Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects Authors Adrian Postelnicu Department of Fluid Mechanics and Thermal Engineering Transilvania University Original

First Online: 01 July 2010 Received: 30 March 2009 Accepted: 15 June 2010 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

C _{p} Specific heat at constant pressure

C _{s} Concentration susceptibility

D _{f} Dufour number

D _{m} Mass diffusivity

f Dimensionless stream function

f _{w} Suction/injection parameter

K Darcy permeability

k _{T} Thermal diffusion ratio

Le Lewis number, α_{m} /D _{m}

N Buoyancy ratio (sustentation) parameter

Ra _{x} Local Rayleigh number

u, v Darcian velocities in the x and y -direction, respectively

U _{0} Reference velocity

v _{w} Suction/injection velocity

S Shape factor

Sh Sherwood number

T Temperature

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

α _{m} Thermal diffusivity

β _{T} Coefficient of thermal expansion

β _{C} 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

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