Numerical investigation of mixed convection and entropy generation in a wavy-walled cavity filled with nanofluid and involving a rotating cylinder

This numerical study considers the mixed convection and the inherent entropy generated in Al₂O₃-water nanofluid filling a cavity containing a rotating conductive cylinder. The vertical walls of the cavity are wavy and are cooled isothermally. The horizontal walls are thermally insulated, except for a heat source segment located at the bottom wall. The dimensionless governing equations subject to the selected boundary conditions are solved numerically using the Galerkin finite-element method. The study is accomplished by inspecting different ranges of the physical and geometrical parameters, namely, the Rayleigh number (10³ ≤ Ra ≤ 10⁶ ), angular rotational velocity (0 ≤ Ω ≤ 750), number of undulations (0 ≤ N ≤ 4), volume fraction of Al₂O₃ nanoparticles (0 ≤ ϕ ≤ 0.04), and the length of the heat source (0.2 ≤ H ≤ 0.8). The results show that the rotation of the cylinder boosts the rate of heat exchange when the Rayleigh number is less than 5 × 10⁵. The number of undulations affects the average Nusselt number for a still cylinder. The rate of heat exchange increases with the volume fraction of the Al₂O₃ nanoparticles and the length of the heater segment.