International Journal of Thermal Sciences 48 (2009) 1161–1175 www.elsevier.com/locate/ijts Entropy analysis due to conjugate-buoyant flow in a right-angle trapezoidal enclosure filled with a porous medium bounded by a solid vertical wall Yasin Varol a , Hakan F. Oztop b , Ioan Pop c,∗ a Department of Mechanical Education, Firat University, 23119 Elazig, Turkey b Department of Mechanical Engineering, Firat University, 23119 Elazig, Turkey c Faculty of Mathematics, University of Cluj, CP 253, 3400 Cluj, Romania Received 8 February 2008; received in revised form 6 August 2008; accepted 6 August 2008 Available online 29 August 2008 Abstract Entropy generation due to buoyancy induced convection and conduction in a right angle trapezoidal enclosure filled with fluid saturated porous medium has been performed numerically. Left vertical solid wall of the trapezoidal enclosure has a finite thickness and conductivity. The outside temperature of the solid wall is higher than that of inclined wall, while horizontal walls are adiabatic. The governing Darcy and energy equations are solved numerically using a finite difference method. The study is performed for different governing parameters including the Rayleigh number (50  Ra  1000), inclination angle of the inclined wall of the enclosure (γ = 35 ◦ , 45 ◦ and 60 ◦ ), dimensionless thickness of the solid vertical wall (S = 0.05, 0.1 and 0.2), and thermal conductivity ratio (k = 0.1, 1.0 and 10). Entropy generation is calculated by using the obtained velocities and temperature distributions from the computer code. Results are presented for the Bejan number, local and mean Nusselt numbers, streamlines, isotherms, iso-Bejan lines and entropy generation contours. It is found that the most important parameters on heat transfer and fluid flow are thermal conductivity ratio and dimensionless thickness of the solid wall of the enclosure. Thus, these parameters also generate entropy for the whole system. It is also found that increasing the Rayleigh number decreases the Bejan number; however, heat transfer is an increasing function of Rayleigh number.  2008 Elsevier Masson SAS. All rights reserved. Keywords: Conjugate trapezoidal enclosure; Entropy generation; Porous medium; Natural convection; Numerical results 1. Introduction Applications of porous media include utilization of geother- mal energy, design of packed bed reactors, oil recovery, insu- lation of buildings and cold storage, drying processes, energy storage systems, solar collectors, heat exchangers, transpiration cooling, powder metallurgy, solidification of binary alloys, agri- cultural engineering, etc. These are some of applications and the most of studies in porous media have been recently excel- lently reviewed by Nield and Bejan [1], Ingham and Pop [2], Ingham et al. [3] and Vafai [4]. The study for an inclined trapezoidal enclosure at different inclination angles filled with a viscous fluid has been analyzed by Lee [5]. He made a numerical analysis to solve the natu- * Corresponding author. Tel.: +40 264 594315; fax: +40 264 591906. E-mail address: pop.ioan@yahoo.co.uk (I. Pop). ral convection heat transfer in an inclined trapezoidal enclosure filled with viscous fluid for different Prandtl numbers Pr using body-fitted coordinate systems. It was shown that for Ra > 10 4 and Pr > 0.1, the heat transfer, in a trapezoidal enclosure with two symmetrical, inclined sidewalls of moderate aspect ratios, is a strong function of the orientation angle of the cavity. Kumar and Kumar [6] used parallel computation technique to analyze the natural convection heat transfer in a trapezoidal enclosure filled with a porous medium. The short bottom and the long top walls are taken adiabatic, while the sloping walls are dif- ferentially heated. They showed that the inclination of the side wall substantially affects the flow and temperature distribu- tions. Baytas and Pop [7] solved to Darcy and energy equation in cylindrical coordinates using ADI method to analyze natu- ral convection in a trapezoidal enclosure filled with a porous medium. It has been observed that up to Rayleigh number Ra = 100, a conduction-dominated regime prevails, and after- wards a two-cellular convective flow regime takes place at the 1290-0729/$ – see front matter  2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2008.08.002