Parametric studies of mixed convective fluid flow around cylinders of different cross-sections

A numerical study of mixed convective heat transfer in a lid-driven square enclosure containing a hot elliptic cylinder is conducted. The impacts of the Grashof number (103 <= Gr <= 106) $({10}<^>{3}\le {Gr}\le 1{0}<^>{6})$, Reynolds number (1.0 <= Re <= 100) $(1.0\le Re\le 100)$, cylinder tilt angle (0 degrees <=phi <= 90 degrees) $({0}<^>{<^>\circ }\le \phi \le {90}<^>{<^>\circ })$, and aspect ratio (1.0 <= AR <= 3.0) $(1.0\le AR\le 3.0)$ have been examined for a fluid of Pr $Pr$ of 0.71. The horizontal enclosure walls are insulated, while its vertical walls are restricted to a nonvarying temperature T-c,T- whereas a sinusoidal temperature of Th+ increment T sin(pi x/L) ${T}_{h}+\unicode{x02206}T\unicode{x0200A}\sin (\pi x/L)$ is imposed on the wall of the elliptical cylinder. The governing equations are solved using COMSOL Multiphysics 5.6 software. The fluid dynamic and the heat transport profiles between the enclosure and the elliptical cylinder walls are represented by the stream function, isothermal contours, and average Nusselt number. Results established that for all the considered aspect ratios, the thermal heating range of 103 <= Gr <= 104 ${10}<^>{3}\le {Gr}\le 1{0}<^>{4}$ is predominantly a conduction mechanism. The critical position of the ellipse where the inclination effect becomes insignificant is determined by the Grashof number and aspect ratio when the Re = 100. The strength of vortices and cell numbers are significantly influenced by the aspect ratio, particularly when the Gr=104 ${Gr}=1{0}<^>{4}$. When AR=1.0 $AR=1.0$, the average heat transfer from the cylinder remains the same regardless of the cylinder's orientation. The impact of cylinder orientation on heat transfer from the cylinder wall is minimal for 1.5 <= AR <= 2.0 $1.5\le AR\le \phantom{\rule{}{0ex}}2.0$. For AR values of 2.5 <= AR <= 3.0 $2.5\le AR\le \phantom{\rule{}{0ex}}3.0$, increasing the inclination angle does not result in improved heat transfer. The influence of the increasing inclination angle on the right wall diminishes as the angle increases, except when the Grashof number is greater than 10(5), where the rate of heat transfer is enhanced for inclination angles beyond 45 degrees.