Abstract

<p>In the present study, the onset of thermal convection in a liquid layer overlying a porous layer in the presence of a free surface with evaporation is investigated. The Navier-Stokes equations are solved for the liquid layer, while the Brinkman model describes the porous layer. Two and three-dimensional geometrical models are considered, with bottom heating and lateral heating. Buoyancy convection, thermocapillary convection and combined convection are studied in detail for different aspect ratios. For the evaporation analysis, two conditions are treated simultaneously at the free surface. In the first, surface tension is assumed to vary linearly with temperature. In the second, a linear saturation temperature is imposed at the free surface to allow evaporation. Different aspect ratios, thickness ratios as well as Marangoni numbers are studied in detail. Results reveal the significant effect evaporation in the liquid layer has on convective flow patterns. </p>

Highlights

  • Darcy was the first to formulate the basic equation o f flow in porous media based on the proportionality between the flow rate and the applied pressure difference that was revealed from experiment [1], Conventionally, Darcy’s law was used as the momentum balance equation in a porous medium

  • For buoyancy convection with bottom heating, it has been confirmed that the flow switches from fluid layer dominated to porous layer dominated convection upon reaching a critical porous layer thickness value o f d2 = 0.9

  • For thermocapillary convection with bottom heating, it was confirmed that the critical porous layer thickness value is 0.96

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Summary

G Non-dimensional overall thermal conductivity

H Length o f cavity in horizontal X-direction hiv Latent heat o f vapourization i.

Introduction
Onset o f Convection in Liquid and Porous Cavity
Evaporation in Liquid
Research Objectives
Model Description
Liquid Layer Governing Equations
Momentum Balance Equation
Porous Layer Governing Equations
23.3 Energy Balance Equation
Non-Dimensional Analysis
Energy Balance Equation d^e a 'g d^e
Two Dimensional Modeling
Three Dimensional Modeling
Lateral Heating
Bottom Heating
CHAPTERS Conclusion
Full Text
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