Analytical and numerical study of MHD natural convection in a slender porous cavity due to lateral uniform heat flux: Effect of LTNE state

Abstract

In this work, the study of local thermal non-equilibrium (LTNE) state on magnetohydrodynamic (MHD) natural convection inside a radiative porous enclosure is investigated numerically as well as analytically. The motion of the flow is induced due to constant heat flux on side walls, while horizontal walls are insulated. A Darcy model to describe the two-dimensional flow governing equations has been adopted. These equations are solved numerically by using the Alternate Direction Implicit (ADI) method and analytically by implementing the parallel flow assumption valid for large aspect ratios. Boundary layer analysis is also carried out to describe the boundary layer thickness $\left(\delta x\sim 2^{1/2}{\left(\frac{R{a}_T}{1+DaH{a}^2}\right)}^{-1/5}\right)$ as well as the heat transfer rate $\left(N{u}_f\sim {\left(\frac{R{a}_T}{1+DaH{a}^2}\right)}^{2/5}\right)$ of the fluid phase. This study is carried out to get a better perspective of the LTNE state between fluid and solid phases inside the radiative porous medium. The influence of LTNE parameters ($H$ and $\gamma$), aspect ratio ($A$), Hartmann number ($Ha$), and radiation parameter $Rd$ on the flow dynamics and heat transfer mechanism are analyzed. From our numerical investigation, it is found that in the entire study, the flow structure is controlled by unicellular, and the average Nusselt number of the solid phase increases with the value of $Rd$. However, on increasing the value of $Rd$, the heat transfer rate of the fluid phase depends on the values of LTNE parameters. For increasing the value of $Rd$ from 1 to 10, the maximum reduction in the heat transfer rate of the fluid (solid) phase is reported to be up to 178% (7.31%) at 10 times enhancement in the electric field. For small values of $H$, the temperature distribution of the solid phase is found to be linear due to conduction mode only, whereas for relatively large values of $H$ it is nonlinear due to both convection and conduction modes.