Numerical Analysis of Conjugate Mixed Convection Heat Transfer with Internal Heat Generation in a Wavy-Walled Lid-Driven Trapezoidal Cavity

This study undertakes a numerical examination of conjugate mixed convection heat transfer in a wavy-walled, lid-driven trapezoidal cavity, utilizing the Galerkin finite element method to resolve the continuity, momentum, and energy equations. Motivated by the need to enhance thermal management in complex systems, the objective is to elucidate the interactions between internal heat generation and cavity wall geometry under varying convective conditions. The research identifies a gap in understanding the precise effects of wavy walls on heat transfer and fluid flow dynamics in such configurations. Computational results reveal that wavy walls significantly amplify heat transfer by increasing the effective surface area and inducing secondary vortices, which improve convective mixing. The transition between forced and natural convection is governed by the Richardson number (Ri), with lower Ri promoting forced convection that effectively disperses heat, while higher Ri leads to buoyancy-dominated, stratified temperature fields. At low Ri, forced convection is dominant, resulting in strong circulation and uniform temperature distributions. As Ri increases, the flow becomes a mix of forced and natural convection at moderate Ri, and predominantly natural convection at high Ri, characterized by stratified flows and significant temperature gradients due to the enhanced mixing effects of the wavy walls. Isotherm analysis under these varying conditions indicates that while low Ri maintains uniform temperature distributions across the cavity, high Ri results in distinctly stratified temperature fields, pointing to the need for optimized cavity designs to manage such variations effectively. Additionally, machine learning-based polynomial regression models integrated later in the study accurately predict critical thermal parameters such as the Nusselt number, drag coefficient, and average temperature, aligning closely with the numerical simulations. These computational insights underscore the efficacy of combining advanced numerical methods and machine learning to optimize thermal systems for critical applications in electronic cooling, energy storage, and heat exchangers.The successful integration of these approaches highlights a significant advancement in the predictive modeling of thermal phenomena in complex geometries.