Mixed convection above a rotating disk

TL;DR

This paper investigates mixed convection flow above a rotating heated disk, presenting steady similarity solutions, analyzing parameter effects, and revealing multiple solutions and critical conditions for flow stability.

Contribution

It provides new steady similarity solutions for mixed convection above a rotating disk with quadratic heating, including analysis of multiple solutions and flow stability limits.

Findings

Multiple solutions exist at fixed Grashof number for finite Prandtl number.

Steady similarity solutions break down beyond a critical Grashand number.

Asymptotic analyses confirm behavior in small and large Prandtl number limits.

Abstract

Mixed convection above a horizontal disk rotating in a semi-infinite fluid is examined when the disk is heated so that its temperature varies quadratically with distance away from its centre. Steady similarity solutions are presented for a range of values of the two dimensionless parameters, a Prandtl number and a Grashof number. The results are corroborated by asymptotic analyses undertaken in the limits of small and large Prandtl number. For finite Prandtl number, the existence of multiple solutions at fixed Grashof number is revealed. The similarity structure for steady solutions fails beyond a critical Grashof number and this is interpreted in terms of a finite-time singularity of the unsteady form of the governing equations.