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Scaling Transformation for the Effect of Temperature-Dependent Fluid Viscosity with Thermophoresis Particle Deposition on MHD-Free Convective Heat and Mass Transfer Over a Porous Stretching Surface

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Abstract

This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results, thus, obtained are presented graphically and discussed.

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Abbreviations

B 0 :

Constant magnetic field of strength

C :

Species concentration of the fluid

C w :

Species concentration of the fluid along the wall

C ∞ :

Species concentration of the fluid away from the wall

c p :

Specific heat at constant pressure

D :

Coefficient of diffusion

g :

Acceleration due to gravity

T :

Temperature of the fluid

T w :

Temperature of the wall

T ∞ :

Temperature of the fluid far away from the wall

u, v:

Velocity components in x and y direction

U(x):

Flow velocity of the fluid away from the wedge

V(x):

Velocity of suction/injection

β :

Coefficient of thermal expansion

β*:

Coefficient of expansion with concentration

ρ :

Density of the fluid

σ :

Electric conductivity

σ 1 :

Stefan–Boltzman constant

κ :

Thermal conductivity of the fluid

μ :

Coefficient of fluid viscosity

μ * :

Constant value of the coefficient of viscosity far away from the sheet

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Authors and Affiliations

  1. Computational Fluid Dynamics, FSSW, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Johor, Malaysia

    R. Kandasamy & I. Muhaimin

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  1. R. Kandasamy
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  2. I. Muhaimin
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Correspondence to R. Kandasamy.

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Kandasamy, R., Muhaimin, I. Scaling Transformation for the Effect of Temperature-Dependent Fluid Viscosity with Thermophoresis Particle Deposition on MHD-Free Convective Heat and Mass Transfer Over a Porous Stretching Surface. Transp Porous Med 84, 549–568 (2010). https://doi.org/10.1007/s11242-009-9519-6

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  • DOI: https://doi.org/10.1007/s11242-009-9519-6

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