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Neural Computing and Applications

, Volume 31, Supplement 1, pp 597–605 | Cite as

On non-Fourier flux in nonlinear stretching flow of hyperbolic tangent material

  • M. WaqasEmail author
  • Gulnaz Bashir
  • T. Hayat
  • A. Alsaedi
Original Article

Abstract

The present study explores the features of hyperbolic tangent material due to a nonlinear stretched sheet with variable sheet thickness. Non-Fourier flux theory is implemented for the development of energy expression. Such consideration accounts for the contribution by thermal relaxation. The resulting nonlinear differential system has been determined for the convergent series expressions of velocity and temperature. The solutions are demonstrated and analyzed through plots. Presented results indicate that velocity decays via larger material power law index and Weissenberg number. Temperature is the decreasing function of Prandtl number and thermal relaxation time.

Keywords

Variable sheet thickness Non-Fourier flux Hyperbolic tangent fluid 

Nomenclature

u , v

Velocity components

μ

Dynamic viscosity

ν

Kinematic viscosity

ρ

Fluid density

q

Heat flux

λ1

Relaxation time of heat flux

k(T)

Variable thermal conductivity

k

Thermal conductivity of ambient fluid

x , y

Space coordinates

Uw(x)

Stretching velocity

cp

Specific heat

a , b

Dimensional constants

Tw

Wall temperature

T

Ambient temperature

τw

Surface shear stress

T

Temperature of fluid

V

Velocity field

S

Extra stress tensor

T

Cauchy stress tensor

ψ

Stream function

α

Wall thickness parameter

Γ

Material constant

λ

Material power law index

n

Power law index

Pr

Prandtl number

γ

Thermal relaxation parameter

We

Weissenberg number

δ

Small parameter regarding the surface is sufficiently thin

ε

Temperature dependent thermal conductivity parameter

Cf

Skin friction coefficient

Rex

Local Reynolds number

f

Dimensionless velocity

θ

Dimensionless temperature

η

Dimensionless space variable

A1

First Rivlin-Ericksen tensor

μ0

Zero shear rate viscosity

μ

Infinite shear rate viscosity

Notes

Compliance with ethical standards

Conflict of interest

The authors declare they have no conflict of interest.

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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • M. Waqas
    • 1
    Email author
  • Gulnaz Bashir
    • 1
  • T. Hayat
    • 1
    • 2
  • A. Alsaedi
    • 2
  1. 1.Department of MathematicsQuaid-I-Azam UnisversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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