Eur. Phys. J. Spec. Top. (2022) 231: 2837-2849
https://doi.org/10.1140/epjs/s11734-022-00596-5

Regular Article

CBS-FEM algorithm for mixed convection of irregular-shaped porous lid-driven cavity utilizing thermal non-equilibrium medium

¹ Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia
² Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

^a sehassan@kku.edu.sa

Received: 8 October 2021
Accepted: 3 May 2022
Published online: 17 May 2022

Abstract

This contribution examines a highly forced convection situation due to the movements of two adjacent wavy and straight walls of two-sided wavy enclosures. An adiabatic obstacle is located within the domain and the top boundary is partially heated. The included porous medium is assumed to be radiant and the two-energy equations system is applied for this proposed. An inclined magnetic force together with heat generation sources is inclusive in the flow area. The governing equations have been solved utilizing the characteristic-based split algorithm under the spirit of finite-element method. Numerical outcomes for the flow and heat transfer for the fluid and solid phases are determined for miscellaneous combinations of the physical factors. Graphical and tabular findings pointing out interesting features of the physics of the problem are presented and discussed. The forced convection mode is dominant at higher values of the undulation parameter $\lambda$ and low values of $\mathrm{the}\mathrm{Hartmann}\mathrm{number}$ Ha. Also, the radiative porous medium reduces the Nusselt coefficient for the solid phase. Furthermore, the rate of the heat transfer is reduced by 80% when the values of the Darcy coefficient are decreased from ${10}^{-2}$ to ${10}^{-5}$.