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Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

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Abstract

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are presented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ, the order of the chemical reaction parameter m, the Soret number S r, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

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Abbreviations

a :

non-dimensional constant

C :

concentration

D :

mass diffusivity

f :

dimensionless stream function

g :

acceleration due to gravity

k :

thermal conductivity

k 1 :

dimensional chemical reaction parameter

k T :

thermal diffusion ratio

K :

permeability for the porous medium

Le :

Lewis number

m :

order of the chemical reaction

n :

viscosity index

N :

buoyancy ratio

Ra :

Rayleigh number

S r :

Soret number

T :

temperature

u, v :

velocity components in the x- and y-directions

x, y :

Cartesian coordinates

α :

thermal diffusivity

α 0 :

threshold gradient (ατ 0/\( \sqrt K \))

β T :

coefficient of thermal expansion

β C :

coefficient of concentration expansion

γ :

dimensionless chemical reaction parameter

η :

similarity variable

θ :

dimensionless temperature

µ:

effective viscosity

ρ :

density of fluid

τ 0 :

yield stress

ϕ :

dimensionless concentration

ψ :

stream function

Ω:

dimensionless rheological parameter

w:

wall conditions

∞:

free stream conditions

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71515, Egypt

    F. S. Ibrahim & F. M. Hady

  2. Department of Science and Mathematics, Faculty of Education, Assiut University, The New Valley, 72111, Egypt

    S. M. Abdel-Gaied & M. R. Eid

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  1. F. S. Ibrahim
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Correspondence to M. R. Eid.

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Communicated by Zhe-wei ZHOU

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Ibrahim, F.S., Hady, F.M., Abdel-Gaied, S.M. et al. Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect. Appl. Math. Mech.-Engl. Ed. 31, 675–684 (2010). https://doi.org/10.1007/s10483-010-1302-9

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  • DOI: https://doi.org/10.1007/s10483-010-1302-9

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