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


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.


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)


Stretching sheet velocity


Specific heat capacity at constant pressure (J/kg K


Dimensionless velocity


Coefficient related to stretching sheet

A*, B*

Space and temperature dependent heat generation or absorption parameters


Velocity power index parameter


Power law index


Magnetic field










Temperature of the fluid (K)


Thermal conductivity (W/mK)


Molecular diffusivity of the species concentration


Thermal diffusion ratio


Concentration susceptibility


Concentration of the fluid (Moles/Kg)


Mean fluid temperature (K)


Temperature of the fluid in the free


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


Maxwell’s reflection coefficient


Dimensional concentration jump parameter


Dimensional concentration jump parameter


Dimensional concentration jump parameter


Concentration accommodation coefficient


Thermal accommodation coefficient




Prandtl number


Space and temperature dependent heat source/sink


Local Weissenberg number


Magnetic parameter


Dufour number


Schmidt number


Soret number


Dimensionless velocity slip parameter


Dimensionless temperature jump parameter


Dimensionless concentration jump parameter


Skin friction coefficient


Local Nusselt number


Local Sherwood number


Local Reynolds number

Greek letters


Dimensionless concentration


Similarity variable


Electrical conductivity of the fluid (S/m)


Ratio of specific heats


Dimensionless temperature


Density of the fluid (Kg/m3)


Dynamic viscosity (Kg/ms)


Kinematic viscosity (m2/s)


Wall thickness parameter

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

Mean free path constants


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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