A Boundary Element Algorithm for Convective Heat Transfer and Steady State Solidification Problems

An efficient numerical algorithm for solving steady state heat transfer and solidification problems is described. The algorithm is of boundary integral type and is based on the formulation of the field variables along the boundary of the domain of interest. Compared with the familiar domain-based methods, such as the finite element and finite difference (or finite volume) methods, this boundary-based method has an advantage of solving fewer unknowns and hence has a potential for reducing computational time significantly. Another and yet more important advantage of the present algorithm is that it is a stable scheme and is not prone to numerical oscillations resulting from convective effects, as often encountered in the domain-based methods. Therefore, no numerical or artificial diffusion (such as streamline upwinding) is necessary. Numerical examples are presented that are drawn from processing systems for producing aluminum-based materials.