A boundary-domain integral equation method for solving convective heat transfer problems

In this paper, a new boundary-domain integral equation for solving energy equation in convective heat transfer problems is derived. The derived integral equation accounts for fluid velocity which is computed using the velocity boundary-domain integral equations presented in (X.W. Gao, 2004, 2005). Numerical implementation of these integral equations is discussed for steady incompressible fluid flows, in which the velocity and pressure integral equations are uncoupled from the temperature equation, and thus can be solved separately. By substituting the velocity, velocity gradient, and pressure integral equations into the energy integral equation, temperatures can be computed without iterative processes. Two numerical examples for 2D problems are given to validate the proposed method.