Boundary Element Method For Heat Conduction Equation In Multi-region Heterogeneous Material

The thermal conductivity of heterogeneous materials is of great significance to the development of aerospace,biomedicine and other fields.It has always been the focus of engineering thermodynamics research.Numerical simulation is the main method to study its unsteady temperature field distribution.Compared with other existing numerical simulation algorithms,the boundary element method has the characteristics of small calculation amount,fast calculation speed and simple data preparation.Therefore,the application of the boundary element method to the study of the temperature field distribution of heterogeneous materials has certain theoretical and practical significance.In this paper,based on the boundary element method and with the help of the basic physical solutions,the boundary integral equation of the unsteady heat conduction equation with thermal contact interface between two adjacent sub-regions on a heterogeneous material in real space is deduced,and the method of discretizing the boundary element integral equation with constant element and linear element is adopted,and the time is iteratively processed,and then it is converted into the boundary integral control equation in matrix form for solving,in which the thermal contact interface is a non-ideal thermal contact interface.or ideal thermal contact interface.In addition,the Laplace transform method is used to deal with the unsteady heat conduction equation in the real space,and the boundary integral equation with thermal contact interface between two adjacent sub-regions on the heterogeneous material in the complex space is deduced.The constant element and the linear element are discretely solved.At this time,iterative processing of time is no longer necessary,which simplifies the calculation process and speeds up the calculation speed.Then,perform stehfest inversion on the numerical results obtained after Laplace transformation,and obtain the temperature field distribution value in real space.Finally,numerical simulations are carried out based on the solution methods of constant element and linear element with several numerical examples under different boundary conditions,which verifies that the method in this paper is effective,and the result of linear element is obviously better than that of constant element.In this paper,a new boundary element integral equation derivation method is used to obtain the theoretical display results of the multi-region unsteady temperature field distribution on heterogeneous materials.The calculation efficiency is high,and the analytical methods and calculation results provide a reference for the study of heterogeneous materials.