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Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium

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Abstract

A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical properties (ρ, μ and c p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and mixed convection. Temperature and velocity profiles are also presented.

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Abbreviations

a :

Amplitude

c p :

Specific heat under constant pressure

d :

Half wavelength

g :

Gravitational acceleration

k :

Thermal conductivity

K b :

Mean bulk modulus of water

K :

Porous medium permeability

p :

Pressure

s :

Salinity

T :

Temperature

u :

Vertical velocity

v :

Horizontal velocity

V :

Specific volume of water

x :

Vertical coordinate

y :

Horizontal coordinate

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Density

τ :

Shear stress

∞:

Ambient

m:

Mean

w:

Wall

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  1. School of Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    Asterios Pantokratoras

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  1. Asterios Pantokratoras
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Pantokratoras, A. Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium. Transp Porous Med 76, 309–325 (2009). https://doi.org/10.1007/s11242-008-9248-2

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