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

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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.

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Abbreviations

u , v :

Velocity components

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Fluid density

q :

Heat flux

λ 1 :

Relaxation time of heat flux

k(T):

Variable thermal conductivity

k ∞ :

Thermal conductivity of ambient fluid

x , y :

Space coordinates

U w(x):

Stretching velocity

c p :

Specific heat

a , b :

Dimensional constants

T w :

Wall temperature

T ∞ :

Ambient temperature

τ w :

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

C f :

Skin friction coefficient

Rex :

Local Reynolds number

f :

Dimensionless velocity

θ :

Dimensionless temperature

η :

Dimensionless space variable

A 1 :

First Rivlin-Ericksen tensor

μ 0 :

Zero shear rate viscosity

μ ∞ :

Infinite shear rate viscosity

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam Unisversity, 45320, Islamabad, 44000, Pakistan

    M. Waqas, Gulnaz Bashir & T. Hayat

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

Authors
  1. M. Waqas
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  2. Gulnaz Bashir
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  3. T. Hayat
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Correspondence to M. Waqas.

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Waqas, M., Bashir, G., Hayat, T. et al. On non-Fourier flux in nonlinear stretching flow of hyperbolic tangent material. Neural Comput & Applic 31 (Suppl 1), 597–605 (2019). https://doi.org/10.1007/s00521-017-3016-6

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  • DOI: https://doi.org/10.1007/s00521-017-3016-6

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