Effect of Prandtl Number and Inclination Angle on MHD Natural Convection in Inclined Open Square Cavity
Issue: 2017 - Volume 14 [Issue 4]
Sheikh Anwar Hossain *
Ishwardi Government College, Pabna, Bangladesh
M. A. Alim
Department of Mathematics, BUET, Dhaka, Bangladesh
Satrajit Kumar Saha
Department of Mathematics, Jahangirnagar University, Savar, Dhaka, Bangladesh
*Author to whom correspondence should be addressed.
MHD natural convection and fluid flow in a two-dimensional open and inclined square cavity with a heated circular cylinder was considered in this work. The opposite wall to the opening side of the cavity was first kept to constant heat flux q, at the same time the surrounding fluid interacting with the aperture was maintained to an ambient temperature T¥. The top and bottom wall was kept to low and high temperature respectively. As a result a natural convection is formed in the cavity due to buoyancy force and temperature difference in the cavity. The governing equations for mass, momentum and energy conservation are expressed in a normalized primitive variables formulation. The streamlines and isotherms are produced, heat transfer parameter Nu are obtained for Prandtl number Pr = 0.72, 2, 5, 7 and inclination angles from 0°, 5°, 20°, 35°, 50° for fixed Hartmann number 60. The results are presented in graphical as well as tabular form. In the result it is found that heat flux is increasing function of Prandtl number Pr, while Rayleigh number is 10000 and heat flux is maximum when inclination angle is 5°. It is observed that fluid moves counterclockwise around the cylinder. Various recirculations are formed around the cylinder and one small vortex is formed into the flow field for 50° inclination and Pr = 0.72 near the cylinder. The almost all isotherm lines are concentrated at the right lower corner of the cavity. The present result agree with the existent heat transfer and boundary layer theory.
Keywords: MHD, finite element method, natural convection, open cavity