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Convective Energy Transmission Within a Porous Trapezoidal Enclosure Under Ascendancy of Magnetic Field with Linearly Heated/Cold Wall

American Journal of Civil and Environmental Engineering
Vol.3 , No. 2, Publication Date: Apr. 27, 2018, Page: 19-36

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Authors

[1]	Ziafat Mehmood, Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan.
[2]	Tariq Javed, Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan.
[3]	Muhammad Arshad Siddiqui, Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan.

Abstract

The present article comprises a numerical analysis of free convection heat transfer inside a porous trapezoidal container influenced by MHD when bottom wall is subject to uniform temperature profile, left wall is provided with linear heating, right wall is taken either cold or linearly heated and upper wall is perfectly insulated. Momentum and energy equations describing the flow problem are modeled and exposed first to Penalty method to remove pressure term from momentum equations and afterwards reduced equations are solved by incorporating the Galerkin weighted residual method. Computed solutions are presented through curves for streamlines, isotherms and local heat transfer rate for various values of involved parameters including Prandtl number Pr (0.026 ≤ Pr ≤ 1000), Hartman number Ha (50 ≤ Ha ≤ 1000) and Darcy number Da (10^-5 ≤ Da ≤ 10^-3) where, Rayleigh number Ra is fixed at 106, considering three different cases of cavity, in which inclination of side walls of enclosure is taken to be 0, 30 and 45 degrees. This inquisition showed that the strength of streamline circulations escalates when Darcy and Prandtl numbers are amplified where, symmetric isotherms and streamlines are observed in case of non-uniform heating for tilt angles 30 and 45 degrees where due to conduction dominance smooth and monotonic isotherms are seen for small Darcy number but increasing Darcy number results in distorted isotherm contours indicating dominance of convection regime.

Keywords

Natural Convection, Penalty Method, Finite Element Method (FEM), Cavity Flow

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