Abstract

The gravity driven film flow down a heated inclined ramp and how it is affected by temperature dependent fluid properties is examined. The five temperature dependent fluid properties examined were: surface tension, mass density, dynamic viscosity, thermal conductivity and specific heat capacity. The investigation utilized a theoretical model based on the conservation of mass, momentum and energy, including the physically appropriate Newton's Law of Cooling to incorporate temperature changes on the surface of the film. A two-scale model of his system was also considered and a Benney equation was derived. A depth-integrated model was also considered and modified Integral Boundary layer (IBL) equations were generated. A linear stability analysis was carried out in all cases. Numberical simulations were carried out on the nonlinear modified IBL equations and their agreement to the linear approximations was good. The nonlinear analysis was also used to determine the evolution of the unstable flow.

Highlights

  • When a gravity-driven fluid film is heated, the variation in its surface tension with temperature can combine with the inertial effects of the flow to generate interfacial instability

  • The investigation will be carried out by implementing a theoretical model based on the conservation of mass, momentum and energy

  • Since we are testing the effects of temperature dependent fluid properties, we allow the properties of the fluid to vary with temperature as follows: ρ = ρ0[1− α (T − Ta )] σ = σ0 − γ(T − Ta )

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Summary

CHAPTER 1 - INTRODUCTION

The purpose of this thesis will be to examine how the flow of a thin fluid film down a heated inclined plane is affected by temperature dependent fluid properties. When a gravity-driven fluid film is heated, the variation in its surface tension with temperature can combine with the inertial effects of the flow to generate interfacial instability. This thesis will examine the combined effect of temperature variation in all the fluid properties. The investigation will be carried out by implementing a theoretical model based on the conservation of mass, momentum and energy. This model will exploit the assumed shallowness of the fluid layer, and will incorporate the physically appropriate temperature dependence of the fluid properties. The nonlinear analysis will be used to determine the evolution of the unstable flow

History
Conservation Equations for the General Case with Variable Fluid Properties
The Form of the Temperature Variation of the Fluid Properties
The Boussinesq Approximation
Interface Conditions
Newton’s Law of Cooling
Scaling
The Full Equations of Motion With Temperature Dependent Properties
CHAPTER 3 – Linear Stability Analysis
Full Equations, Special Case with Bi=0
Full Equations, Special Case with λ=0 and Λ=0
Another Approach
Long Wave Expansions
16 Re xxx 16 Re
Comparisons and Discussion
Numerical Analysis
Re δ h3
Nonlinear Stability Analysis
Full Text
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