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

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## 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

*u*,*v*Velocity components

*x*,*y*Space coordinates

*U*_{w}(*x*)Stretching velocity

*U*_{e}(*x*)Free stream velocity

*U*_{0},*U*_{∞}Reference velocities

*N*Micro-rotation variable

*g*Gravitational accelerational

*β*_{1}Linear thermal expansion coefficient

*β*_{2}Nonlinear thermal expansion coefficient

*γ**Spin gradient viscosity

*j*Micro-inertia

*m*_{0}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

*c*_{p}Specific heat

*b*Dimensional constant

*T*_{w}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

*Gr*_{x}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

*C*_{f}Skin friction coefficient

*τ*_{w}Surface shear stress

- Re
_{x} Local Reynolds number

*f*_{0}(*η*),*g*_{0}(*η*)Initial approximations for velocity

*θ*_{0}(*η*)Initial approximations for temperature

*L*_{f},*L*_{g},*L*_{θ}Linear operators

*C*_{i}Arbitrary constants

- ℏ
_{f}, ℏ_{g}, ℏ_{θ} Auxiliary variables

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