Slip Effects on Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow Through a Porous Channel

  • Bamdeb Dey
  • Rita ChoudhuryEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 755)


The problem of MHD flow of visco-elastic fluid through a horizontal channel has been analysed in the presence of heat and mass transfer. The fluid is subjected to a transverse magnetic field and the slip velocity at the lower wall of the channel taken into consideration. A mathematical model (Walters liquid model B′) has been analyzed using appropriate mathematical techniques. Expressions for velocity, temperature, concentration, wall shear stress and rate of heat and mass transfer have been obtained. Variations of the quantities with different parameters are computed by using MATLAB software. The results are discussed graphically to measure the impact of visco-elasticity.


Visco-elastic MHD Slip velocity Free convection Shear stress 




The mean-free path


The Maxwell’s reflexion


Transverse magnetic field


Co-efficient of mass diffusivity


The mean width of the channel




Temperature distribution

x, y

Cartesian co-ordinate

u, v

Velocity components along x and y axis


Co-efficient of thermal conductivity

T1′, T2

Wall temperatures

\( C_{1}^{{\prime }} ,C_{2}^{{\prime }} \)

Wall concentrations


Visco-elastic parameter \( \left( {\frac{{K_{0} V_{0} }}{{\eta_{0} d}}} \right) \)

Dimensionless Parameters


Magnetic Parameter \( \left( {\frac{{\sigma B_{0}^{2} \mu {\prime }d^{2} }}{{\mu_{0} }}} \right) \)


Prandtl number \( \left( {\frac{{\mu C_{p} }}{K}} \right) \)


Suction parameter \( \left( {\frac{{v_{0} d}}{\upsilon }} \right) \)


Schmidth number \( \left( {\frac{{v_{0} d}}{Dm}} \right) \)

Greek Symbols

The amplitude parameter


Frequency parameter \( \left( {K_{0} d} \right) \)

\( \upsilon \)

Kinematic viscosity \( \left( {\frac{{\mu^{\prime}}}{\rho }} \right) \)

\( \rho \)


\( \sigma \)

Electric conductivity

\( \theta \)

Dimensionless temperature

\( \phi \)

Dimensionless concentration


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsGauhati UniversityGuwahatiIndia

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