Numerical Analysis of Unsteady Natural Convection Flow and Heat Transfer in the Existence of Lorentz Force in Suddenly Expanded Cavity Using Open FOAM

Abstract

The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity. The Lorentz force based magnetohydrodynamics (MHD) solver using electric potential formulation coupled with the energy equation by the means of Boussinesq approximation is developed in the open-source CFD tool OpenFOAM. The unsteady flow is generated by the buoyancy force keeping the Rayleigh number (Ra) at 109, at the fixed Prandtl number (Pr) of 0.71. The effects of the magnetic field on the flow and heat transfer are explained for various orientations of magnetic field (Bx, B45, and By) in terms of Hartmann number (Ha=0, 50, 100, 300 and 500). The increase in the magnetic field increases the strength of the Lorentz force, which regulates the flow pattern and suppresses down the unsteady nature of flow and heat transfer into the steady-state. It is perceived that the average Nusselt number decreases as the intensity of Bx and B45 magnetic field increases. However, for By magnetic field the average Nusselt number increases up to Ha of 100 as compared to the non-MHD case (Ha=0). The distribution of Lorentz force in the domain plays a significant role in the governing of the fluid flow and heat transfer.