MHD Free Convective Flow along with Internal Heat Generation and Joule Heating in a Two Layer Discretely Heated Chamber Partially Filled with Porous Medium

Abstract

This study introduces a novel approach by combining MHD with Joule heating, incorporating a partially porous layer and internal heat generation into the investigation of natural convective flow in a square chamber. It also considers a wavy-shaped porous-fluid layer interface to better represent real-world phenomena. The study evaluates the thermal performance of a discretely heated source with varying magnetic and heat generation effects. For simplification, other geometric constraints, such as porous layer thickness, inter-facial geometry, and heater configuration, are held constant. Numerical solutions are obtained by solving the governing equations for fluid and porous domains using the Galerkin finite element weighted residual method. The parametric variations in the study include Rayleigh numbers (103 ≤ Ra ≤ 107), Hartmann numbers (Ha = 0, 50, 100), and the heat generation coefficient (∆ = 0, 3).The results are quantitatively presented through Nusselt number along the heated strip and mean fluid temperature across the domain, complemented by qualitative visualizations of streamlines and isotherms. Upon analysis, it is evident that heat generation has a weaker impact at higher Rayleigh numbers. However, at lower Rayleigh numbers, a reduction in Nusselt number is observed, indicating that weaker convection may not effectively offset the generation rate as stronger convection does. Volumetric heat generation is expected to result in higher domain temperatures. Additionally, higher heat transfer is evident at higher Rayleigh numbers, regardless of Hartmann number variations.

Keywords: Magnetohydrodynamics; Free Convection; Internal Heat Generation; Joule Heating; Porous Medium