Mixed Convective Heat Transfer Analysis by Heatlines on a Lid-Driven Cavity Having Heated Wavy Wall Containing Tilted Square Obstacle

Abstract

The current problem studies the mixed convective heat transport by heatlines in lid-driven cavity having wavy heated walls with two diamond-shaped obstacles. The left and right vertical walls are both cold, whereas the top wall is adiabatic, and the bottom wavy wall is heated. The relevant governing equation has been calculated through using the finite element method as well as the Galerkin weighted residual approach. The implications of the Reynolds number $\left(10\le \mathrm{R}\mathrm{e}\le 500\right)$ , Richardson number $\left(0.01\le \mathrm{R}\mathrm{i}\le 10\right)$ , Hartman number $\left(0\le \mathrm{H}\mathrm{a}\le 100\right)$ , Prandtl number $\left(0.015\le \mathrm{P}\mathrm{r}\le 10\right)$ , Undulations number $\left(1\le N\le 4\right)$ , and inner diamond shape obstacle are depicted by the streamlines, isotherms, and the heatlines. The convection heat transfer is observed to be fully developed at a high Prandtl number, whereas heat conduction happens at poor Pr. In particular, the undulations number has the greatest effect on the streamlines and isotherm contrast to a flat area. The Nusselt numbers increase as the Reynolds and Prandtl numbers rise as well. The isotherm, streamlines, heatlines, Nusselt number, and fluid flow are shown graphically for several relevant dimensionless parameters. The result demonstrates that a single oscillation of a heated wall with such a poor Richardson number is optimal heat transport in the cavity. The presence of undulations minimizes the cavity area; the case N = 3 makes quicker fluid motions and better heat transfer in the present research. Additionally, the interior obstacle size reduces the amount of space it takes up within the wavy cavity, and it was observed that the obstacle with diamond size D = 0.15 is better than that with any other size.