Meccanica

, Volume 47, Issue 4, pp 863–876 | Cite as

Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink

Article
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Abstract

The boundary layer flow and heat transfer of a fluid through a porous medium towards a stretching sheet in presence of heat generation or absorption is considered in this analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. These transformations are used to convert the partial differential equations corresponding to the momentum and the energy equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity decreases with increasing temperature-dependent fluid viscosity parameter up to the crossing-over point but increases after that point and the temperature decreases in this case. With the increase of permeability parameter of the porous medium the fluid velocity decreases but the temperature increases at a particular point of the sheet. Effects of Prandtl number on the velocity boundary layer and on the thermal boundary layer are studied and plotted.

Keywords

Scaling group of transformations Temperature-dependent fluid viscosity Porous medium Stretching sheet Heat generation/absorption 

Nomenclature

F

non-dimensional stream function.

F∗

variable.

F′

first order derivative with respect to η.

F′′

second order derivative with respect to η.

F′′′

third order derivative with respect to η.

k

permeability of the porous medium.

k1

permeability parameter.

Pr

Prandtl number.

Q0

dimensional heat generation/absorption coefficient.

p, q

variables.

T

temperature of the fluid.

Tw

temperature of the wall of the surface.

T∞

free-stream temperature.

u, v

components of velocity in x and y directions.

z

variable.

Greek symbols

α1, α2, α3, α4, α5, α6, α′, α′′

transformation parameters.

β′, β′′

transformation parameters.

η

similarity variable.

Γ

Lie-group transformations.

κ

the coefficient of thermal diffusivity.

λ

heat source/sink parameter.

μ

dynamic viscosity.

μ∗

reference viscosity.

ν∗

reference kinematic viscosity.

ψ

stream function.

ψ∗

variable.

ρ

density of the fluid.

θ

non-dimensional temperature.

θ∗, \(\bar{\theta}\)

variables.

θ′

first order derivative with respect to η.

θ′′

second order derivative with respect to η.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsThe University of BurdwanBurdwanIndia

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