MHD Mixed Convection with Joule Heating Effect in a Lid-Driven Cavity with a Heated Semi-Circular Source Using the Finite Element Technique

Abstract

A computational fluid dynamics simulation of heat transfer characteristics on the conjugate effect of Joule heating and magnetic field acting normal to the lid-driven cavity with a heated semi-circular source on one wall under constant temperature is investigated. The left wall of the cavity moves in an upward (case I) or downward (case II) direction, and buoyancy forces are also effective. Horizontal walls are adiabatic. The governing mass, momentum, and energy equations along with boundary conditions are expressed in a normalized primitive variables formulation. The finite element method is used in the solution of the normalized governing equations. The study is performed for pertinent parameters such as the Rayleigh number, Hartmann number, and Joule heating parameter. It is found that the average Nusselt number can be decreased with the increasing of the Rayleigh number in the presence of Joule effect. The magnetic field can be a good control parameter for heat transfer and fluid flow.