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Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel

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Abstract

The main aim of the present work is to investigate the flow and heat transport properties of non-Newtonian Casson-Williamson fluid through an upright microchannel along with entropy generation analysis, and explore the effects of convective boundary conditions, Couette-Poiseuille flow, and nonlinear radiation. The movement of liquid is scrutinized with the Hall effect and exponential heat source. The rheological characteristics of the Casson-Williamson fluid model are also considered. By considering the desirable similarity variables, the equations of motion are reduced to nonlinear ordinary differential equations. The Runge-Kutta-Fehlberg fourth-fifth order method along with the shooting method is adopted to solve these dimensionless expressions. The detailed investigation is pictorially displayed to show the influence of effective parameters on the entropy generation and the Bejan number. One of the major tasks of the exploration is to compare the Casson fluid and the Williamson fluid. The results show that the rate of heat transfer in the Casson fluid is more remarkable than that in the Williamson fluid.

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Abbreviations

Re :

Reynolds number

N r :

radiation parameter

Be :

Bejan number

N s :

dimensionless entropy generation number

T h :

hot fluid temperature, K

T a :

ambient temperature, K

T :

nanofluid temperature, K

u :

primary velocity, m/s

Ec :

Eckert number

Gr :

Grashof number

Pr :

Prandtl number

M :

Hartmann number

q r :

radiative heat flux, W/m2

B 0 :

magnetic field, A/m

p :

pressure, Pa

c p :

specific heat, J/(kg · K)

P :

pressure gradient parameter

y :

transversal coordinate, m

g :

acceleration due to gravity, m/s2

k :

thermal conductivity, W/(m · K)

a :

distance between channels, m

F :

dimensionless axial velocity component

k* :

mean absorption coefficient, m−1

We :

Weissenberg number

w :

secondary velocity, m/s

B i :

Biot number

E g :

entropy generation, J/K

Q e :

exponential heat source parameter

G :

dimensionless transverse velocity component

v 0 :

suction/injection velocity, m/s

h 1,h 2 :

convective heat transfer coefficients, W/(m2 · K).

μ :

viscosity coefficient, kg/(m · s)

β * :

thermal expansion coefficient, K−1

ρ :

fluid density, kg/m3

σ * :

Stefan-Boltzmann constant, W/(m2 · K4)

θ :

dimensionless temperature

β :

Casson fluid parameter

λ:

upper wall motion parameter

Γ:

Williamson fluid parameter.

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Authors and Affiliations

  1. Department of Post Graduation Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451, India

    B. J. Gireesha & L. Anitha

  2. Department of Mathematics, Adichunchanagiri Institute of Technology, Chikkamagaluru, 577102, India

    L. Anitha

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Citation: GIREESHA, B. J. and ANITHA, L. Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel. Applied Mathematics and Mechanics (English Edition), 43(12), 1951–1964 (2022) https://doi.org/10.1007/s10483-022-2929-8

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Gireesha, B.J., Anitha, L. Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel. Appl. Math. Mech.-Engl. Ed. 43, 1951–1964 (2022). https://doi.org/10.1007/s10483-022-2929-8

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