This study investigates the impact of momentum slip and thermal slip on magnetohydrodynamic (MHD) two-phase fluid flow in an inclined channel containing both porous and fluid regions. Analytical analysis and visualization of results are conducted to elucidate the complex interactions between various parameters affecting fluid flow and heat transfer. The research focuses on convective flow and heat transfer in an inclined channel bounded by two rigid plates held at constant different temperatures, with one region filled with a porous matrix saturated with a viscous fluid and another region with a clear viscous fluid. The coupled nonlinear governing equations are solved using the Finite Element Method. Results are presented for a wide range of governing parameters including the Grashof number, porous parameter γ, angle of inclination Ψ, ratio of heights, slip parameters, Nusselt number, skin friction of the two layers, and the ratio of viscosities. Key findings reveal Ψ influences velocity and temperature, with reduced significance for large γ values within porous regions. Slip parameters and porous geometry affect convective heat transfer and frictional drag, with elevated slip parameters correlating with diminished heat transfer efficiency and heightened skin friction. These findings offer valuable insights for optimizing various engineering systems and advancing the scientific understanding of convective heat transfer mechanisms in porous media.
Rai et al. (2026) studied this question.