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

  • C. S. K. Raju
  • M. M. Hoque
  • P. Priyadharshini
  • B. Mahanthesh
  • B. J. Gireesha
Technical Paper
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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.

Keywords

Cross diffusion Carreau fluid Slip parameters Slendering surface Non-uniform heat source/sink 

List of symbols

u, v

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

uw

Stretching sheet velocity

Cp

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

U0

Constant.

B0

Constant

C0

Constant

T0

Constant

T

Temperature of the fluid (K)

k

Thermal conductivity (W/mK)

Dm

Molecular diffusivity of the species concentration

kT

Thermal diffusion ratio

Cs

Concentration susceptibility

C

Concentration of the fluid (Moles/Kg)

Tm

Mean fluid temperature (K)

T

Temperature of the fluid in the free

C

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

f1

Maxwell’s reflection coefficient

h1*

Dimensional concentration jump parameter

h2*

Dimensional concentration jump parameter

h3*

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

h1

Dimensionless velocity slip parameter

h2

Dimensionless temperature jump parameter

h3

Dimensionless concentration jump parameter

Cf

Skin friction coefficient

Nux

Local Nusselt number

Shx

Local Sherwood number

Rex

Local Reynolds number

Greek letters

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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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • C. S. K. Raju
    • 1
  • M. M. Hoque
    • 2
  • P. Priyadharshini
    • 3
  • B. Mahanthesh
    • 4
    • 5
  • B. J. Gireesha
    • 5
  1. 1.Department of MathematicsGITAM School of TechnologyBangaloreIndia
  2. 2.Department of Chemical EngineeringThe University of NewcastleCallaghanAustralia
  3. 3.Department of MathematicsBharatiar UniversityCoimbatoreIndia
  4. 4.Department of MathematicsChrist UniversityBangaloreIndia
  5. 5.Department of Studies and Research in MathematicsKuvempu UniversityShimogaIndia

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