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Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium: a numerical study

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Abstract

The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed. Further, the effects of the viscous forces, Joule heating, heat source/sink, and radiation on the flow are taken into account. The non-dimensional transformations are used to solve the governing equations. Then, the reduced system is resolved by the fourth-fifth order Runge-Kutta-Fehlberg method along with the shooting technique. The effects of different physical parameters on the heat transfer and entropy generation are discussed in detail through graphs. From the perspective of numerical results, it is recognized that the production of entropy can be improved with the Joule heating, viscous dissipation, and convective heating aspects. It is concluded that the production of entropy is the maximum with increases in the Casson parameter, the angle of inclination, and the Hartmann number. Both the Reynolds number and the radiation parameter cause the dual impact on entropy generation.

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Abbreviations

Bi 1, Bi 2 :

Biot numbers for each plate

B 0 :

magnetic field strength

Be :

Bejan number

c p :

specific heat, J·kg−1·K−1

Da :

Darcy number

Ec :

Eckert number

E 0 :

characteristic entropy generation

E g :

volumetric rate of entropy generation, kg·m2·s−2·K−1

e ij :

(i, j)th rate of deformation component

Q* T :

heat source/sink

Q t :

ratio of heat source/sink

Re :

Reynolds number

T :

temperature, K

T a :

cold fluid temperature

T h :

hot fluid temperature

V :

axial velocity, m·s−1

v :

dimensionless axial velocity

L :

characteristic temperature ratio

F :

Forchheimer parameter

Gr :

Grashof number

g :

gravity term, m·s−2

Ha :

Hartmann number

h 1, h 2 :

coefficients of convective heat transfer for each plate

k :

thermal conductivity, W·m−1·K−1

k′:

Rosseland absorption coefficient

N h :

irreversibility due to heat transfer

N v :

irreversibility due to viscous dissipation

N s :

non-dimensional entropy production

Pr :

Prandtl number

p :

pressure, Pa

P y :

fluid yield stress

P :

constant pressure gradient

μ B :

plastic dynamic viscosity

α :

inclination of angle, (°)

β :

Casson term

β* :

thermal expansion coefficient, K−1

ρ :

fluid density, kg·m−3

μ :

fluid dynamic viscosity, kg·m−1·s−1

y :

coordinate axis

ξ :

dimensionless coordinate axis

σ :

fluid electrical conductivity, kg−1·m−3·s3·A2

v 0 :

suction/injection

σ′ :

Stefan-Boltzmann constant

θ :

dimensionless temperature

φ :

product of the rate of deformation component with itself

φ c :

critical value

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Authors and Affiliations

  1. Department of PG Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Shimoga, Karnataka, 577451, India

    A. Roja, B. J. Gireesha & B. Nagaraja

Authors
  1. A. Roja
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  2. B. J. Gireesha
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  3. B. Nagaraja
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Correspondence to B. J. Gireesha.

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Roja, A., Gireesha, B.J. & Nagaraja, B. Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium: a numerical study. Appl. Math. Mech.-Engl. Ed. 42, 95–108 (2021). https://doi.org/10.1007/s10483-021-2681-9

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  • DOI: https://doi.org/10.1007/s10483-021-2681-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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