the invention now is described in detail in a preferred embodiment in reference to the drawings for better understanding its method , features and effects . referring to fig1 and 2 , the tcc mold of the invention is composed of two water - cooled wide copper plates 1 , 2 which are opposite to each other in front and back direction and two water - cooled narrow copper plates 3 , 4 which are opposite to each other in right and left direction . the water - cooled wide copper plates 1 , 2 both include an upper portion and a lower portion . the two lower portions have vertical planar surfaces with a space between them ( they are the planar portions of the lower portions of the water - cooled wide copper plates ), nevertheless , the vertical planar surfaces can be omitted . the two upper portions have inclined curved surfaces which are open upwards and outwards with a biggest inclination angle θ being less than 12 °. the two water - cooled narrow copper plates 3 , 4 are flat plates opposite to each other . all the wide and narrow copper plates form an upper casting sprue 5 and a lower mold cavity 7 . in addition , there is provided a submerged nozzle 6 . the inside profile curve of the casting sprue 5 in a horizontal section at any height of each water - cooled wide copper plate 1 , 2 is composed of a curve segment in the middle and two linear segments at opposite ends , or composed of only a curve segment . throughout the inside profile curve ( including linear segments ) in any horizontal section , the first derivative , second derivative and curvature of the curve are all varied continuously . the inside profile curve in a vertical section of the casting sprue 5 at any transverse position of each water - cooled wide copper plate 1 , 2 is composed of a curve segment in the middle , an upper inclined linear segment connected to the upper end of the curve segment and a lower vertical linear segment connected to the lower end of the curve segment . optionally , the lower vertical linear segment can be omitted . throughout the inside profile curve ( including linear segments ) in any vertical section , the first derivative , second derivative and curvature of the curve are all varied continuously . that is , at any point of the curved surfaces ( including curved surfaces and planar surfaces ) of the inside profile of the wide copper plates of a tcc mold of the invention , curvature is varied continuously . the overall length of an inside profile curve in a horizontal section of the casting sprue 5 at any height of each water - cooled wide copper plate 1 , 2 is gradually reduced in an up - to - down direction , which complies with the solidification shrinkage of the shell of the slab . the surface configuration and its design method of the water - cooled wide copper plates of a tcc mold of the invention are described below in detail . referring to fig3 , the area encircled by letters a , b , c , g , d , e and f is a curved surface area of the water - cooled wide copper plate of a tcc mold , and the remainder is a planar surface area . the area encircled by letters a , c , g and f is a curved surface area of the wide copper plates of the tcc mold , which is in the vertical direction and formed of linear lines . the area encircled by letters g , d , e and f is a curved surface area of the wide copper plates of the tcc mold , which is in the vertical direction and formed of curves . h is the biggest opening height of the tcc mold , l is an opening length of the tcc mold , d is the biggest height at which the curved surface of the sprue in vertical direction of the tcc mold is terminated , d − d is the height of the sprue curved surface in the vertical direction of the tcc mold , which is formed of linear lines , d + d 0 is an overall height of the tcc mold , b is an overall width of the tcc mold . for a simpler manufacture process , in determining a surface configuration of water - cooled wide copper plates , the midpoint o of segment de is selected as the coordinate origin . the three - dimensional model function can be solved by converting it into a two - dimensional function , and then treated by superposition . a coordinate system as shown in fig4 and 21 is established for inside profile curves in a horizontal direction of a tcc mold . the inside profile curve of the casting sprue in a horizontal section at any height of each water - cooled wide copper plate 1 , 2 is composed of a curve segment in the middle and two linear segments at opposite ends . an intersection point of a vertical line at the position of ½ opening width on the curved segment in x direction and a horizontal linear line connecting the two ends of the curved segment in y direction is taken as a coordinate origin . the equation is constrained by the conditions : at points p and q which are the connection points of a curve and a linear line , its assignment in y direction is the same as that for a linear segment ; its first derivative and second derivative are the same as those for a linear segment ; at the position of ½ opening width on the curved segment in x direction , there is a maximum h in y direction , and its first derivative is zero . for example , in the case that the opening length l in x direction is required in processing to be 900 mm , a maximum h in y direction is 50 mm . according to the above constraints , it can be derived that an equation y =− 6 . 02 × 10 − 15 x 6 + 3 . 66 × 10 − 9 x 4 − 7 . 41 × 10 − 4 x 2 + 50 for a profile curve in horizontal direction of the upper sprue of a tcc mold . thereby it is possible to make the curvature of the inside profile curve of the casting sprue in a horizontal section at any height of each water - cooled wide copper plate 1 or 2 be varied continuously , that is , curvatures at the connection points of curves and linear lines are equal . a coordinate system as shown in fig8 and 22 is established for inside profile curves in a horizontal direction of a tcc mold . the inside profile curve of the casting sprue in a vertical section at any transverse position of each water - cooled wide copper plate 1 , 2 is composed of a curve segment in the middle , an upper inclined linear segment connected to the upper end of the curve segment and a lower vertical linear segment connected to the lower end of the curve segment . the lower endpoint of the curve segment is taken as a coordinate origin . this equation is constrained by the conditions : at points m and n which are the connection points of a curve and a linear line , its assignment in y direction is the same as that for a linear segment ; and its first derivative and second derivative are the same as those for a linear segment . the overall depth d is taken to be 700 mm , the depth d at which the linear segment of the sprue terminates is taken to be 100 mm . assuming that the height of the sprue in y direction is expressed by kf ( x ) after the linear segment terminates , the height in y direction on a tcc mold is expressed by f ( x ), and k is assigned by 0 . 12 , if f ( x ) at the center of the curve on a tcc mold is assigned by 50 mm , then the curve segment in vertical direction at the center of the sprue of a tcc mold can be expressed by equation y = 1 . 40 × 10 − 9 z 5 − 3 . 87 × 10 − 7 z 4 + 3 . 07 × 10 − 5 z 3 , and the inclined linear segment connected to the upper end of the curve segment can be expressed by equation y = 7 . 33 × 10 − 2 z − 1 . 33 . therefore , the curvature of the inside profile curve ( including linear segment ) in a vertical section of the casting sprue at any transverse position of each water - cooled wide copper plate can be made be varied continuously . if a different coordinate is established , the functional equations derived from the above analysis may have some changes . nevertheless , the functional equations will still be in the form that y = a 0 + a 1 x + a 2 x 2 + a 3 x 3 + a 4 x 4 + a 5 x 5 + a 6 x 6 , and y = b 0 + b 1 z + b 2 z 2 + b 3 z 3 + b 4 z 4 + b 5 z 5 . now , it is explained only by an example in which a different coordinate is established to solve the inside profile curves in different horizontal cross sections of the sprue portion of the water - cooled wide copper plates . referring the coordinate as shown in fig2 , a maximum h in y direction is 50 mm , and the opening length l in x direction is 900 mm . according to the constraints that the second derivatives at points p and q which are intersection points of a curve and two linear lines must be continuous , an equation y =− 6 . 02 × 10 − 15 x 6 + 1 . 63 × 10 − 11 x 5 − 1 . 46 × 10 − 8 x 4 + 4 . 39 × 10 − 6 x 3 is derived . it can be known from the above detailed description and comparison with reference to the drawings , a tcc mold can be improved in its performance greatly if the second derivative of the profile curves of its cavity is varied continuously . furthermore , if the third derivative , fourth derivative and even higher order derivatives of the profile curves are required to be continuous , it is possible to determine polynomials of even higher order as equations for the curve segment of the profile curves . now , it is explained only by an example in which the connection points ( points p and q ) of the curve segment with the two linear segments of the profile curves in any horizontal section of the cavity of water - cooled wide copper plates of a tcc mold meet that their third derivative are continuous . referring to the coordinate as shown in fig4 and 23 , a maximum h in y direction is 50 mm , and the opening length l in x direction is 900 mm . according to the constraints that the third derivatives at points p and q must be continuous , an equation y = 2 . 97 × 10 − 20 x 8 − 2 . 41 × 10 − 14 x 6 + 7 . 32 × 10 − 9 x 4 − 9 . 88 × 10 − 4 x 2 + 50 is derived . in fig4 , h 1 , h 2 , h 3 and h 4 are opening width in y direction at different heights of a tcc mold . the curves are each composed of a curve segment in the middle and two linear segments at both ends or composed of only a curve . in the case there is not any linear segment , it is still possible to determine the profile curves by use of the above method , but it needs to suppose that linear lines are connected to both ends of the curve . referring to fig5 , the first derivatives of the profile curves ( corresponding to the curve in fig4 ) in horizontal direction of the cavity of the water - cooled wide copper plates of a tcc mold is varied continuously . referring to fig6 , the second derivative of the profile curves ( corresponding to the curve in fig4 ) in horizontal direction of the cavity of the water - cooled wide copper plates of a tcc mold is varied continuously . referring to fig7 , the curvature of the profile curves ( corresponding to the curve in fig4 ) in horizontal direction of the cavity of the water - cooled wide copper plates of a tcc mold is varied continuously . in fig8 , l 1 , l 2 , l 3 and l 4 are opening length between two different positions in transverse direction of a tcc mold . the curves are composed of a curve segment in the middle , an upper inclined linear segment connected to the upper end of the curve segment and a lower vertical linear segment connected to the lower end of the curve segment . optionally , the lower vertical linear segment connected to the lower end of the curve segment can be omitted . in the case there is not the lower vertical linear segment , it is still possible to determine the profile curves by use of the above method , but it needs to suppose that a lower vertical linear segment is connected . referring to fig9 , the first derivatives of the profile curves ( corresponding to the curve in fig8 ) in vertical direction of the cavity of the water - cooled wide copper plates of a tcc mold is varied continuously . referring to fig1 , the second derivatives of the profile curves ( corresponding to the curve in fig4 ) in vertical direction of the cavity of the water - cooled wide copper plates of a tcc mold is varied continuously . referring to fig1 , the curvature of the profile curves ( corresponding to the curve in fig4 ) in vertical direction of the cavity of the water - cooled wide copper plates of a tcc mold is varied continuously . referring to fig1 , it can be seen that the difference between curve segment and linear segment ( at different heights of a tcc mold ) of the profile curves of the cavity of a tcc mold is gradually reduced from up to down , and so is the overall length of curves , and that the length variation of the profile curves of horizontal cross sections in height direction of a tcc mold is in the form of a curved uneven shrinkage , complying with the solidification shrinkage of a slab shell . in fig1 , a comparison of the upper opening curves in horizontal direction between a tcc mold of the prior art and a tcc mold of the invention is shown . in the figure , α denotes the prior art , and β denotes the present invention . this also applies to fig1 - 20 . in fig1 , a comparison of the first derivatives of upper opening curves in horizontal direction between a tcc mold of the prior art and a tcc mold of the invention is shown . in fig1 , a comparison of the second derivatives of upper opening curves in horizontal direction between a tcc mold of the prior art and a tcc mold of the invention is shown . in fig1 , a comparison of the curvatures of upper opening curves in horizontal direction between a tcc mold of the prior art and a tcc mold of the invention is shown . similarly , in fig1 , a comparison of the central curves in vertical direction between a tcc mold of the prior art and a tcc mold of the invention is shown . in fig1 , a comparison of the first derivatives of central curves in vertical direction between a tcc mold of the prior art and a tcc mold of the invention is shown . in fig1 , a comparison of the second derivatives of central curves in vertical direction between a tcc mold of the prior art and a tcc mold of the invention is shown . in fig2 , a comparison of the curvatures of central curves in vertical direction between a tcc mold of the prior art and a tcc mold of the invention is shown . as can be seen from these figures , for the profile curves of the cavity curved surfaces of a tcc mold of the prior art , only the first derivative of them is varied continuously , whereas for the profile curves of the cavity curved surfaces of a tcc mold of the invention , both the first derivative and the second derivative thereof are varied continuously . this contributes to solve the technical problems in the prior art as mentioned above . preferably , a ratio of the length of a profile curve of a horizontal cross section of the upper opening of a tcc mold to the length of linear lines connected to two ends of the curve is selected to be between 1 . 02 and 1 . 15 . and , the length variation of the profile curves of horizontal cross sections in height direction of a tcc mold is in the form of curvedly and unevenly shortening . preferably , the ratio of the upper opening width between two narrow water - cooled copper plates to the lower opening width of them is selected to be 1 . 0 - 1 . 05 . in a process for implementing the present invention , firstly , two wide water - cooled copper plates and two narrow water - cooled copper plates are manufactured in accordance with the configuration and dimension requirements for a tcc mold of the invention , and then , the four water - cooled copper plates are assembled together in a proper interrelation , so that a tcc mold is ready for use . it should be understood that the above description of the preferred embodiment is illustrative and exemplary and is in no way intended to limit the scope of the present invention . any modifications , variations and equivalents without departing from the spirit of the invention all fall into the scope of the invention claimed in the claims .