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Influence of variable permeability on combined free and forced convection flow past a semi-infinite vertical plate in a saturated porous medium

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Abstract

Combined free and forced convection flow of viscous incompressible fluid past a semi-infinite vertical plate embedded in a porous medium incorporating the variation of permeability and thermal conductivity are studied. Similarity solutions are obtained, for two cases namely uniform permeability (UP) and variable permeability (VP). Velocity and temperature profiles are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tabular form. The effects of the parameters Gr/Re 2 (Gr – Grashof number, Re – the Reynolds number), α (coefficient of viscosity’s of the fluid and porous medium), σ (the Darcy number), σ* (ratio of thermal conductivity of the solid to the liquid), Pr (the Prandtl number) and E (the Eckert number) on the flow field are discussed.

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Abbreviations

C p :

Specific heat at constant pressure

d :

Constant defined in Eq. (8)

d*:

Constant defined in Eq. (8)

E :

Eckert number

f :

Nondimensionless stream function

g :

Acceleration due to gravity

Gr :

Grashof number

K(y):

Permeability of the porous medium

K 0 :

Permeability of the porous medium at the edge of the boundary layer

k :

Thermal conductivity

Re :

Reynolds number

T :

Temperature of the fluid near the plate

T w :

Temperature of the plate

T ∞ :

Ambient temperature

u, v :

Velocity components along x and y directions

U 0 :

Free stream velocity

x, y :

Coordinate axes along and perpendicular to the plate

α(y):

Thermal diffusivity

α*:

Ratio of viscosities

α0 :

Thermal diffusivity at the edge of the boundary layer

β:

Coefficient of volume expansion

ɛ(y):

Porosity of the saturated porous medium

ɛ0 :

Porosity of the saturated porous medium at the edge of the boundary layer

η:

Dimensionless similarity variable

θ:

Dimensionless temperature

μ:

Viscosity of porous medium

EquationSource% MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqiVd0Mbae % baaaa!37B7! \( \bar \mu \) :

Effective Viscosity of the fluid

ν:

Kinematics viscosity of the fluid

ψ:

Stream function

ρ:

Density of fluid

σ*:

Ratio of thermal conductivity of the solid to the liquid

σ:

Permeability parameter

τ′:

Skin friction

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, South Valley University

    A. A. Mohammadein & N. A. El-Shaer

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  1. A. A. Mohammadein
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  2. N. A. El-Shaer
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Correspondence to N. A. El-Shaer.

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Mohammadein, A.A., El-Shaer, N.A. Influence of variable permeability on combined free and forced convection flow past a semi-infinite vertical plate in a saturated porous medium. Heat and Mass Transfer 40, 341–346 (2004). https://doi.org/10.1007/s00231-003-0430-3

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