Pr > 1 unsteady thermal flows and heat transfer in a finned cavity with a uniform heat flux

Unsteady thermal flows in a differentially heated cavity with a fin on the sidewall are extensively present in industrial systems. In this study, Pr > 1 unsteady thermal flows in a finned cavity with a uniform heat flux are investigated using scaling analysis and numerical simulation. The dynamics and heat transfer of unsteady thermal flows on the finned sidewall are analyzed. The scaling analysis indicates that there are four flow scenarios for the intrusion but three for the starting plume around a fin, depending on the Rayleigh number and the Prandtl number. In a typical scenario, the intrusion can move under an unsteady viscous conduction regime, an unsteady inertial conduction regime, an unsteady inertial convection regime, a steady inertial convection regime, a steady inertial conduction regime or a steady viscous conduction regime, but the starting plume can ascend under an unsteady and a steady inertial conduction regime or under a steady viscous conduction regime. Additionally, the scaling laws of the intrusion and the starting plume under different regimes are presented and verified by numerical results. There is good agreement between numerical results and the scaling predictions.