Wave Instability of Natural Convection on Inclined Surfaces Accounting for Nonparallelism of the Basic Flow

Abstract

Neutral stability results for Prandtl numbers of 6.7 and 0.733 were obtained by solving disturbance equations that take account of the nonparallelism of the basic flow. Compared with the results for the conventional parallel-flow model, the neutral curves are shifted to higher Grashof numbers and higher wave numbers but maintain their characteristic shapes. The effect of varying the plate inclination from downward-facing to upward facing is to increase the susceptibility of the flow to instability. The critical Grashof numbers are substantially lower than the Grashof numbers of experiments where instability was due to natural disturbances.