecting whether or not a film boilng temperature is reached . in this case , it is difficult to insert a thermometer into the enlarged - diameter poriton 8 . therefore , it is effective to detect the variation in curve b in fig4 at time t 1 or at a time prior to t 1 by comparing the variation in surface temperature at the model or sampling point a when the metal pipe line 1 is heated while the air pocket 9 remains with the temperature variation at the same point when the metal pipe line 1 is heated under the same conditions after the remaining air has been discharged and obtaining a temperature diffence therebetween so as to use as a reference thereafter , while the single - wall pipe section 2 is induction heated by the coil x , the double - wall pipe section 3 is induction heated by the coil y so that the pipe line 1 is heated by both the induction heating coils x and y and the temperature differences as shown at t 1 and t 2 in fig4 are produced between the nozzle 5 and the pipe wall adjacent to the welded join 10 ( between the model or sampling points a and b ). in this case , the heating time t 2 - t 1 can be obtained by the following equation : the heating time ( t 2 - t 1 ) is short so that the so - called super - accelerating - heating is effected . fig6 shows a temperature distribution in the pipe wall of the metal pipe line 1 at time t 2 . for instance , the temperatures at the model or sampling points a and b are 450 ° c . and 180 ° c ., respectively , and the temperature difference between the model or sampling points a and b is sufficient enough to cause thermal stresses in excess of a yield point . furthermore , a substantially uniform temperature distribution can be established in the direction of thickness over the whole heated portion of the metal pipe line as shown in fig6 . thereafter the metal pipe line 1 is cooled at a substantially uniform rate . then residual compressive stresses would be caused in the portions in contact with cooling water . however , in the case of the metal pipe line 1 shown in fig1 there exists a large difference in cooling capacity between the flowing cooling water and the dead water so that when heating is stopped simultaneously , the portion in contact with the flowing cooling water is first cooled and , for instance , the model or sampling points a and b of the double - wall pipe section 3 remain as so - called hot spots . as a result , the residual - stress - improvement is degraded . therefore , the induction heating by means of the induction heating coil y is stopped and the cooling of the double - wall pipe section 3 is started first as indicated at t 2 or t 3 in fig4 . in this case , the time ( t 3 - t 2 ) required for cooling is generally obtained by the following relation : when the induction heating coil x is de - energized at t 3 under these conditions and the cooling is started , the residual compressive stresses are caused as shown in fig7 . more particularly , the residual stresses caused in the inner wall surfaces of the metal pipe line 1 except the thermal sleeve 6 consist of hoop stresses ( solid lines ) in the peripheral direction and the axial stresses ( the broken lines ) in the axial direction . especially at the portion adjacent to the welded joint such as the model or sampling point b where stresses are desired to be improved and where an air pocket tends to be left , even when the residual compressive stresses are caused and even when a fluid flowing through the metal pipe line 1 includes compounds tending to cause corrosion , cracks due to the corrosive compounds can be inhibited . furthermore , even when there do exist some corrosion cracks prior to the heat treatment is carried out , propagation of cracks can be prevented . mesh - like divited portions in fig7 show limited elements for obtaining residual stresses and the intersection between a vertical line drawn from a given limited element at the inner surface of the metal pipe line 1 and a curve indicates a corresponding magnitude of residual stress . for the heat treatment method of the present invention has been described in detail in conjunction with the metal pipe line as shown in fig1 but it is to be understood that the present invention may be equally applied to a pipe assembly or line laid in any desired direction . for instance , the heat treatment method of the present invention can be advantageously applied to a single wall pipe line in which an air pocket or dead water tends to be left . the effect , features and advantages of the present invention may be summarized as follows : ( a ) even when a pipe line is laid horizontally so that dead water tends to be left therein or even when component parts of a pipe line are so designed and assembled that an air pocket tends to be left in an assembled pipe line , the residual - stress - improvement of the inner wall surfaces of the pipe line can be carried out so that corrosion cracks can be inhibited and prevented . ( b ) an air pocket can be liminated while the heat treatment is being carried out so that variations in improvement of residual stresses in the peripheral direction of a metal pipe line can be reduced to a minimun so that reliability of the pipe line can be remarkably improved . ( c ) even when the shape of assembled pipe line component parts is complicated , the residual - stress improvement can be carried out by effecting the induction heating of individual parts not simultaneously but one after another leaving a predetermined time interval . furthermore the heat treatment method of the present invention can be easily applied to various pipe lines .