Heat and Mass Transfer

, Volume 46, Issue 8, pp 831–840

Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects

Authors

    • Department of Fluid Mechanics and Thermal EngineeringTransilvania University
Original

DOI: 10.1007/s00231-010-0633-3

Cite this article as:
Postelnicu, A. Heat Mass Transfer (2010) 46: 831. doi:10.1007/s00231-010-0633-3

Abstract

Dufour and Soret effects on flow at a stagnation point in a fluid-saturated porous medium are studied in this paper. A two dimensional stagnation-point flow with suction/injection of a Darcian fluid is considered. By using an appropriate similarity transformation, the boundary layer equations of momentum, energy and concentration are reduced to a set of ordinary differential equations, which are solved numerically using the Keller-box method, which is a very efficient finite differences technique. Nusselt and Sherwood numbers are obtained, together with the velocity, temperature and concentration profiles in the boundary layer. For the large suction case, asymptotic analytical solutions of the problem are obtained, which compare favourably with the numerical solutions. A critical view of the problem is presented finally.

List of symbols

C

Concentration

Cp

Specific heat at constant pressure

Cs

Concentration susceptibility

Df

Dufour number

Dm

Mass diffusivity

f

Dimensionless stream function

fw

Suction/injection parameter

K

Darcy permeability

kT

Thermal diffusion ratio

Le

Lewis number, αm/Dm

N

Buoyancy ratio (sustentation) parameter

Rax

Local Rayleigh number

u, v

Darcian velocities in the x and y-direction, respectively

U0

Reference velocity

vw

Suction/injection velocity

S

Shape factor

Sh

Sherwood number

T

Temperature

x, y

Cartesian co-ordinates along and normal to the body surface, respectively

αm

Thermal diffusivity

βT

Coefficient of thermal expansion

βC

Coefficient of concentration expansion

ϕ

Dimensionless concentration

μ

Dynamic viscosity

ν

Kinematic viscosity

θ

Dimensionless temperature

ρ

Density

ψ

Stream function

Subscripts

w

Condition at the wall

Condition at infinity

Superscript

Differentiation with respect to η

Copyright information

© Springer-Verlag 2010