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Effect of thermal stratification on MHD free convection with heat and mass transfer over an unsteady stretching surface with heat source, Hall current and chemical reaction

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Abstract

The present investigation is concerned with the effect of thermal stratification on magnetohydrodynamic free convection boundary layer flow with heat and mass transfer of an electrically conducting fluid over an unsteady stretching sheet in the presence of strong magnetic field. The electron–atom collision frequency is assumed to be relatively high, so that the Hall effect is assumed to be exist, while induced magnetic field is neglected. The transformed nonlinear boundary layer equations are solved numerically by applying Keller-box method. Effect of Prandtl number, magnetic parameter, Hall parameter, heat source parameter, radiation parameter, Schmidt number, chemical reaction parameter, Grashof number, modified Grashof number, as well as the local skin friction coefficient, heat and mass transfer rates are depicted graphically and in tabulated form. It has been found that these parameters affect considerably the considered flow characteristics.

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Abbreviations

C f :

Local skin friction

c p :

Specific heat at constant pressure

M :

Magnetic parameter

m :

Hall parameter

D :

Mass diffusion coefficient

g :

Magnitude of acceleration due to gravity

Gr x :

Grashof number

Gc x :

Modified Grashof number

Sc :

Schmidt number

Nu x :

Nusselt number

Sh x :

Sherwood number

Pr:

Prandtl number

q r :

Radiative heat flux

R :

Thermal radiation parameter

Rex :

Local Reynolds number

T :

Temperature of the fluid

t :

Time

U :

Surface velocity

u :

Fluid velocity in x-direction

v :

Fluid velocity in y-direction

w :

Fluid velocity in z-direction

x, y, z :

Cartesian co-ordinates

T w :

Surface temperature

T ∞ :

Free stream temperature

n, c :

Constants

C w :

Surface concentration

C ∞ :

Free stream concentration

B :

Magnetic field

k 0 :

rate of chemical reaction

k* :

Mean absorption coefficient

β:

Heat source parameter

γ:

Chemical reaction parameter

ξ:

Similarity variable

η:

Similarity variable

ψ:

Stream function

κ:

Thermal conductivity

μ:

Dynamic viscosity of the fluid

ν:

Kinematic viscosity

ρ:

Density of fluid

σ* :

Stefan–Boltzmann constant

β:

Coefficient of thermal expansion

β* :

Coefficient of expansion with concentration

σ:

Electrical conductivity of the fluid

ϕ:

Similarity concentration function

θ:

Similarity temperature function

′:

Differentiation with respect to η

w :

Surface condition

∞:

Free stream condition

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Acknowledgments

We are thankful to the editor and the referees for making constructive suggestions, which have improved the presentation of this work and the Research Management Centre—UTM for the financial support through vote number 4F109 and 03J62 for this research.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia JB, 81310, Skudai, Johor, Malaysia

    Aurangzaib, A. R. M. Kasim, N. F. Mohammad & Sharidan Shafie

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  1. Aurangzaib
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Correspondence to Sharidan Shafie.

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Aurangzaib, Kasim, A.R.M., Mohammad, N.F. et al. Effect of thermal stratification on MHD free convection with heat and mass transfer over an unsteady stretching surface with heat source, Hall current and chemical reaction. Int J Adv Eng Sci Appl Math 4, 217–225 (2012). https://doi.org/10.1007/s12572-012-0066-y

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