Role of internal heat generation, magnetism and Joule heating on entropy generation and mixed convective flow in a square domain

Abstract

This study has computationally inspected the role of internal heat generation, magnetism, and Joule heating on mixed convective flow and entropy generation in an air-filled square domain. The right cold wall of the differentially heated domain is sliding in its plane at a fixed speed, giving rise to two distinct flow configurations: aiding and opposing flows based on the direction of the sliding wall. In addition, a uniform magnetic field is applied horizontally parallel to the domain with the facility of Joule heating and volumetric heat generation. The fluid flow and the heat transfer within the square domain are formulated by continuity, momentum, and heat energy conservation equations, which are solved using the Galerkin finite element method after imposing appropriate boundary conditions. Numerical simulations are carried out under five distinct cases over a specific range of Reynolds number (31.623 ≤ Re ≤ 316.23), Grashof number (103 ≤ Gr ≤ 105), Richardson number (0.1 ≤ Ri ≤ 10) for mixed convective laminar flow consideration, Hartmann number (0 ≤ Ha ≤ 17.783), and Stuart number (0 ≤ N ≤ 3.162) for the variation of the strength of the uniform magnetic field under Joule heating, and volumetric heat generation coefficient (0 ≤ Δ ≤ 2) for internal thermal generation. The detailed quantitative results incorporate both the thermal and mechanical performances of the system, leading to several important conclusions outlined in their respective cases. It is found that increasing both Re and Ha or increasing Re and decreasing N with fixed Gr lead to higher heat transfer and reduction of the average fluid temperature inside the domain with less experienced drag and higher total entropy generation. Meanwhile, pure mixed convection exhibits higher heat transfer with increasing Gr, particularly when no internal heat is generated.