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Nonlinear convection flow of micropolar liquid: an application of improved Fourier’s expression

  • T. Hayat
  • M. Zubair
  • M. Waqas
  • M. Ayub
  • A. Alsaedi
Technical Paper
  • 52 Downloads

Abstract

Here, improved Fourier’s expression is utilized for heat transfer in nonlinear convection flow of micropolar liquid. The flow is generated due to a stretchable surface with variable thickness. Application of non-Fourier conduction phenomenon illustrates the characteristics of thermal relaxation factor. Temperature-dependent conductivity of liquid is also adopted. The set of partial differential equations governing the flow of micropolar liquid and heat transfer through non-Fourier heat conduction concept is established. The relevant transformations provide the highly nonlinear ordinary differential system. Homotopy theory is employed to acquire convergent solutions for nonlinear differential systems. Coefficient of skin friction is computed and examined for distinct embedded variables. Our presented analysis shows that temperature is decaying for larger thermal relaxation time.

Keywords

Nonlinear convection flow Micropolar liquid Improved Fourier’s expression Variable thermal conductivity Stagnation point flow 

List of symbols

uv

Velocity components

xy

Space coordinates

Uw(x)

Stretching velocity

Ue(x)

Free stream velocity

U0U

Reference velocities

N

Micro-rotation variable

g

Gravitational accelerational

β1

Linear thermal expansion coefficient

β2

Nonlinear thermal expansion coefficient

γ*

Spin gradient viscosity

j

Micro-inertia

m0

Boundary parameter

q

Heat flux

λ

Relaxation time of heat flux

K(T)

Variable thermal conductivity

K

Thermal conductivity of ambient fluid

μ

Dynamic viscosity

ν

Kinematic viscosity

ρ

Fluid density

k

Vortex viscosity

cp

Specific heat

b

Dimensional constant

Tw

Variable temperature at the sheet

T

Variable temperature away from the sheet

δ

Small parameter regarding the surface is sufficiently thin

K

Micropolar parameter

λ

Local buoyancy parameter

Grx

Local Grashof number

δ

Nonlinear convection

Pr

Prandtl number

γ

Thermal relaxation parameter

α

Wall thickness parameter

n

Power law index

\(\in\)

Temperature dependent thermal conductivity parameter

ψ

Stream function

η

Dimensionless variable

f(η)

Dimensionless velocity

g(η)

Dimensionless micro-rotation velocity

θ(η)

Dimensionless temperature

Cf

Skin friction coefficient

τw

Surface shear stress

Rex

Local Reynolds number

f0(η),g0(η)

Initial approximations for velocity

θ0(η)

Initial approximations for temperature

Lf,Lg,Lθ

Linear operators

Ci

Arbitrary constants

f, ℏg, ℏθ

Auxiliary variables

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • T. Hayat
    • 1
    • 2
  • M. Zubair
    • 1
  • M. Waqas
    • 1
  • M. Ayub
    • 1
  • A. Alsaedi
    • 2
  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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