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Impact of thermophoresis particle deposition and chemical reaction on unsteady non-Darcy mixed convective flow over a porous wedge in the presence of temperature-dependent viscosity

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Abstract

An analysis is presented to investigate the effect of thermophoresis particle deposition and temperature dependent viscosity on unsteady non-Darcy mixed convective heat and mass transfer of a viscous and incompressible fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform non-Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Numerical calculations are carried out for different values of dimensionless parameters arising in the problem. The results are compared with available ones in the literature and excellent agreement is obtained. An analysis of the obtained results shows that the flow field is influenced appreciably by the chemical reaction and thermophoresis particle deposition.

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Abbreviations

C :

Species concentration in the boundary layer [kg m−2]

c p :

Specific heat due to constant pressure [J kg−1 K−1]

C w :

Species concentrations of wall

C ∞ :

Species concentrations of the ambient fluid

D :

Molecular diffusivity

f :

Dimensionless stream function

N t :

Thermophoresis parameter

\(\operatorname{Pr}_{A}\) :

Ambient Prandtl number

\(\operatorname{Pr}_{v}\) :

Variable Prandtl number

\(\operatorname{Re}_{x}\) :

Local Reynolds number

Sc :

Schmidt number

T :

Temperature of the fluid

T w :

Temperature at the wall surface

T r :

Reference temperature of the fluid [K]

T ∞ :

Temperature of the ambient fluid [K]

x,y :

Axis in direction along and normal to the wedge [m]

U :

Free stream velocity [m s−1]

u,v :

The x- and y-component of the velocity field [m s−1]

V T :

Thermophoretic velocity

β 1 :

Wedge angle parameter

γ :

Chemical reaction parameter

δ :

Time dependent length scale

κ :

Thermophoretic coefficient defined

ρ :

Fluid density [kg m−3]

ψ :

Stream function [m2 s−1]

η :

Similarity variable

ν :

Kinematic viscosity [m2 s−1]

μ :

Fluid viscosity [Pa s]

μ ∞ :

Ambient fluid viscosity [Pa s]

τ :

Thermophoretic parameter

θ :

Dimensionless temperature

ϕ :

Dimensionless concentration

λ u :

Unsteadiness parameter

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Acknowledgements

The authors wish to express their cordial thanks to our beloved The Vice Chancellor and The Dean, Faculty of Science, technology and Human Development, Universiti Tun Hussein Onn Malaysia, for their encouragements.

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Authors and Affiliations

  1. Research Centre for Computational Mathematics, FSTPi, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Johor, Malaysia

    I. Muhaimin, R. Kandasamy, Azme B. Khamis & Rozani bin Roslan

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  1. I. Muhaimin
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  2. R. Kandasamy
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  3. Azme B. Khamis
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  4. Rozani bin Roslan
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Correspondence to R. Kandasamy.

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Muhaimin, I., Kandasamy, R., Khamis, A.B. et al. Impact of thermophoresis particle deposition and chemical reaction on unsteady non-Darcy mixed convective flow over a porous wedge in the presence of temperature-dependent viscosity. Meccanica 48, 1415–1430 (2013). https://doi.org/10.1007/s11012-012-9675-6

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