Magneto-convection in an anisotropic porous cavity due to nonuniform heat flux at bottom wall

Abstract

In the present article, a comprehensive numerical investigation of the magneto-convection in an electrically conducting isotropic, and hydro-dynamically as well as a thermally anisotropic porous cavity, is presented. The motion of the flow is due to the applied nonuniform heat flux on the bottom wall of the cavity and the insulation of other walls. The non-Darcy model has been adopted that includes Darcy and Brinkman terms in the momentum equations. The coupled governing equations are solved numerically by using the finite volume method (FVM). The impact of periodicity parameter (N), Hartmann number (Ha), and anisotropy parameters $(K^{*},\varphi , \mathrm{ }\text{and}\mathrm{ } k^{*})$ on the dynamics of flow as well as heat transfer rate have been investigated. From rigorous numerical experiments, it has been found that the structure of streamlines is unicellular except for the inner kernel in some situations. In general, the profile of local heat transfer rate possesses $(N-1)$ points of singularity for sinusoidal heat flux with periodicity parameter (N), and the profile of local Nusselt number is not symmetric for even values of N. The heat transfer rate is highly affected by a relatively large value of thermal conductivity ratio ($k^{*}$) as well as Ha, and the absolute difference between the maximum and minimum temperature of the system increases as a function of $k^{*}$ as well as Ha, whereas the strength of flow decreases gradually with increasing Ha.

Keywords:

• Anisotropic porous medium
• magneto-convection
• non-Darcy model
• nonuniform heating
• SIMPLER algorithm

Declaration of competing interest

We are certified that, this article has not been submitted in any other archive journal as well as conference. Financial support for this manuscript has been taken from the Ministry of Human Resource Development (MHRD) India.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

One of the authors, Harish Chandra, is grateful to M.H.R.D India for providing financial support (MHRD Grant No.: OH-31-23-200428) during the preparation of this manuscript.