eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2016-10-28 4 5 161 168 10.12691/ajams-4-5-4 AJAMS2016454 article Muhammad Sajjad Hossain msh80_edu@yahoo.com 1 M. A. Alim 2 Kazi H Kabir 3 Department of Arts and Sciences, Ahsanullah University of Science & Technology (AUST), Dhaka-1208, Bangladesh Department of Mathematics, Bangladesh University of Engineering & Technology (BUET), Dhaka-1000, Bangladesh Department of Mathematics, Mohammadpur Kendriya College, Dhaka, Bangladesh 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. http://pubs.sciepub.com/ajams/4/5/4/ajams-4-5-4.pdf MHD natural convection Galerkin finite element method trapezoidal cavity uniform heating circular block