NUMERICAL SOLUTIONS FOR COMBINED FREE AND FORCED LAMINAR CONVECTION IN HORIZONTAL RECTANGULAR DUCTS BY CONJUGATE GRADIENT METHOD

Abstract

A numerical solution using the conjugate gradient method is presented for the heat transfer problems of fully developed combined free and forced laminar convection with high Prandtl number fluid in horizontal rectangular ducts, where the wall heat flux is axially uniform and the wall temperature is peripherally uniform. The S. O. R. method frequently fails to obtain a stable solution for large values of ReRaPr. However, the proposed method gives a stable converged solution even when the values of ReRaPr are large.
Based on the numerical calculation, the relationships of Nu/Nu₀ vs. ReRaPr for various aspect ratios are presented in a graph and by the following equation:
Nu/Nu_o=a(ReRaPr)^b
where 0 denotes pure forced convection, and a and b are related to the aspect ratio and ReRaPr. In addition, the streamlines and isothermals are obtained for various aspect ratios and ReRaPr.