Influence of Prandtl Number on Buoyancy Driven Flow Between Vertical Parallel Plates

Abstract

The Nusselt number and Reynolds number of buoyancy driven flow between vertical parallel plates have been determined for Rayleigh numbers from 0.1 to 10 6 and Prandtl numbers from 0.007 to 700. Results are obtained using finite element simulations for a two dimensional channel including an upstream volume, and constant pressure boundary conditions are applied at inlet and outlet. The investigation is restricted to the thermal boundary condition of uniform wall heat flux. The flow is assumed laminar which means that combinations of large Rayleigh numbers and small Prandtl numbers are not included. It is found that the heat transfer for a wide range of Rayleigh numbers is larger than for a single vertical plate. There is thus a Rayleigh number that provides maximum heat transfer. This Rayleigh number depends on the Prandtl number, and the ratio of the channel Nusselt number at maximum heat transfer to the single plate Nusselt number also depends on the Prandtl number. The Reynolds number is a function of Rayleigh number, Prandtl number, and channel aspect ratio H/S.