A study of unsteady mixed convection in porous corrugated enclosures with magnetic fields

In this study, we performed a numerical analysis of unsteady two-dimensional coupled natural and mixed convective flows in a porous corrugated geometry under the influence of magnetic field. A higher order compact (HOC) scheme is employed to discretize the nonlinear coupled transport equations. The outcomes of simulations are analyzed across a range of critical parameters, including the Darcy Number ($10^{-5}$ to $10^{-1}$), Reynolds Number ($100$ to $1000$), Grashof Number ($10^3$ to $10^6$), Richardson number ($0.1$ to $100$), Hartmann number ($25$ to $150$), and Prandtl Number ($0.015$ to $10.0$). Also, analyzing three distinct configurations based on the height of heat sources can provide valuable insights into their thermal performance and Nusselt number variations. The maximum augmentation of the mean Nusselt values on the thermal and non-thermal boundary surfaces in ascending and descending patterns at different critical parameters are viz. $Gr$ ($87.65\text{\%}$ & $81.12\text{\%}$), $Da$ ($217.16\text{\%}$ & $62.23\text{\%}$), $Ha$ ($510.30\text{\%}$ & $45.51\text{\%}$), $Re$ ($42.41\text{\%}$ & $36.13\text{\%}$), and $Pr$ ($474.38\text{\%}$ & $32.74\text{\%}$), for case 1, $Gr$ ($19.61\text{\%}$ & $598.34\text{\%}$), $Da$ ($18.10\text{\%}$ & $66.56\text{\%}$), $Ha$ ($79.62\text{\%}$ & $49.97\text{\%}$), $Re$ ($41.53\text{\%}$ & $0.0\text{\%}$), and $Pr$ ($442.10\text{\%}$ & $29.70\text{\%}$), for case 2, $Gr$ ($323.78\text{\%}$ & $0.0\text{\%}$), $Da$ ($08.54\text{\%}$ & $53.27\text{\%}$), $Ha$ ($97.22\text{\%}$ & $37.92\text{\%}$), $Re$ ($88.43\text{\%}$ & $52.31\text{\%}$), and $Pr$ ($739.15\text{\%}$ & $19.77\text{\%}$), for case 3. The influence of the permeability of the porous medium is prominently observed across various combinations of the considered parameters, resulting in diverse flow patterns.