BEM formulation for steady-state conduction-convection problems with variable velocities

Development of a boundary-element method (BEM) for steady-state conduction-convection problems with an arbitrary velocity field is the principal focus of this article. The steady-state fundamental solution for a moving heat source is used in the present approach. An arbitrary velocity field is decomposed into a constant part and a variable part. In addition to the boundary integrals for the constant-velocity case, variable velocity requires a domain integral in the BEM formulation. Both iterative and noniterative schemes have been used to solve the BEM equation including the domain integral term. Numerical results obtained from the proposed formulation are first validated against analytical results. Other example problems are then investigated and a detailed parametric study is conducted to understand the effects of the decomposition level and mesh refinement. The proposed BEM formulation is found to produce stable and accurate solutions under a variety of conditions for steady-state conduction-convection problems with arbitrary velocity fields.