Entropy generation due to natural convection in non-uniformly heated porous isosceles triangular enclosures at different positions 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 article info Article history: Received 1 July 2008 Received in revised form 22 August 2008 Available online 10 November 2008 Keywords: Entropy generation Porous medium Natural convection Isosceles triangular Non-isothermal temperature profile Numerical results abstract Entropy generation due to natural convection in isosceles triangular enclosures with inclination angles (u) filled with a fluid-saturated porous medium has been studied numerically. The enclosure has differ- ent inclination angles and it is non-uniformly heated from one side. The finite difference technique was adopted to solve the governing equations of this natural convection problem. Then, entropy generation due to heat transfer irreversibility (HTI) and fluid friction irreversibility (FFI) was calculated from its def- inition using dependent variables of velocities and temperature fields. Calculations were performed for different Rayleigh numbers Ra in the range of 100 6 Ra 6 1000 and inclination angle, 0  6 u 6 180  . It is found that both inclination angles and Rayleigh numbers make important effect on natural convection heat transfer, fluid flow and entropy generation. The highest entropy generation due to HTI and FFI and stream function are observed at u ¼ 90  . Multiple cells were formed at this angle. Streamlines, isotherms and entropy contours are symmetric inside the enclosure for both u ¼ 0  and u ¼ 180  . Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Porous layers have been studied extensively in last years due to its wide applications in geothermal systems as reviewed by Cheng [1] and Bejan [2]. Based on their paper, these kinds of applications can be found for geothermal energy extraction, grain storage, ther- mal insulation, etc. Wide application can be found in several books on porous media Nield and Bejan [3], Ingham et al. [4], Ingham and Pop [5], Vafai [6] and Vadasz [7]. Bejan and Poulikakos [8] pro- posed the using of porous material inside the attic space to de- crease the heat transfer. Many researchers have studied the natural convection heat transfer and fluid flow in triangular shaped enclosures filled with viscous fluid due to its important applications as attics, roofs, elec- tronic equipments or different shaped building materials. Natural convection analysis in such geometries has been performed by Akinsete and Coleman [9], Asan and Namli [10,11], Ridouane et al. [12], Holtzman et al. [13], for isothermal and Basak et al. [14,15] for non-isothermal boundary conditions. All of these stud- ies indicate that both aspect ratio of triangular enclosure and Ray- leigh number affects the heat transfer and flow fields. The number of studies on natural convection in triangular enclosures filled with fluid-saturated porous media is very limited. Basak et al. [14] made recently a numerical study solving the Navier–Stokes and energy balance equations for a triangular enclo- sure filled with a porous medium using a penalty finite element analysis with bi-quadratic elements. They analyzed two cases based on temperature boundary conditions as case I: two inclined walls are uniformly heated while the bottom wall is isothermally cooled and case II: two inclined walls are non-uniformly heated while the bottom wall is isothermally cooled. They found that the local Nusselt numbers for the bottom wall are maximum at the bottom corner points for uniform heating. On the other hand the local Nusselt number shows little variations due to non-uni- form heating especially for the Darcy number Da in the limit Da 6 10 4 . Varol et al. [16–18] have performed studies on natural convection in porous right-angle triangular enclosures by adding some solid objects to control heat transfer. Further, Basak et al. [19,20] investigated the natural convection in triangular enclo- sures filled with porous media. The wide theory on entropy generation is given by Bejan [21,22]. Entropy generation in systems in which natural convec- tion occurs is an important issue in engineering applications be- cause it gives information about local and global losses of energy due to heat transfer and fluid friction irreversibility. Thus, the energy saving can be obtained by reducing these losses. The subject is mostly analyzed for rectangular, square or circle shaped porous enclosures in the literature. Baytas [23] and Zahmatkesh [24] investigated the entropy generation for inclined square and horizontal square enclosures, respectively. They observed that en- 0017-9310/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2008.08.026 * Corresponding author. Tel.: +90 424 237 0000x4219; fax: +90 424 236 7064. E-mail address: ysnvarol@gmail.com (Y. Varol). International Journal of Heat and Mass Transfer 52 (2009) 1193–1205 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt