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Influence of chemically reacting species in MHD stagnation point flow of an Oldroyd-B fluid with partial slip

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Abstract

This paper looks into the influence of chemically reacting species on the magnetohydrodynamics stagnation point flow and mass transfer of an electrically conducting Oldroyd-B fluid over a stretching sheet with partial slip at the surface. The slip boundary condition for a two-dimensional Oldroyd-B fluid is obtained for the first time. A similarity solution for the system of equations is obtained using finite difference method in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The quantities of interest like fluid velocity and concentration of species are shown graphically and discussed under the influence of emerging parameters. An excellent agreement of the present results with existing values in special cases is achieved.

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Abbreviations

u, v :

Components of velocity in x-, y-direction [m s−1]

x, y :

Spatial coordinates [m]

a, b, d :

Constants stretching rates [s−1]

A, B :

Positive constants

u w, u e :

Wall and free stream velocities

L :

Slip length or the velocity slip parameter (velocity)−1

p :

Pressure of fluid

S :

Extra stress tensor

F :

Component of body force

k n :

nth-order homogeneous chemical reaction rate constant

B 0 :

Magnetic field [T]

f :

Dimensionless velocity

c :

Particle concentration

a i :

Components of acceleration vector

D :

Diffusion coefficient of the diffusing species in the fluid

Sc :

Schmidt number [=ν/D]

M 2 :

Hartmann number [=σB 20 /ρb]

η :

Similarity variable

τ :

Cauchy stress tensor

δ :

Components of identity tensor

μ :

Dynamics viscosity

ν :

Kinematics viscosity [m2 s−1]

γ 1, γ 2 :

Relaxation and retardation times [s−1]

σ :

Electrical conductivity of fluid [s m−1]

ϕ :

Dimensionless concentration field [=c−c ∞/c w−c ∞]

λ 1, λ 2 :

Dimensionless fluid parameters

β :

Velocity slip parameter \([={\text{ L}}\sqrt {{\text{b/}}\nu } ]\)

γ :

Chemical reaction rate parameter [=k n /b]

ɛ :

Ratio of external flow rate to stretching rate [=a/b]

w :

Surface condition

e, ∞:

Conditions far away from the surface

n :

nth-order chemical reaction rate

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Acknowledgements

We are thankful to the anonymous reviewers for their useful suggestions to improve the version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Z. Abbas & Fatima Taiba Gull

  2. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    M. Sajid

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  1. Z. Abbas
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  2. Fatima Taiba Gull
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  3. M. Sajid
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Correspondence to Z. Abbas.

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Technical Editor: Cezar Negrao.

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Abbas, Z., Gull, F.T. & Sajid, M. Influence of chemically reacting species in MHD stagnation point flow of an Oldroyd-B fluid with partial slip. J Braz. Soc. Mech. Sci. Eng. 39, 2159–2169 (2017). https://doi.org/10.1007/s40430-017-0726-8

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  • DOI: https://doi.org/10.1007/s40430-017-0726-8

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