1 Copyright © 2010 by ICFD 10 Proceedings of ICFD 10: Tenth International Congress of Fluid Dynamics December 16-19, 2010, Stella Di Mare Sea Club Hotel, Ain Soukhna, Red Sea, Egypt ICFD10-EG-3018 Non-Darcy Effects on Conjugate Natural Convection in Saturated Porous Layer Sandwiched by Finite Thickness Walls Al-Farhany , K. School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UK Khaled.AlFarhany@postgrad.manchester.ac.uk Turan, A. School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UK A.Turan@manchester.ac.uk ABSTRACT Unsteady conjugate natural convective heat transfer in a two-dimensional variable porosity layer sandwiched between two walls has been studied numerically. The Generalization model has been used to solve the governing equations in the saturated porous region. The Boussinesq approximation assumed to be valid. The vertical walls are impermeable and subjected to a horizontal gradient of temperature while the horizontal walls are adiabatic. A finite volume approach has been used to solve the dimensionless governing equations and the pressure velocity coupling is treated with the SIMPLE algorithm. The model has been validated with available experimental, analytical/computational studies. A correlation to evaluate the average Nusselt number has been proposed as a function of Rayleigh number, Darcy number, including a number of physical geometrical and material property ratios. KEYWORDS: Heat transfer, natural convection, porous media, non-Darcy, Conjugate, CFD and finite volume. INTRODUCTION An equally large body of research has emerged with respect to investigations of convective heat and mass transfer in rectangular porous cavities and vertical surfaces with uniform/non-uniform heat flux and surface temperatures. The classical Darcy formulation has been used as well as the Darcy- Brinkman model, the Darcy-Forscheimmer model and Darcy- Brinkman-Forscheimmer model. These areas have been thoroughly reviewed recently by Nield and Bejan [1]. Sen [2] considered the Darcy-Brinkman convective flow in a shallow porous rectangular cavity with adiabatic upper and lower plate boundaries and differentially heated sidewalls. An important non-Darcian study also has been presented by Lauriat and Prasad [3] for a heated vertical porous cavity. The inertia and viscous forces on natural convection is examined via the Darcy-Brinkman-Forchheimer. Nithiarasu [4] studied the effect of the differences in existing porous medium flow models on flow and heat transfer in the context of heat flux boundary condition. The results showed that the effects of non- linear drag term and porosity are significant at higher Rayleigh and Darcy numbers. Numerical investigation for transient free convection in a two-dimensional square cavity filled with a porous medium conducted by Saeid and Pop [5]. These results are in good agreement with the results obtained by Walker and Homsy [6], Bejan [7], Weber [8], Gross et al [9] and Manole and Lage [10], Bankvall [11] .Also, the results show that the time required to get to steady state is shorter for the high Rayleigh number and longer for low Rayleigh number. In the last three decades, a wide range of studies have been published in the literature emphasizing the conjugate heat transfer phenomena in a porous media. It is of practical importance in for example, high performance insulation for buildings and cold storage installations. Nield and Bejan [1] presented many reviews of the existing studies on such topics. In addition to Ingham and Pop [12,13], Pop and Ingham [14], Vafai [15] and Al Amiri [16] studies. Numerical investigations for non-Darcian effects on transient conjugate natural convection-conduction heat transfer from a two-dimensional vertical plate fin embedded in a high-porosity medium were carried out by Hung et al [17]. The results have shown that the inertial effects on heat transfer characteristic are negligible at earlier times. On the other hand the effect becomes increasingly important at longer times. Furthermore, as mentioned above, two-dimensional transient conjugate free convection due to a vertical plate in a porous medium was investigated both analytically and numerically by Vynnycky and Kimura [18] and Kimura et al [19].