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Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block
International Journal of Theoretical and Applied Mathematics
Volume 5, Issue 6, December 2019, Pages: 74-82
Received: Oct. 14, 2019; Accepted: Nov. 9, 2019; Published: Nov. 21, 2019
Authors
Md. Raihanul Haque, Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
Md. Abdul Alim, Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Md. Mahmud Alam, Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
Md. Shahidul Alam, Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
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Abstract
In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.
Keywords
Finite Element Method, Numerical Simulation, Natural Convection and Square Block, Rectangular Cavity
Md. Raihanul Haque, Md. Abdul Alim, Md. Mahmud Alam, Md. Shahidul Alam, Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 6, 2019, pp. 74-82. doi: 10.11648/j.ijtam.20190506.11
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