Investigation on the Conjugate Effect of Joule heating and Magnetic Field on Combined Convection in a Lid-driven Cavity with Undulated Bottom Surface

Abstract

Considering the Joule-heating effect on magneto-hydrodynamic mixed convection, the flow and heat transfer characteristics in a lid-driven cavity with a sinusoidal wavy bottom surface is analyzed numerically. The cavity vertical walls are well insulated while the wavy bottom surface is sustained at a uniform temperature higher than the top sliding lid. The governing equations along with appropriate boundary conditions are solved by the finite element method. The effects of Hartmann number (Ha), Joule heating parameter (J) and number of undulations (λ) on the flow structure and heat transfer characteristics are examined in detail while, Prandtl number (Pr), Rayleigh number (Ra) and Reynolds number (Re) are considered fixed. The average Nusselt number (Nu) at the heated surface and maximum temperature (θmax) of the fluid are also presented. The trend of the local heat transfer is found to follow a wavy pattern. The outcomes point out that the flow and temperature field are significantly dependent on the aforesaid parameters.