An analytical/numerical solution of convective heat transfer in the thermal entrance region of irregular ducts

Abstract

This study presents an analytical/numerical solution to convective heat transfer in the thermal entrance region of irregular ducts (i.e., square, rectangular and equilateral triangular ducts) that are subjected to a constant wall temperature accounting for fully developed velocity. The developing temperature field in these ducts is obtained analytical from solution of the energy equation employing the method of lines (MOL). The resulting system of first order differential equations is readily solved analytically or numerically on a personal computer. Furthermore, the paper discusses in detail the proposed methodology where all calculations are based on a coarse grid with sixteen lines or, a fine grid with twenty-five lines, in the cross-stream direction of the duct. Based on the temperature fields, the representative curves illustrating variations of the bulk temperature and the Nusselt numbers with pertinent parameters are plotted. The computed results are compared against some limited analytical and numerical findings reported in the literature. In all cases, satisfactory comparison is obtained.