Numerical study of magnetohydrodynamic mixed convection in a lid-driven wavy top cavity containing two circular cylinders

Abstract

The problem of mixed convection and heat transfer in presence of magnetic field in a Lid-driven wavy top cavity containing two circular cylinders, two cases have been considered: (I) Variation of cylinders position vertically keeping size (radius, r) of the cylinders as a constant and (II) Variation of cylinders size (radius, r) keeping cylinders position at CP1 (0.1, 0.4) and CP2 (0.6, 0.4) as a constant. The bottom wall is kept at a constant hot temperature Th and the wavy top wall is kept at a constant cold temperature Tc maintaining Th > Tc, while the other wallsare assumed to be adiabatic or insulated. The left wall and wavy top walls have a lid velocity where left wall moves from lower to upper and the wavy top wall moves from left to right with constant velocity. The gravitational force acts in the vertically downward direction and uniform magnetic field with a constant magnitude(B_0) is applied parallel to the x-axis. The cavity is filled with fluid with Pr = 0.71 that is considered Newtonian and incompressible where the fluid flow is assumed to be laminar. The physical problems have been represented mathematically by different sets of governing equations along with the corresponding boundary conditions.The nondimensional governing equations are discretized by using Galerkin weighted residual method of finite element formulation. The numerical results have been reported for the effect of Richardson numbers and magnetic field parameter, Hartmann numbers . Three positions (0.6, 0.4), (0.6, 0.55) and (0.6, 0.25) of the semi heated cylinder CP2 have been considered in case (I) where the size (radius, r) of the cylinders has maintained as a constant (r = 0.1 m). Besides, in case (II), the size (radius, r) of the semi heated cylinders has been altered from r = 0.10 to 0.20 m keeping cylinders position at CP1 (0.1, 0.4) and CP2 (0.6, 0.4) as a constant.The strength of the velocity magnitude has been improved for both cases with the increase of Richardson number. But the strength of the velocity magnitude has been declined improved for both cases with the increase of Hartmann number. The maximum average velocity magnitude (2.66 m/s) is found for CP1 at (0.1, 0.4) and CP2 at (0.6, 0.4) is found for Ri = 10, Pr = 0.71, Ha = 50and cylinder size, r = 0.20 m.Finally, the appreciable effects of heat transfer rate have been illustrated for the size variation of the semi heated cylinders compared to the position variation. The results indicate that the heat transfer rate increase with the increase of Richardson number and that, Hartmann number is a good control parameter for heat transfer in the flow. Comparisons with previously published work are performed and the results are found to be in excellent agreement.