On natural convection from a vertical plate with a prescribed surface heat flux in porous media |
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Authors: | S D Wright D B Ingham I Pop |
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Institution: | (1) Department of Applied Mathematical Studies, University of Leeds, LS2 9JT Leeds, UK;(2) Faculty of Mathematics, University of Cluj, R-3400 Cluj, Romania |
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Abstract: | This paper presents a theoretical and numerical investigation of the natural convection boundary-layer along a vertical surface, which is embedded in a porous medium, when the surface heat flux varies as (1 +x
2)), where is a constant andx is the distance along the surface. It is shown that for > -1/2 the solution develops from a similarity solution which is valid for small values ofx to one which is valid for large values ofx. However, when -1/2 no similarity solutions exist for large values ofx and it is found that there are two cases to consider, namely < -1/2 and = -1/2. The wall temperature and the velocity at large distances along the plate are determined for a range of values of .Notation
g
Gravitational acceleration
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k
Thermal conductivity of the saturated porous medium
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K
Permeability of the porous medium
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l
Typical streamwise length
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q
w
Uniform heat flux on the wall
- Ra
Rayleigh number, =gK(q
w
/k)l/(v)
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T
Temperature
- Too
Temperature far from the plate
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u, v
Components of seepage velocity in the x and y directions
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x, y
Cartesian coordinates
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Thermal diffusivity of the fluid saturated porous medium
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The coefficient of thermal expansion
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An undetermined constant
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Porosity of the porous medium
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Similarity variable, =y(1+x
)
/3/x
1/3
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A preassigned constant
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Kinematic viscosity
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Nondimensional temperature, =(T – T
)Ra1/3
k/qw
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Similarity variable, = =y(loge
x)1/3/x
2/3
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Similarity variable, =y/x
2/3
-
Stream function |
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Keywords: | natural convection boundary-layers surface heat flux |
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