FEM analysis of the impact of surface undulations on the natural convective flow of viscous fluid in a permeable trapezoidal enclosure

Examination of the transport mechanism in a permeable trapezoidal enclosure with an undulation effect is commenced. A formulation describing naturally convective flow in a permeable domain is conceded by employing Boussinesq and Darcy approximations. Uniform temperature is provided at the circular cylinder and base wall of the enclosure, whereas non-parallel side extremities are kept cold. No heat flux condition is applied at a wavy surface (upper) to maintain the potential difference in temperature for generation of convection. A finite element scheme is opted to resolve the governing system for accounted physical problems. The grid sensitivity test is also executed to assure the credibility of the code and results. A wide range of physical parameters is selected to comprehend their impact on streamlines and isotherm patterns. Results are revealed comparatively for zero undulation (upper solid straight wall) and with undulations (wavy wall). Heat flux and kinetic energy are also enumerated as key quantities against concerning parameters. It is depicted that the average Nusselt number and kinetic energy are more in the absence of undulations than when it is present. Additionally, it is manifested that the placement of a heated cylinder helps transfer heat in the domain and the production of thermal convective potential.