Numerical analysis of an advective diffusion domain coupled with a diffusive heat source

This paper presents a formulation of the boundary element method (BEM) for the study of heat diffusion and advective effect in isotropic and homogeneous media. The proposed formulation has a time independent fundamental solution obtained from the two-dimensional Laplace equation. Consequently, the formulation is called D-BEM since it has domain integrals in the basic integral equation. The first order time derivative that appears in the integral equations is approximated by a backward finite difference scheme. Homogeneous subregions are considered in the analysis in a specific model simulating a nonuniform flow passing by a circular obstacle under internal heat generation. Results from numerical models are compared with the available analytical solutions. The correlation estimator R2 is employed to validate the numerical model and to demonstrate the accuracy of the proposed formulation.