# Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

M. M. Rahman, J. H. Merkin*, I. Pop

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

## Abstract

The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. $${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether $${m > \frac{1}{5}}$$m>15 or $${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For$${0 <m <\frac{1}{5}}$$0 \frac{1}{5}}$$m>15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m  \frac{1}{5}}m>15.

Original language English 2441-2460 20 Acta Mechanica 226 8 https://doi.org/10.1007/s00707-015-1334-2 Published - Mar 20 2015

## ASJC Scopus subject areas

• Mechanical Engineering
• Computational Mechanics