MHD free convective flow and entropy production of glycerin in a square domain with Joule heating and internal heat generation

Abstract

This study inspects MHD free convective flow and entropy production inside a square domain (e.g., a nuclear reactor thermal cooling system) with Joule heating and internal heat generation. The left edge of the domain is set to a higher temperature than the right edge, and the top and bottom edges are insulated. The domain is filled with a heat-generating and electrically conducting fluid (glycerin) with fixed thermo-physical properties. This study has practical significance in many engineering applications, including nuclear reactor cooling systems, cooling electronics, designing solar thermal collectors, designing heat exchangers, etc. The primary objective of this study is to enhance heat transfer by examining optimal system characteristics. The Navier-Stokes and heat energy equations, which govern heat and fluid flow in the domain, are solved via the Galerkin finite element technique. Numerical simulation is performed over specific ranges of Rayleigh number (103 ≤ Ra ≤ 106), Joule heating parameter (0 ≤ J ≤ 7.31 × 10−9), Hartmann number (0 ≤ Ha ≤ 36.98), and volumetric heat generation coefficient (0 ≤ Δ ≤ 2) under laminar flow consideration. The parametric conditions for achieving the desired thermal performance can be controlled by determining the mean Nusselt number of the heated edge. Notably, heat transfer enhancement ensues with the simultaneous increment of Ra and Ha at a fixed Joule heating parameter. On the other hand, introducing internal heat generation reduces thermal performance inside the system, which has also been observed in terms of mean fluid temperature, total entropy production, and average Bejan number.