Optimization of system parameters during conjugate mixed convective flow in a square domain with an oscillating...

A computational analysis has been executed to analyze the combined conduction-mixed convection heat transfer of a rotationally oscillating solid cylinder in a differentially heated square box filled with air. The conjugate mixed convective flow initiates the heat transfer process, where the left-side boundary is isothermally kept to a higher temperature, and the right-side boundary is maintained at a lower temperature. Conduction heat transfer takes place inside the solid cylinder. Navier-Stokes and heat energy conservation equations model the system in the dimensionless pressure-velocity formulation. All these equations are solved via the Galerkin finite element approach. Three different combinations of Grashof (10³-10⁵), Reynolds (32-316), and Richardson (0.1-10) numbers are examined to systematically investigate the variations of governing parameters on instantaneous Nusselt numbers and the respective time-averaged values along the hot wall. In each combination, the impacts of the oscillating amplitude and frequency and the variation of cylinder diameter are examined to perform the optimization study. Power spectrum analysis is also done using the Fast Fourier Transform in the frequency domain to visualize the principal frequency of the system. The instantaneous values of the Nusselt number exhibit a wavering pattern over time owing to the recurrent waning and waxing of the thermal boundary layer. For all the cases, the maximum diameter and oscillating amplitude of the cylinder are found to maximize the heat transfer. However, the optimized frequency of the oscillation strongly depends on the selection of the governing parameters. In addition, the principal thermal frequency of the system is determined to be independent of the oscillation frequency.