On the importance of thermal boundary conditions in heat transfer and entropy generation for natural convection inside a porous enclosure

The aim of the present paper is to analyze the importance of thermal boundary conditions of the heated/cooled walls in heat transfer and entropy generation characteristics inside a porous enclosure, heated from below. Both the heating and the cooling are carried out uniformly and non-uniformly and the results are compared. The laminar, steady, natural convection heat transfer is calculated by solving numerically the mass, momentum, and energy conservation equations whilst viscous dissipation and the work of pressure forces are included in the energy equation. Moreover, the generation of entropy is calculated taking into account both heat transfer irreversibility and fluid friction irreversibility. As the thermal boundary conditions, sinusoidal temperature distributions are invoked for the non-uniformly heated/cooled walls. Comparison between the results of the present numerical model with the previously published works provides excellent agreement. Results are presented in terms of streamlines, isothermal lines, iso-entropy generation lines, and iso-Bejan lines. Additionally, variations of average Nusselt number, global entropy generation rate, and global Bejan number are analyzed over a wide range of Darcy-modified Rayleigh number (10 < Ra < 1000). Inspection of the results indicates that thermal boundary conditions are of profound influences on the induced flow as well as heat transfer characteristics and possess prominent consequences on entropy generation rates. It is demonstrated that, the optimum case with respect to heat transfer as well as entropy generation could be achieved by non-uniform heating. (C) 2007 Elsevier Masson SAS. All rights reserved.