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Effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a wedge with heat generation/absorption in the presence of suction or injection

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Abstract

The purpose of this work is to study the effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a vertical wedge with heat generation/absorption in the presence of uniform suction or injection. The fluid is assumed to be viscous and incompressible. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Both accelerating and decelerating free stream flows are considered. Non-similar solutions are obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are carried out for different values of dimensionless parameters on velocity, temperature and concentration profiles graphically reported in the present study. Also, numerical results are presented for the local skin friction coefficient, the local Nusselt number and the local Sherwood number. Results indicate that the time effect is crucial on velocity, temperature and concentration profiles, and on the local skin friction coefficient, the local Nusselt and Sherwood numbers. The buoyancy assisting force causes overshoot in the velocity profile for lower Prandtl number fluids. Results are compared with previously published work and are found to be in an excellent agreement.

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Abbreviations

A :

Surface mass transfer parameter

\(c_p\) :

Specific heat at constant pressure

C :

Species concentration

\(C_{fx}\) :

Local skin friction coefficient in the x-direction

D :

Mass diffusivity

f :

Dimensionless stream function

F :

Dimensionless velocity along x-direction

g :

Acceleration due to gravity

\(Gr_L, Gr_L^*\) :

Grashof numbers due to temperature and concentration distributions, respectively

\(k_c\) :

Chemical reaction rate

L :

Characteristic length

m :

Pressure gradient parameter

N :

Ratio of the buoyancy parameters or ratio of Grashof numbers

\(Nu_x\) :

Local Nusselt number

Pr :

Prandtl number

Q :

Heat generation coefficient

\(R(t^*)\) :

Unsteady function of \(t^*\)

\(Re_L\) :

Reynolds number based on length L

\(Re_x\) :

Reynolds number based on length x

S :

Heat generation or absorption parameter

Sc :

Schmidt number

\(Sh_x\) :

Local Sherwood number

\(t, t^*\) :

Dimensional and dimensionless times, respectively

T :

Temperature

u, v :

Velocity components in the x- and y-directions, respectively

x, y :

Axial and vertical co-ordinates

\(\bar{x}\) :

Dimensionless axial distance

\(\alpha \) :

Thermal diffusivity

\(\beta , \beta ^*\) :

Volumetric coefficients of thermal and concentration expansions, respectively

\(\gamma \) :

Vertical angle of the wedge

\(\varDelta \) :

Chemical reaction parameter

\(\varepsilon \) :

Acceleration/deceleration parameter

\(\theta \) :

Dimensionless temperature

\(\lambda , \lambda ^*\) :

Buoyancy parameters due to temperature and concentration gradients, respectively

\(\mu \) :

Dynamic viscosity

\(\nu \) :

Kinematic viscosity

\(\rho \) :

Density

\(\phi \) :

Dimensionless concentration

\(\psi \) :

Dimensional stream function

\(\xi , \eta \) :

Transformed variables

e :

Condition at the edge of the boundary layer

i :

Initial condition

\(w, \infty \) :

Conditions at the wall and at infinity, respectively

\(\xi , \eta , t^*\) :

Denote the partial derivatives with respect to these variables, respectively

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Acknowledgments

Authors express sincere thanks to the anonymous reviewers for their detailed and very useful comments in improving the quality of the manuscript. One of the authors EM thanks the National Research Foundation of South Africa for their support.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli, 620 015, Tamil Nadu, India

    M. Ganapathirao & R. Ravindran

  2. Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa

    E. Momoniat

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  1. M. Ganapathirao
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  2. R. Ravindran
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Correspondence to E. Momoniat.

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Ganapathirao, M., Ravindran, R. & Momoniat, E. Effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a wedge with heat generation/absorption in the presence of suction or injection. Heat Mass Transfer 51, 289–300 (2015). https://doi.org/10.1007/s00231-014-1414-1

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