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Thermal-diffusion and diffusion-thermo effects on squeezing flow of unsteady magneto-hydrodynamic Casson fluid between two parallel plates with thermal radiation

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Abstract

Present numerical study examines the heat and mass transfer characteristics of unsteady magneto-hydrodynamic squeezing flow of Casson fluid between two parallel plates with viscous and Joule dissipation effects in the presence of chemical reaction. The influence of Soret and Dufour parameters on squeezing flow is investigated along with thermal radiation and heat source/sink effects. The heat and mass transfer behaviour of squeezing flow is analysed by considering the rheological Casson fluid model. The present physical problem is governed by the set of nonlinear coupled time-dependent partial differential equations (PDEs). The method of similarity transformation approach is used to reduce the system of PDEs to a system of nonlinear ordinary differential equations (ODEs). Further, the Runge–Kutta fourth order integration scheme with shooting method (RK-SM) is used to solve the reduced ODEs. Numerical computations are performed for different sets of control parameters. The non-Newtonian flow behaviour of Casson fluid is presented in terms of graphs and tables. It is remarked that the temperature field is enhanced for increasing values of Hartmann number. Also, increasing Casson fluid parameter increases the velocity field. Concentration field is diminished for enhancing values of Soret parameter. Finally, the comparison between present similarity solutions and previously published results shows the accuracy of the current results.

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Abbreviations

\( S \) :

squeezing number

\( Ha \) :

Hartmann number

\( Ec \) :

Eckert number

\( R \) :

radiation parameter

\( Q \) :

heat generation or absorption parameter

\( Q^{*} \) :

volumetric heat generation or absorption coefficient

\( Pr \) :

Prandtl number

\( Sc \) :

Schmidt number

\( Sr \) :

Soret number

\( Du \) :

Dufour number

\( Kr \) :

chemical reaction parameter

\( \kappa \) :

thermal conductivity (W m−1 K−1)

\( k^{*} \) :

absorption coefficient (m−1)

\( D_{m} \) :

coefficient of mass diffusion

\( C_{f} \) :

skin-friction coefficient

\( Nu \) :

Nusselt number

\( Sh \) :

Sherwood number

\( Re_{x} \) :

Reynolds number

\( p \) :

pressure (Pa)

\( C_{p} \) :

specific heat capacity at constant pressure (J kg−1 K−1)

\( C_{s} \) :

specific heat capacity at constant concentration

\( B_{0} \) :

uniform magnetic field

\( l \) :

initial distance between the parallel plates (m)

\( T \) :

dimensional fluid temperature (K)

\( T_{w} \) :

wall temperature (K)

\( T_{\infty } \) :

ambient fluid temperature (K)

\( C \) :

dimensional fluid concentration (mol/m3)

\( C_{w} \) :

wall concentration (mol/m3)

\( C_{\infty } \) :

ambient fluid concentration (mol/m3)

\( k_{1} \) :

chemical reaction coefficient

\( u, v \) :

dimensional velocity components along \( x, y \) directions (m s−1)

\( F^{\prime}, F \) :

non-dimensional velocity components along axial and radial directions

\( \beta \) :

Casson fluid parameter

\( \sigma \) :

electrical conductivity (s m−1)

\( \sigma^{*} \) :

Stefan–Boltzmann constant (W m−2 K−4)

\( \eta \) :

similarity variable

\( \theta \) :

dimensionless temperature

\( \phi \) :

dimensionless concentration

\( \rho \) :

fluid density (kg m−3)

\( \mu \) :

dynamic viscosity (Ns m−2)

\( \alpha \) :

characteristic parameter of the squeezing motion of the plate (s−1)

\( \nu \) :

kinematic viscosity of the fluid (m2 s−1)

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Acknowledgements

The authors wish to express their gratitude to the reviewers who highlighted important areas for improvement in this earlier draft of the article. Their suggestions have served specifically to enhance the clarity and depth of the interpretation of results in the revised manuscript. One of the author, Usha Shankar, wishes to thank Karnataka Power Corporation Limited, Raichur Thermal Power Station, Shaktinagar, for the encouragement.

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Authors and Affiliations

  1. Department of Mathematics, Gulbarga University, Kalaburagi, 585 106, India

    N B Naduvinamani & Usha Shankar

  2. Department of Karnataka Power Corporation Limited, Raichur Thermal Power Station, Shaktinagar, Raichur, 584 170, India

    Usha Shankar

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  1. N B Naduvinamani
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Correspondence to N B Naduvinamani.

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Naduvinamani, N.B., Shankar, U. Thermal-diffusion and diffusion-thermo effects on squeezing flow of unsteady magneto-hydrodynamic Casson fluid between two parallel plates with thermal radiation. Sādhanā 44, 175 (2019). https://doi.org/10.1007/s12046-019-1154-5

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