Discretization of Thermofluidic Behavior of the Combined Effects of MHD Conjugate Mixed Convection and Joule Heating in a Lid‐Driven Z‐Shaped Cavity Containing Double Rotating Cylinders

ABSTRACT The present numerical study focuses on investigating the effects of magnetohydrodynamic mixed convection and Joule heating in a lid‐driven Z‐shaped cavity containing double rotating cylinders in a comprehensive manner. An ample range of practical applications, including nuclear reactor cooling, magnetically controlled solar collectors, metallurgical processes, and electronic device cooling, makes it a captivating field of research. The current study considers a Z‐shaped cavity that has a hot wall at the lower portion of the cavity and a cold wall at the top, which is a moving lid, and other walls are kept adiabatic. It comprises two rotating circular cylinders that can rotate in both clockwise (CW) and counterclockwise directions. The Galerkin finite element method‐based computational process is utilized to resolve two‐dimensional steady continuity, momentum, and energy equations under specified boundary conditions. Both quantitative and qualitative outcomes are assessed to predict the fluid flow and thermal behavior for a limited range of some pertinent parameters: Hartmann number ( Ha = 20, 30, and 40), rotational Reynolds number ( Re c = −10 and 10), heat generation coefficient (∆ = 0, 2, and 5), Grashof number (10³ ≤ Gr ≤ 10⁶), and Reynolds number (100 < Re < 700). Results reveal a maximum 40% and 45% reduction in the Nusselt number occurring for enhancing the magnetic effect and heat generation coefficient, respectively. Moreover, CW rotation of the cylinders or aiding flow facilitates over 38% elevation in the Nusselt number by improving overall flow circulation in the cavity. Increasing the fluid Reynolds number leads to a 150% augmentation in the Nusselt number due to intensified turbulent flow. Hence, the comparative results of this meticulous numerical study, blended with novel geometrical contour, can be utilized to improve the thermal efficiency of other intricate systems.