The Flow of a Variable Viscosity Fluid down an Inclined Plane with a Free Surface

Author:

Tshehla M. S.1ORCID

Affiliation:

1. Department of Mathematics, Faculty of Military Science, University of Stellenbosch, Private Bag X2, Saldanha 7395, South Africa

Abstract

The effect of a temperature dependent variable viscosity fluid flow down an inclined plane with a free surface is investigated. The fluid film is thin, so that lubrication approximation may be applied. Convective heating effects are included, and the fluid viscosity decreases exponentially with temperature. In general, the flow equations resulting from the variable viscosity model must be solved numerically. However, when the viscosity variation is small, then an asymptotic approximation is possible. The full solutions for the temperature and velocity profiles are derived using the Runge-Kutta numerical method. The flow controlling parameters such as the nondimensional viscosity variation parameter, the Biot and the Brinkman numbers, are found to have a profound effect on the resulting flow profiles.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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