Mixed convection flow through a hot porous elliptic cylinder in a cavity with two-sided lid motion: A local radial basis functions-based meshless approach

This paper presents a numerical investigation of unsteady, two-dimensional, laminar mixed convection flow of an incompressible, Newtonian fluid within a cavity with two-sided lid motion and a hot porous elliptical cylinder inserted inside. The opposing lid-driven motions induce flow within the cavity, while the high-temperature cylinder affects the flow dynamics. Flow through the porous cylinder is characterized using the Brinkman and Forchheimer corrected Darcy model, which incorporates the effects of the porous medium. The simulation employs the local radial basis function (RBF) based meshless technique to model the flow across the cavity. The developed model is validated against previously reported findings from both experimental data and conventional CFD approaches, with good agreement. Computed results are analyzed for various cavity inclination angles and ellipse orientations across a range of key parameters including the Richardson number $(0.01\le Ri\le 100)$, Darcy number $(10^{-6}\le Da\le 10^{-2})$ and Prandtl numbers ($Pr=0.71$ for air and $Pr=6.9$ for water). To examine the impact of the chosen parameters, the results are presented in the form of streamlines, isotherms, velocity profiles, and plots of local and average Nusselt numbers. The numerical results suggest that, at a fixed Grashof number ($Gr$), an increase in Richardson number ($Ri$) decreases the average Nusselt number ($\overline{\text{Nu}}$), while an increase in Darcy number ($Da$) increases $\overline{\text{Nu}}$, with the cavity inclination angle having a minimal effect on the convection rate. Overall, the local RBF scheme demonstrates its robustness and suitability for simulations in complex geometries with curved internal boundaries in mixed convection problems.