Free Convection in Channel-an Alternative Numerical Approach and Illustrations

Abstract

SUMMARYA ®nite dierence method of solving problems of free convection in a parallel plate channel with or without internal obstructions is presented. It uses the steady-state governing equations including the axial diusion terms, and it does not require pressure matching or conditions to obtain the solution. The buoyancy-induced upward velocity is self-generated without requiring any extra eort or strategy over that normally used for iterative ®nite dierence solution of elliptic equations. The method simply uses the average upward velocity from one iteration to the next until convergence. Comparison and a few illustrations are included to indicate the validity and usefulness of the method.

Optimum natural convection from square cylinder in vertical channel

“…A numerical finite difference scheme based on the Residual Method of Finite Differencing Algorithm given by Bhattacharyya (1997) is used to solve the governing equations. The numerical scheme uses a staggered non-uniform grid and a finite difference formulation by local analytical solution.…”