Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Abstract

SUMMARYA two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two-and threedimensional problems demonstrates the effect of the dimensionality.

Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transfer

“…Figures 12(b) and (c) show the responses at = 1.0 s using a temperature contour plot. The comparison of these plots with those provided by Gordeliy et al [46] and by Furman and Neuman [47] indicates that the results are identical if one allows for the two misprints in Figure 5 of [47].…”

“…The proposed coupling solutions are then verified by computing the heat diffusion in a system composed of a circular solid inclusion (Medium 1), buried in an unbounded fluid Medium (Medium 3) hosting two other circular inclusions made of different materials (Media 2 and 4) (see Figure 4(b)). The responses are compared against analytical solutions obtained by applying, as above, the separation of variables method to the Helmholtz equation in each medium, following the technique described by Gordeliy et al [46]. Appendix B outlines the way in which the solution is computed.…”

“…To verify the correctness of the solution given by this methodology, the time-dependent temperature field is compared with a reference solution. The reference solution used is the published solution provided by Gordeliy et al [46] and by Furman and Neuman [47], where a line heat…”