Effect of thermal conductivity of porous media on thermo-fluid fields of free convective flow around a circular cylinder inside a square cavity

A steady two-dimensional laminar natural convective heat transfer from a hot inner circular cylinder located in a square cavity filled with air mixed by saturated porous medium has been numerically analyzed to investigate the effect of porous media thermal conductivity on the flow and heat transfer characteristics. The study has been presented at a constant radius ratio of 3.5. The bottom wall of the enclosure is insulated, while the other walls are maintained at constant cold temperature. The governing equations and boundary conditions were converted to dimensionless form and solved numerically employing the nodal-based spectral-element method. The computational domain was commonly subdivided roughly into a series of 448 discrete macro-elements. Prandtle number and Darcy number in this study are 0.71 and 0.01, respectively. The study has covered three values of Grashof number, which are 5 × 106, 107, 5 × 107 to ensure that the flow is laminar and justify the steady-state condition. Also, the material porosity (𝜀) in the present study is 1.0, and the values of the solid to the fluid thermal conductivity ratio (𝑘𝑟) are 0.1, 0.5, 1.0, 2.5, 5, 7.5, and 10. No-slip boundary conditions are held along both the inner and the outer walls. The results are presented by streamlines, isotherms, mean Nusselt numbers, velocity development, and temperature development for different parameters of the thermal conductivity ratio, and Grashof number. It is found that increasing the thermal conductivity of fluid at the expense of thermal conductivity of porous material gives strong convection currents on the top of cylinder towards the upper region of cavity and a strong conduction heat transfer at the other regions of enclosure.