Abstract
In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.
Highlights
Introduction and Literature Review1.1 IntroductionA vertically stacked system of porous and fluid layers.1 with heat and mass transfer taking place through the interface.1 is related to many natural phenomena and various industrial applications
From this figure we can see that for the thickness ratio d = 0.50 the flow is limited to the liquid layer only
For the buoyancy convection case, it has been found that the switching of the flow from fluid layer don1inated to porous layer dominated convection depends upon the thickness ratio, aspect ratio, Prandtl number and Rayleigh number of the liquid
Summary
Velocity component in the x direction u Non-di1nensional velocity cmnponent in the X direction = _!!__ Uo Characteristic velocity =-Jg. f3r· 11T. L. Velocity con1ponent in the y direction v Non-di1nensional velocity co1nponent in the Y direction = ~ Uo. So1uta1Ray1e1.gh number 1c.0r porous 1ayer= .g.:.::f:3::c..../.1..C:~-.-d---2-=.=K--. Therma1Ray1et.gh number 1c.0r porous 1ayer= g .f3r .11T.d2. Sr f3c Solutal expansion fJr Thennal volume expansion y
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