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Effects of Nonuniform Heating and Wall Conduction on Ntural Convection in a Square Porous Cavity Using LTNE Model

[+] Author and Article Information
Ammar Alsabery

School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia
ammar e 2011@yahoo.com

Ali J. Chamkha

Mechanical Engineering Department, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi ArabiaPrince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia
achamkha@pmu.edu.sa

Ishak Hashim

School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia
ishak_h@ukm.edu.my

Pradeep G. Siddheshwar

Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore 560 056, India
mathdrpgs@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4037087 History: Received March 06, 2017; Revised May 26, 2017

Abstract

The effects of non-uniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal non-equilibrium (LTNE) model are studied numerically using the finite difference method. The finite thickness horizontal wall of the cavity is heated either uniformly or non-uniformly and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer.

Copyright (c) 2017 by ASME
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