Robust finite difference scheme for the magnetohydrodynamics natural convection in a quadrant-shaped enclosure with radiation effect

Venkatadri, K; Saravana, R; Anwar Bég, O; Kuharat, S; Leonard, H J

Abstract

Modern hybrid fuel cells and electromagnetic batch processes feature many complex nonlinear phenomena that can be investigated using advanced numerical methods. Motivated by these applications, the main focus of the present study is to examine the hydromagnetic laminar natural convection in a quadrant-shaped enclosure containing an electrically conducting liquid. The horizontal straight boundary is thermally insulated; the right wall is hot, while the curved boundary is cold. Rosseland's radiative diffusion flux model is deployed. A vorticity-stream finite difference approach was adopted to obtain a numerical solution for the dimensionless nonlinear transport equations. A comprehensive parametric analysis of the impact of Hartmann magnetic number, Rosseland-Boltzmann radiative parameter, and Rayleigh (natural convection) number on streamline and isotherm contour distributions in the enclosure is conducted. With increasing radiative parameters, the vortex cell structure becomes more homogenous and contracts from an elliptical to a circulator configuration, and isotherms are intensified at the upper and vertical boundaries. More homogenous heat distributions are produced deeper into the enclosure from the curved wall. A noticeable improvement in Nusselt number is generated along the hot boundary with increasing Rayleigh number and radiative parameter whereas significant depletion is computed with greater Hartmann number.

• Journal Article Type: Article
• Acceptance Date: Jul 27, 2024
• Deposit Date: Jul 28, 2024
• Print ISSN: 2190-5444
• Electronic ISSN: 2190-5444
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Keywords: Quadrant enclosure; Hydromagnetics; Stream function-velocity formulation; Natural convection, curved boundary; Finite difference method (FDM); radiative heat transfer; Rayleigh number; fuel cells