Solution of a time-dependent heat conduction problem by an integral-equation approach

In this paper the authors develop an algorithm for solving the time-dependent heat conduction equation [8] in an analytical, exact fashion for a two-component domain. The Green’s function approach [1] and [4] is used to get the formal solution of the problem. As an intermediate result an integral-equation for the temperature history at the domain interface is formulated which can be solved analytically. The Green’s function approach in conjunction with the integral-equation method is very useful in cases were strong discontinuities or jumps occur. The system parameters and the initial conditions of the investigated problem give rise to two jumps in the temperature field. In conjunction to the analytical solution a pure numerical solution is obtained by using the FEM (finite element method) [7], and compared with the solution obtained by the integral-equation approach.

Algorithm for solving the time-dependent heat conduction equation in an analytical fashion for a two-component domain. Green’s function approach to get the formal solution. Integral-equation for the temperature history at the domain interface. Integral-equation solved by a computer algebra system (CAS).