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MHD-mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall

T. Javed (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)
Z. Mehmood (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)
Ioan Pop (Department of Applied Mathematics, Babes-Bolyai University, Cluj, Romania)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 5 June 2017

Abstract

Purpose

The purpose of this paper is to analyze numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal cavity in the presence of a uniform magnetic field.

Design/methodology/approach

In this study, the authors have considered three different cases, in which left and right walls of the cavity are tilted at different angles of 0, 30 and 45 degrees, respectively. Both left and right side walls of the cavity are taken cold and the upper wall is insulated and assumed moving with constant speed, whereas the bottom wall is considered to be heated uniformly/non-uniformly. To eliminate pressure term, penalty method is applied to governing Navier–Stokes’ equations. The reduced equations are solved by Galerkin weighted residual technique of finite element method. Grid-independent results are obtained and shown in terms of plots for streamlines, isotherms, Nusselt number and average Nusselt number for a wide range of flow parameters, including Rayleigh numbers Ra, Prandtl number Pr and Hartman number Ha.

Findings

It has been observed that the effects of moving lid become negligible for Ra = 100,000, whereas increasing Rayleigh number results in stronger streamline circulation and convection dominant effects inside the enclosure. Local Nusselt number Nu along the bottom wall is observed to be maximum at edges and it reduces while moving toward the center from edges, and attains minimum value at the center of the bottom wall.

Research limitations/implications

The problem is modeled for laminar and incompressible flow, induced magnetic field has been considered negligibly small and local thermal equilibrium has been assumed.

Originality/value

In this investigation, the authors have presented new and original results for mixed convection flow inside a lid-driven trapezoidal cavity under the influence of a magnetic field. Hence, this study would be important for the researchers working in the area of heat transfer in cavity flows involving magnetic effects to become familiar with the flow behavior and properties.

Keywords

Acknowledgements

Authors want to acknowledge the support of Higher Education Commission (HEC) Pakistan under the scheme “National Research Program for Universities” through project number 3713. Authors are also grateful to the editor and anonymous reviewers for their valuable comments that helped to improve the manuscript.

Citation

Javed, T., Mehmood, Z. and Pop, I. (2017), "MHD-mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 6, pp. 1231-1248. https://doi.org/10.1108/HFF-01-2016-0029

Publisher

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Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited