After the interface heat flow and temperature field data are solved by the inverse calculation program, the part of the inverse calculation program to solve the interface heat transfer coefficient is carried out, and the variation curve of the interface heat transfer coefficient with time is inversely calculated. As shown in the figure, the time-varying curves of interface heat transfer coefficients of ring sand mold castings and flat sand mold castings with different sizes are obtained by back calculation, in which (a), (b) and (c) represent the interface heat transfer coefficients of outer sand mold and inner sand core of 30 / 80mm, 50 / 100mm and 70 / 120mm Ring Castings respectively, and (d) is the interface heat transfer coefficient of 50mm thick flat sand mold castings.

After the liquid metal is filled into the mold cavity, the interface heat transfer coefficient will rise to the peak value quickly in a very short time. This is due to the response delay of the initial thermocouple and the large thermal resistance of molding sand, which makes the actual interface heat flow underestimated, so that the initial inverse calculation interface heat transfer coefficient is lower than the real value. With the continuous correction and iteration of the inverse calculation model, The interfacial heat transfer coefficient then rises and tends to the real value [75]; In fact, when the temperature of liquid metal is above the liquidus, the interface heat transfer coefficient basically remains unchanged. This is due to the influence of turbulence generated in the initial pouring and mold filling process, which makes the error between the initial back calculated interface heat transfer coefficient and the actual interface heat transfer coefficient larger. In the initial rising process, the interface heat transfer coefficient is replaced by the peak interface heat transfer coefficient to reduce the error with the actual interface heat transfer coefficient, The variation curve of interface heat transfer coefficient with time is obtained as shown in the figure.

It can be seen from the figure that the maximum values of heat transfer coefficient of sand core interface in 30mm, 50mm and 70mm are 263 (w / m2 ℃), 183 (w / m2 ℃) and 110 (w / m2 ℃) respectively; The maximum values of interface heat transfer coefficient of 80mm, 100mm and 120mm outer sand mold are 131 (w / m2 ℃), 127 (w / m2 ℃), 103w / m2 ℃); The difference of the heat transfer coefficient between the two groups of sand mold is higher than that of the whole sand mold; With the increase of solidification time, the interfacial heat transfer coefficient of the inner sand core begins to stabilize with the formation of eutectic composition. The interfacial heat transfer coefficient of the outer sand mold will reduce the interfacial heat transfer coefficient in the eutectic stage and the cooling zone of the sand mold casting, which is due to the different location and geometric structure of the inner sand core and the outer sand mold, It is caused by the difference of heat transfer caused by the change of internal and external interface contact state. Comparing the changes of internal and external interface heat transfer coefficients of three groups of ring sand mold castings, it is obvious that with the increase of internal and external diameter, the peak value of interface heat transfer coefficient of inner sand core and outer sand mold and the interface heat transfer coefficient of the whole solidification process will also decrease. It can also be found by comparing it with the interface heat transfer coefficient of flat sand mold castings with equal thickness, The interfacial heat transfer coefficient of the inner sand core is always higher than that of the flat sand mold casting, and the variation law and value of the interfacial heat transfer coefficient of the flat sand mold casting are close to that of the outer sand mold.

Observe the changes of heat transfer coefficient of sand mold and sand core interface in (a), (b) and (c) in the figure. The heat transfer coefficient of sand core interface will fluctuate greatly in 3000-4000s, but there is no obvious fluctuation of sand mold. Carefully observing the measured temperature curve, it can be found that the sand core temperature of three groups of annular sand mold castings will reach thermal saturation successively within 3000-4000s, forming a reverse heat flow; According to the macroscopic solution of the interface heat transfer coefficient formula, the formation of reverse heat flow will inevitably greatly affect the change of the interface heat transfer coefficient, resulting in the instability of the 3000-4000s time period of the interface heat transfer coefficient of sand core (a), (b) and (c) in the figure. With the increase of iteration time, this phenomenon will be gradually eliminated.