Proceedings of 3rd BSME-ASME International Conference on Thermal Engineering 20-22 December, 2006, Dhaka, Bangladesh NATURAL CONVECTION FLOW IN A SQUARE CAVITY WITH TEMPERATURE DEPENDENT HEAT GENERATION Md. Mamun Molla 1* , M. M. A. Sarker 2 1 Department of Mechanical Engineering, University of Glasgow, Glasgow G12 8QQ, UK 2 Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh. * Corresponding author: E-mail: m.molla@mech.gla.ac.uk (M. M. Molla), Tel: +44 (0)141 330 8463 ABSTRACT: Unsteady natural convection laminar flows in a square cavity formed by insulated bot- tom and top walls, uniformly heated left wall and the cooled right wall has been inves- tigated numerically. The governing equations are transformed into non-dimensional form and the resulting partial differential equations are solved applying upwind finite difference method together with Successive Over-Relaxation (SOR) scheme. The effect of the heat generation and the Rayleigh number on streamlines and isotherms as well as on the rate of heat transfer from the heated wall of the cavity are presented. Key words: Natural convection, Unsteady laminar flow, Heat generation, Square cavity 1. INTRODUCTION Ostrach [1] provided a comprehensive review article and extensive bibliography on natu- ral convection in cavities up to 1988. De Vahl Davis [2] investigated the natural convection of air in a square cavity. Valencia and Frederick [3] investigated the heat transfer in square cavities with partially active vertical walls. Selamet et al. [4] studied the laminar buoyancy driven flows in an enclosure. Natural convection heat transfer in rectangular cavities heated from the bottom had been investigated by Hasnaoui et al. [5]. Sundstrom and Kimura [6] ob- served the phenomena on laminar free convection in inclined rectangular enclosure. Novem- ber and Nansteel [7], Ganzarolli and Milanez [8], investigated the natural convection in rec- tangular enclosures heated form below and cooled from the sides. De Vahl Davis [2], Dixit and Babu [9] have recently investigated natural convection of air in square cavity by using lat- tice Boltzmann method. A large number of physical phenomena involve natural convection driven by heat genera- tion. The study of heat generation in moving fluids is important from the view point of several physical considerations such as those dealing with chemical reactions and those concerned with dissociating fluids. Possible heat generation effects may alter the temperature distribu- tion and, therefore, the particle deposition rate. This may occur in applications related to nu- clear reactor cores, fire and combustion modelling, electronic chips and semiconductor wa- fers. The literature is replete with examples dealing with the heat transfer in laminar flow of viscous fluids. All of the above authors ignored the effect of temperature dependent heat gen- eration due to molecular interaction within the cavities which is not less important from the angle of practical applications. Vajravelu and Hadjinolaou [10] studied heat transfer characteristics in a laminar boundary layer flow of viscous fluid. Molla et al. [11-13] studied natural convection flow with heat generation along a uniformly heated vertical wavy surface, horizontal cylinder and sphere.