A new approach for solving heat conduction under zero and non-zero initial conditions

This paper provides a new approach for the analysis of transient heat diffusion arising from conduction. The diffusion is subject to zero and non-zero initial conditions in a two-dimensional domain, containing confined heterogeneous subdomains. This system can be subjected to a heat source. A new formulation is presented, in the frequency domain. It allows coupling between the boundary element method (BEM) and other methods (such as the method of fundamental solutions (MFS), the finite element method (FEM), the finite difference method (FDM), the meshless Petrov-Galerkin (MLGP) method, the virtual element method (VEM), and analytical for-mulations). The BEM is used for the homogeneous exterior domain and the other method is used to evaluate the solutions for the non-homogeneous confined subdomains, to overcome the specific limitations of each of these methods. An inverse fast Fourier transform was used to provide the time domain responses and the results were then compared with those of reference solutions. It was then possible to demonstrate that the proposed algorithm could be used in the frequency and time domains by performing simulation analyses to study heat diffusion in the neighbourhood of heterogeneous inclusions within a solid medium.

Automated summary

This paper presents a new approach to analyze the transient heat diffusion resulting from conduction in a two-dimensional domain with confined heterogeneous subdomains. By coupling the boundary element method with other methods, the proposed formulation allows overcoming the limitations of each method. The time domain responses are obtained using inverse fast Fourier transform, and the results are compared with reference solutions to validate the algorithm's effectiveness.