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Analysis of Eyring–Powell liquid flow in curved channel with Cattaneo–Christov heat flux model

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Abstract

The article concentrates on the analysis of heat transfer phenomena incorporated with Cattaneo–Christov model of heat flux in magnetohydrodynamic Eyring–Powell fluid flow in a semipermeable curved channel. The flow equations are modeled by introducing the curvilinear coordinates system. The governing mathematical equations are reformed into ordinary differential equations by utilizing nonlinear type of similarity variables. The obtained mathematical model is solved numerically by utilizing shooting method. The obtained results are also validated with the well-known finite difference algorithm known as Keller-box method. The impact of diverse parameters on the flow and physical quantities like rate of heat transport and shear stress is investigated and discussed in detail via graphs and table. It is noticed that an increase in the fluid parameter increases the velocity of the fluid, whilst an increase in the thermal relaxation parameter decreases the temperature of the fluid.

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Abbreviations

B 0 :

Constant magnetic field

R 1 :

Radius of the curved channel

b :

Eyring–Powell constant

A 1 :

First Rivlin–Ericksen tensor

f :

Dimensionless fluid velocity in r-direction

\(f^{{\prime }}\) :

Dimensionless fluid velocity in s-direction

k 1 :

Thermal conductivity of the fluid

H :

Distance between the walls of the curved channel

M :

Dimensionless magnetic parameter

p :

Pressure of the fluid

P :

Dimensionless pressure

Pr:

Prandtl number

r :

Distance normal to surface of the curved channel

q w :

Heat flux at the wall

\(\bar{L}\) :

Horizontal length scale

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{K}\) :

Dimensionless radius of curvature

s :

Flow directional coordinate along the curved wall of the channel

\(\bar{u}\) :

Velocity component in the s-direction

\(\bar{v}\) :

Velocity component in the r-direction

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}\) :

Temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}_{\text{w}}\) :

Surface temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}_{0}\) :

Ambient fluid temperature

U :

Fluid velocity

α :

Thermal relaxation parameter

β :

Eyring–Powell constant

η :

Dimensionless variable

μ :

Dynamic viscosity of the fluid

ν :

Kinematics viscosity of the fluid

ρ :

Density of fluid

\(\bar{\delta }\) :

Boundary layer thickness

λ E :

Relaxation time of heat flux

λ 1, λ 2 :

Fluid parameters

λ :

Reynolds number

\(\bar{\tau }\) :

Stress tensor

\(\bar{\tau }_{\text{rs}}\) :

Wall shear stress

c p :

Specific heat at constant pressure

σ :

Electrical conductivity

\(\bar{\gamma }\) :

Constant

θ :

Dimensionless fluid temperature

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Acknowledgements

We are thankful to the reviewers for their encouraging comments and constructive suggestions to improve the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Z. Abbas & M. Rafiq

  2. Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, 64200, Pakistan

    M. Naveed

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  1. Z. Abbas
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Correspondence to M. Naveed.

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Technical Editor: Cezar Negrao.

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Abbas, Z., Rafiq, M. & Naveed, M. Analysis of Eyring–Powell liquid flow in curved channel with Cattaneo–Christov heat flux model. J Braz. Soc. Mech. Sci. Eng. 40, 390 (2018). https://doi.org/10.1007/s40430-018-1312-4

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