Flows and heat transfer of the transition to an unsteady state in a finned cavity for different Prandtl numbers

Flows and heat transfer of the transition to an unsteady state in a finned cavity are studied for Prandtl numbers (Pr) from 0.1 to 100 and Rayleigh numbers (Ra) from 107 to 1010. Transient flows are described in the finned cavity. Critical Rayleigh numbers of the transition to an unsteady state are obtained for different Prandtl numbers and the relation between two dimensionless parameters is given. The spectral analysis is applied for the oscillations of unsteady flows and the dominant frequency dependent on governing parameters is presented. Heat transfer of the transition to an unsteady flow is quantified and the corresponding relations dependent on the Prandtl number and Rayleigh number are gained. It is demonstrated that the flow rate and the Nusselt number of the finned cavity significantly increase due to the presentence of the fin, which depend on the Prandtl number and the Rayleigh number.