Analysis of heat transfer in a parallelogram-shaped cavity with porous medium under non-uniform temperature

Abstract

This study investigates fluid flow and natural convection heat transfer in a parallelogram-shaped cavity with a porous medium under non-uniform temperature condition. The bottom wall is heated with a non-uniform temperature, the side walls are cooled, and the upper wall is adiabatic. The governing equations, along with corresponding boundary conditions, are formulated in dimensionless stream function and vorticity using the extended Darcy model for the porous medium. The equations are solved by employing the finite difference method. The study presents outcomes for isotherms, streamlines, and Nusselt numbers across range of parameters, including the Rayleigh number (104≤Ra≤108), Darcy number (10−1≤Da≤10−6), Prandtl numbers (Pr=0.71,1,7.1), fluid porosity (ϵ=0.8), and inclination angles (30∘≤ϕ≤90∘), about flow and heat transfer characteristics. The results indicate that an increase in Ra, Pr, and ϕ, along with a decrease in Da, leads to an enhancement in the strength of vortexes. It is observed that for constant Ra⁎=RaDa, Rate of heat transfer increases with an increase in Ra and a decrease in Da. The maximum value observed is 10.15. Also rate of Heat transfer increases with the increase in angle and maximum rate of heat transfer is observed at ϕ=90∘.

Keywords

• Natural convection
• Non-uniform temperature
• Porous medium
• Parallelogram enclosure
• Inclined angle
• Extended Darcy model