# Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet

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## Abstract

In this study, an analysis has been performed for heat and mass transfer with radiation effect of a steady laminar boundary-layer flow of a micropolar flow past a nonlinearly stretching sheet. Parameters *n*, *K*, *k* _{0}, *Pr*, *Ec*, and *Sc* represent the dominance of the nonlinearly effect, material effect, radiation effect, heat and mass transfer effects which have presented in governing equations, respectively. The similar transformation, the finite-difference method and Runge–Kutta method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, the wall unknown values of *θ*′(0) and *ϕ*′(0) for calculating the heat and mass transfer of the similar boundary-layer flow are carried out as functions of *n*, *Ec*, *k* _{0}, *Pr*, *Sc*. The value of *n*, *k* _{0}, *Pr* and *Sc* parameters are important factors in this study. It will produce greater heat transfer efficiency with a larger value of those parameters, but the viscous dissipation parameter *Ec* and material parameter *K* may reduce the heat transfer efficiency. On the other hand, for mass transfer, the value of *Sc* parameter is important factor in this study. It will produce greater heat transfer efficiency with a larger value of *Sc*.

## Keywords

Prandtl Number Boundary Layer Thickness Schmidt Number Thermal Boundary Layer Micropolar Fluid## List of symbols

*A*Constant

*B*Parameter related to the surface stretching speed

*C*Concentration, kg/m

^{3}*c*_{p}Specific heat at a constant pressure, J/kg K

*D*Mass diffusing, m

^{2}/s*Ec*Eckert number

*f*Dimensionless stream function

*g*Microrotation parameter

*J*The micro-inertial per unit mass, N/kg

- \( k_{0} = {\frac{{3N_{R} }}{{3N_{R} + 4}}} \)
Radiation parameter

*k**Mean absorption coefficient

*k*_{1}Fluid thermal conductivity, W m/K

*K*Vortex viscosity or the material parameter

*L*Reference length, m

*n*Parameters related to the surface stretching speed

*N*Microrotation component

- \( N_{R} = {\frac{{k_{T} k^{*} }}{{4\sigma^{*} T_{\infty }^{3} }}} \)
Radiation parameter

*Pr*Prandtl number

*q*_{r}Radiative heat flux, J/m

^{2}- \( Sc = \upsilon / {\text{D}} \)
Schmidt number

*T*Temperature across the thermal boundary layer, K

*T*_{∞}Temperature of the fluid far away from the plate, K

*T*_{w}Temperature of the plate, K

*u*,*v*Velocity components along

*x*and*y*directions, respectively, m/s*x*,*y*Cartesian coordinates along the plate and normal to it, respectively, m

*α*Thermal diffusivity, m

^{2}/s*γ*Spin gradient viscosity

*η*Dimensionless similarity variable

*θ*Dimensionless temperature

*μ*Dynamic viscosity, kg m/s

*υ*Kinematic viscosity, m

^{2}/s*ρ*Fluid density, kg/m

^{3}*τ*Shear stress, N/m

^{2}*σ*^{*}Stefan Boltzmann constant

*ϕ*Non-dimensional concentration variable

## Notes

### Acknowledgments

The author would like to thank the good comments which provided by the reviewers and would like to thank National Science Council R.O.C for the financial support through Grant. NSC 98-2221-E-434-009-.

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