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Cross diffusion effects on magnetohydrodynamic slip flow of Carreau liquid over a slendering sheet with non-uniform heat source/sink

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Abstract

Magnetohydrodynamic flow of Carreau fluid over a slendering sheet (variable thickness) has been numerically studied by considering the multiple slips effect. Thermosolutal boundary layer analysis is also accounted in the presence of cross diffusion and non-uniform heat source/sink. The governing nonlinear coupled partial differential equations are transformed to nonlinear coupled ordinary differential equations before being integrated numerically using Runge–Kutta based Newton’s schemes. The effects of various parameters involved in the present problem were elaborately discussed with help of graphs and tables. The present results in a limiting sense are found to accord with the previous study. The present results indicate that the cross diffusion and slip parameters had a tendency to control the flow. The influence of slip is more evident in Carreau fluid case on contrast with the Newtonian fluid case.

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Abbreviations

u, v :

Velocity components in x and y directions (m/s)

u w :

Stretching sheet velocity

C p :

Specific heat capacity at constant pressure (J/kg K

f :

Dimensionless velocity

A :

Coefficient related to stretching sheet

A*, B*:

Space and temperature dependent heat generation or absorption parameters

m :

Velocity power index parameter

n :

Power law index

B(x):

Magnetic field

U 0 :

Constant.

B 0 :

Constant

C 0 :

Constant

T 0 :

Constant

T :

Temperature of the fluid (K)

k :

Thermal conductivity (W/mK)

D m :

Molecular diffusivity of the species concentration

k T :

Thermal diffusion ratio

C s :

Concentration susceptibility

C :

Concentration of the fluid (Moles/Kg)

T m :

Mean fluid temperature (K)

T ∞ :

Temperature of the fluid in the free

C ∞ :

Concentration of the fluid in the free stream (Mole/Kg)

f 1 :

Maxwell’s reflection coefficient

h *1 :

Dimensional concentration jump parameter

h *2 :

Dimensional concentration jump parameter

h *3 :

Dimensional concentration jump parameter

d :

Concentration accommodation coefficient

a :

Thermal accommodation coefficient

b :

Constant

Pr:

Prandtl number

q′′′:

Space and temperature dependent heat source/sink

We:

Local Weissenberg number

M :

Magnetic parameter

Du:

Dufour number

Sc:

Schmidt number

Sr:

Soret number

h 1 :

Dimensionless velocity slip parameter

h 2 :

Dimensionless temperature jump parameter

h 3 :

Dimensionless concentration jump parameter

C f :

Skin friction coefficient

Nu x :

Local Nusselt number

Sh x :

Local Sherwood number

Re x :

Local Reynolds number

ϕ :

Dimensionless concentration

ζ:

Similarity variable

σ :

Electrical conductivity of the fluid (S/m)

γ :

Ratio of specific heats

θ :

Dimensionless temperature

ρ :

Density of the fluid (Kg/m3)

μ :

Dynamic viscosity (Kg/ms)

ν :

Kinematic viscosity (m2/s)

δ :

Wall thickness parameter

\(\xi_{1} , \xi_{2} , \xi_{3}\) :

Mean free path constants

Γ :

Positive characteristic time

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Authors and Affiliations

  1. Department of Mathematics, GITAM School of Technology, Bangalore, 562163, India

    C. S. K. Raju

  2. Department of Chemical Engineering, The University of Newcastle, Callaghan, Australia

    M. M. Hoque

  3. Department of Mathematics, Bharatiar University, Coimbatore, India

    P. Priyadharshini

  4. Department of Mathematics, Christ University, Bangalore, 560029, India

    B. Mahanthesh

  5. Department of Studies and Research in Mathematics, Kuvempu University, Shankarghatta, Shimoga, 577451, India

    B. Mahanthesh & B. J. Gireesha

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  1. C. S. K. Raju
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  3. P. Priyadharshini
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  5. B. J. Gireesha
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Correspondence to B. J. Gireesha.

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Technical Editor: Cezar Negrao.

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Raju, C.S.K., Hoque, M.M., Priyadharshini, P. et al. Cross diffusion effects on magnetohydrodynamic slip flow of Carreau liquid over a slendering sheet with non-uniform heat source/sink. J Braz. Soc. Mech. Sci. Eng. 40, 222 (2018). https://doi.org/10.1007/s40430-018-1142-4

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