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Entropy Generation Analysis for a Radiative Micropolar Fluid Flow Through a Vertical Channel Saturated with Non-Darcian Porous Medium

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Abstract

In this study, an analytical investigation of convective heat transfer and entropy generation analysis of flow of micropolar fluid is presented. The infinite channel is assumed to be saturated with porous material and the walls are maintained at different constant temperatures. The Eringen thermo-micro-polar material model is used to simulate the rheological flow in the channel. The fluid is assumed to be gray, absorbing, emitting but non-scattering medium, and the Rosseland’s approximation is utilized to simulate the radiative heat flux component of heat transfer in energy transport equation. The resulting governing equations are then solved under physically viable boundary conditions at the channel walls using the Adomian decomposition method. The influences of emerging thermophysical parameters are addressed through graphs. The computations show that the increase in the Grashof number and radiation parameter causes to increase the entropy generation. Further, the effect of viscous dissipation was taken into account since it significantly affects heat transfer and entropy generation characteristics and cannot be ignored.

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Abbreviations

Be :

Bejan number

Br :

Brinkman number

\(\hbox {Br}/\Omega \) :

Viscous dissipation parameter

c :

Coupling number

\(C_f\) :

Forchheimer coefficient or constant

Da:

Darcy number

Ec :

Eckert number

2h :

Width of the free channel

\(\overline{\mathbf{h}}\) :

Heat flux

\(\overline{g}\) :

Acceleration due to gravity

K:

Permeability of the porous media

k :

Thermal conductivity of the fluid

\(k^{*}\) :

Mean absorption coefficient

\(N_H \) :

Entropy generation due to radiative heat transfer

\(N_P \) :

Entropy generation due to viscous dissipation

Nr :

Radiation parameter

Ns :

Total entropy generation number

P :

Pressure

Pr :

Prandtl number

\(\overline{q}\) :

Velocity vector

\(q_r\) :

Radiative heat flux

R :

Reynolds number

s:

Couple stress parameter

\(\hbox {S}_{\mathrm{G}}\) :

Entropy generation rate

\(\hbox {T}\) :

Non-dimensional temperature

\(\hbox {T}_{o}\) :

Reference temperature

u :

Dimensionaless velocity in X-direction

\(U_o\) :

Characteristic velocity

X, Y :

Space co-ordinates

\(\beta , \gamma \) :

Gyro-viscosity coefficients

\(\rho \) :

Density

\(\delta \) :

Rheological parameter

\(\sigma ^{*}\) :

Stefan–Boltzmann constant

\(\Delta T\) :

Temperature difference \((T_{II} -T_I )\)

\(\mu \) :

Dynamic viscosity coefficients

\(\kappa \) :

Eringen vortex viscosity coefficients

\(\overline{\nu }\) :

Microrotation

\(\Omega \) :

Dimensionless temperature difference

\(\phi \) :

Dimensionless angular velocity in X-direction

\(\varphi \) :

Irreversibility distribution ratio

\(\theta \) :

Non-dimensional temperature

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Acknowledgements

The authors are thankful to the reviewers for their valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Meghalaya, Shillong, 793002, India

    Srinivas Jangili

  2. Department of Mathematical Sciences, Redeemer’s University, P. O. Box 230, Ede, Osun State, Nigeria

    S. O. Adesanya

  3. Department of Physical Sciences, Redeemer’s University, Ede, Osun State, Nigeria

    J. A. Falade

  4. Department of Mathematics, GITAM University, Hyderabad Campus, Hyderabad, Telangana, 502329, India

    Nagaraju Gajjela

  5. Department of Mathematics, Vaal University of Technology, Private Bag X021, Vanderbijlpark, 1911, South Africa

    S. O. Adesanya

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  1. Srinivas Jangili
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Jangili, S., Adesanya, S.O., Falade, J.A. et al. Entropy Generation Analysis for a Radiative Micropolar Fluid Flow Through a Vertical Channel Saturated with Non-Darcian Porous Medium. Int. J. Appl. Comput. Math 3, 3759–3782 (2017). https://doi.org/10.1007/s40819-017-0322-8

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