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Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects

Abstract

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subjected to a chemical reaction is numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The transformed governing equations are solved by a very efficient numerical method, namely, a modified version of the Keller-box method for ordinary differential equations. The parameters of the problem are Lewis, Dufour and Soret numbers, sustentation parameter, the order of the chemical reaction n and the chemical reaction parameter γ. Local Nusselt number and local Sherwood number variations and dimensionless concentration profiles in the boundary layer are presented graphically and in tables for various values of problem parameters and it is concluded that γ and n play a crucial role in the solution.

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Abbreviations

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

K :

Darcy permeability

K 1 :

dimensional chemical reaction parameter

k T :

thermal diffusion ratio

Le :

Lewis number, αm/D m

N :

sustentation parameter

Nu x :

local Nusselt number

n :

order of the chemical reaction

Ra x :

local Rayleigh number

u, v :

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

S r :

Soret number

Sh x :

local Sherwood number

T :

temperature

x, y :

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

αm :

thermal diffusivity

βT :

coefficient of thermal expansion

βC :

coefficient of concentration expansion

ϕ:

dimensionless concentration

γ:

dimensionless chemical reaction parameter

η:

similarity variable

υ:

kinematic viscosity

θ:

dimensionless temperature

ρ:

density

ψ:

stream function

w :

condition at wall

∞:

condition at infinity

′:

differentiation with respect to η

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Correspondence to Adrian Postelnicu.

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Postelnicu, A. Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects. Heat Mass Transfer 43, 595–602 (2007). https://doi.org/10.1007/s00231-006-0132-8

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Keywords

  • Porous Medium
  • Natural Convection
  • Rayleigh Number
  • Sherwood Number
  • Local Nusselt Number