The basic theory of heat transfer and the solution method of inverse heat transfer problem are systematically expounded. Combined with the geometric structure of sand mold castings used in the experiment, a mathematical model for solving one-dimensional temperature field is established; Combined with Beck nonlinear estimation method, the mathematical back calculation model for solving the interface heat flow and interface heat transfer coefficient of flat, ring sand mold casting and casting / sand core is established, and the back calculation program for solving the interface heat transfer coefficient is compiled by MATLAB software.
(1) Based on the basic theory of heat transfer, several basic forms of heat transfer, heat conduction differential equations and several boundary conditions are introduced in detail.
(2) The inverse problem of heat conduction is proposed, and the solution ideas of forward and inverse problems of heat conduction are compared. The inverse heat conduction problem is classified, and several characteristics of the inverse heat conduction problem compared with the forward problem are analyzed: ill posed, nonlinear and large amount of calculation.
(3) Based on the law of energy conservation and implicit finite volume method, the heat transfer mathematical models of one-dimensional temperature field of flat casting and sand mold, sand mold and sand core in annular casting are established in rectangular coordinate system, which connects the interface heat flow and mold temperature field.
(4) Using the subsection processing of sand mold casting interface heat flow and Beck nonlinear method, combined with the estimation of interface heat flow and interface heat transfer coefficient, the back calculation mathematical model of sand mold casting interface heat transfer is established, and the corresponding back calculation program is compiled with MATLAB software. For the convenience of data import and model selection, we also design the GUI Graphical interface.