Numerical Analysis on MHD Natural Convection within Trapezoidal Cavity Having Circular Block

Muhammad Sajjad Hossain^1, , M. A. Alim² and Kazi H Kabir³

¹Department of Arts and Sciences, Ahsanullah University of Science & Technology (AUST), Dhaka-1208, Bangladesh

²Department of Mathematics, Bangladesh University of Engineering & Technology (BUET), Dhaka-1000, Bangladesh

³Department of Mathematics, Mohammadpur Kendriya College, Dhaka, Bangladesh

Cite this paper

Muhammad Sajjad Hossain, M. A. Alim and Kazi H Kabir. Numerical Analysis on MHD Natural Convection within Trapezoidal Cavity Having Circular Block. American Journal of Applied Mathematics and Statistics. 2016; 4(5):161-168. doi: 10.12691/AJAMS-4-5-4

Abstract

In this paper, we have studied MHD natural convection within trapezoidal cavity having circular block with uniformly heated bottom wall with inclination angles (ф). To investigate the effects of uniform heating with the circular block a Galerkin finite element method is studied and also used for solving the Navier-Stokes equations for different angles Φs. Here left and right walls are considered as cold and upper wall is considered as thermal insulated in a trapezoidal cavities. Rayleigh number (Ra) from 10³ to 10⁵, Hartmann number (Ha = 20) and Prandtl number (Pr) from 0.026 to 0.7 with various tilt angles Ф = 45⁰, 30⁰ and 0⁰ (square) are concerned with the fluid. By different sets of governing equations along with the corresponding boundary conditions are used to set the physical problems. Results are shown in terms of streamlines, isotherms, heat flux and heat transfer rates for different Ra and Pr. It is seen that for different angles Φs conduction dominant region changes for different Pr when Ra increases. Local and average nusselt numbers are also used for heat transfer analysis for different irrespective Φs.

Keywords

MHD, natural convection, Galerkin finite element method, trapezoidal cavity, uniform heating, circular block

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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