Numerical Simulation of Thermal Newtonian Fluid Flow Driven by Horizontal Convection in A Porous Cavity

Abstract Horizontal convection is a distinct form of natural convection where flow is generated by uneven buoyancy along a horizontal boundary. This study presents a numerical simulation of horizontal convection within a porous rectangular cavity. The flow is driven by a non-uniform heating on the top surface, while the other boundaries are thermally insulated. We derive a governing equation involving four dimensionless parameters: the Darcy number, the Rayleigh number, the viscosity ratio, and the geometric aspect ratio. This equation is solved numerically through the finite difference method. Our investigation emphasizes how the Rayleigh number and viscosity ratio influence the flow of the thermal fluid. The results show that viscosity inhibits convection, thereby weakening the thermal boundary layer.