Effects of internal heat production and Joule heating on MHD conjugate mixed convection and entropy production inside a thermally non-homogeneous cooling system

Abstract

The current investigation explores MHD combined free-forced convection and entropy generation within a square enclosure (e.g., a nuclear reactor heat removal system) incorporating resistive heating and interior heat production. The cavity features a centrally positioned rotating cylinder, with the leftmost edge kept at a greater temperature than the rightmost boundary. The upper and lower boundaries of the enclosure are thermally insulated throughout the analysis. The solid cylinder rotates clockwise or counterclockwise, generating an aiding or opposing flow configuration. The Galerkin finite element approach solves the two-dimensional Navier-Strokes and thermal energy equations. Four different cases are analyzed through numerical simulations within predetermined ranges of Grashof (103 ≤ Gr ≤ 105), Reynolds (31.623 ≤ Re ≤ 316.23), and Richardson (0.1 ≤ Ri ≤ 10) numbers to analyze conjugate laminar mixed convective flow. Besides, Hartmann (0 ≤ Ha ≤ 17.783) and Stuart (0 ≤ N ≤ 3.162) numbers are varied to address the change in the magnetic field’s intensity considering resistive heating. Finally, the volumetric internal heat production factor (0 ≤ Δ ≤ 3) is considered to account for internal heat generation. This study’s comprehensive quantitative findings encompass the system’s thermal performance, leading to significant conclusions in their respective cases. It is observed that elevating Ri while decreasing Ha or increasing both Ri and N leads to enhanced heat transfer and a reduced average fluid temperature. In contrast, during pure mixed convective flow, Nu rises with simultaneous increments in Gr and Re and decreases in N. Conversely, internal heat production results in lower heat transfer and notable increases in entropy generation and thermal performance criterion. Significantly, during pure mixed convection (Ri = 1) with an aiding flow configuration, the introduction of internal heat generation results in a 36.47 % degradation in heat transport at constant Gr, Re, and N. However, under identical conditions (fixed Gr, Re, and N) and Δ = 0, the aiding flow exhibits 26.91 % better thermal performance than the opposing flow.