Heat transfer characteristics of mixed convection inside a differentially heated square cavity containing an oscillating porous cylinder

The current study presents mixed convective flow inside a square chamber holding a centrally placed and thermally conductive oscillating porous circular cylinder. The left boundary's temperature is kept larger than that of the right edge, and the horizontal edges are preserved at adiabatic settings. The circumferential speed of the cylinder is sinusoidal and oscillating in nature. The fluid region within the chamber is modeled employing 2D Navier-Stokes and heat energy equations. Furthermore, the fluid circulation and heat transmission within the porous cylinder are modeled using the Darcy-Brinkman-Forchheimer formulation. The leading equations are discretized utilizing the Galerkin finite element technique. The parametric study is undertaken considering three distinct diameters of the porous cylinder and three distinct oscillation frequencies. The instant Nusselt number is evaluated along the heated wall, which varies in an oscillatory pattern owing to the repeated contraction and enlargement of the thermal boundary layer. The Nusselt number is averaged over time once the value becomes statistically stationary. The study is conducted within a mixed convection region with Reynolds (Re = 100), Richardson (0.1 ≤ Ri ≤ 10), and Grashof (10³ ≤ Gr ≤ 10⁵) numbers. Upon thorough examination, it becomes clear that the system's thermal performance shows promising improvement with the largest cylinder diameter and the lowest oscillation frequency. Specifically, the average Nusselt number shows a maximum improvement of 21.50 % at the largest cylinder diameter.