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Natural and Mixed Convection

Finite Element Simulation of Magnetohydrodynamic Mixed Convection in a Double-Lid Driven Enclosure With a Square Heat-Generating Block

[+] Author and Article Information
M. M. Rahman1

Centre of Research UMPEDAC, Level 4, Engineering Tower, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia;  Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladeshm71ramath@gmail.com;m71ra@yahoo.com

M. M. Billah

 Department of Arts and Sciences, Ahsanullah University of Science and Technology (AUST), Dhaka-1208, Bangladesh

N. A. Rahim

 Centre of Research UMPEDAC, Level 4, Engineering Tower, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

R. Saidur, M. Hasanuzzaman

Centre of Research UMPEDAC, Level 4, Engineering Tower, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia;  Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia

1

Corresponding author.

J. Heat Transfer 134(6), 062501 (May 02, 2012) (8 pages) doi:10.1115/1.4006010 History: Received January 10, 2011; Revised September 06, 2011; Published April 30, 2012; Online May 02, 2012

Magnetohydrodynamic (MHD) mixed-convection flow and heat transfer characteristics inside a square double-lid driven enclosure have been investigated in this study. A heat-generating solid square block is positioned at the centre of the enclosure. Both of its vertical walls are lid-driven and have temperature Tc and uniform velocity V0 . In addition, the top and bottom surfaces are kept adiabatic. Discretization of governing equations is achieved using finite element technique based on Galerkin weighted residuals. The computation is carried out for a wide range of pertinent parameters such as Hartmann number, heat-generating parameter, and Richardson number. Numerical results are reported for the effects of aforesaid parameters on the streamline and isotherm contours. In addition, the heat transfer rate in terms of the average Nusselt number and temperature of the fluid as well as block center are presented for the mentioned parametric values. The obtained results show that the flow and thermal fields are influenced by the above-mentioned parameters.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the problem

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Figure 2

Effect of grid refinement test on average Nusselt number Nu, while Q = 1, Ri = 1, and Ha = 10

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Figure 3

(a) Streamlines and (b) isotherms for different values of Hartmann number (Ha) and Richardson number (Ri), while Q = 1

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Figure 4

Effect of Ha on (a) average Nusselt number Nu, (b) average fluid temperature θav , and (c) temperature θc at the block center, while Q = 1

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Figure 5

Optimum condition of average heat transfer for Hartmann number Ha, while Q = 1

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Figure 6

(a) Streamlines and (b) isotherms for different values of heat-generation parameter Q and Richardson number Ri, while Ha = 10

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Figure 7

Effect of Q on (a) average Nusselt number, (b) average fluid temperature, and (c) temperature at the cylinder center, while Ha = 10

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Figure 8

Optimum condition of average heat transfer for heat-generation parameter Q, while Ha = 10.0

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