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.
Highlights
The study of the flow of a viscous fluid with temperature dependent properties is of great importance in industries such as food processing, coating, and polymer processing, see Macosko and Oron et al [1, 2]
This illustrates the relations between temperatures of the fluid with the Brinkman number. This is widely studied by several references, such as Myers et al [3] who studied the application in a closed channel and Makinde [15, 18, 19] who investigated the application with a free surface flow
When ∝ increases, the temperature of the fluid increases due to heat generation by the internal friction caused by the collision of the fluid particles
Summary
The study of the flow of a viscous fluid with temperature dependent properties is of great importance in industries such as food processing, coating, and polymer processing, see Macosko and Oron et al [1, 2]. External heating such as the ambient temperature and high shear rates can lead to a high temperature being generated within the fluid This may have a significant effect on the fluid properties. Elbashbeshy and Bazid [6] investigated the effect of temperature dependent viscosity on heat transfer over a moving surface. In their investigation, the fluid viscosity model varies as an inverse linear function of temperature. The present paper is aimed at investigating the effect of convective heat transfer on the flow of a viscous fluid with exponential temperature dependent viscosity, down an inclined plane with a free surface
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