Transient flows on an evenly heated wall with a fin

Transient natural convection flows on an evenly heated wall with a fin are common in industrial systems. In this paper, transient flows around the fin are investigated using scaling analysis and numerical simulation. The dynamics and heat transfer of transient flows are discussed. The scaling analysis shows that there are four flow scenarios for the intrusion but three for the plume bypassing the fin, which are dependent on the Rayleigh number and the Prandtl number. In a typical flow scenario, the intrusion could travel under different regimes such as 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 could ascend under an unsteady and a steady inertial conduction regime or under a steady viscous conduction regime. Further, the scaling laws of the intrusion and the plume under different regimes are obtained. Numerical simulation is employed to validate the scaling laws of the velocity and the thickness of transient flows. The scaling predictions are consistent with numerical results.