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Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect

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Abstract

In the present paper, we study the effects of radiation on the thermal boundary layer flow induced by a linearly stretching sheet immersed in an incompressible micropolar fluid with constant surface temperature. Similarity transformation is employed to transform the governing partial differential equations into ordinary ones, which are then solved numerically using the Runge-Kutta-Fehlberg method. Results for the local Nusselt number as well as the temperature profiles are presented for different values of the governing parameters. It is found that the heat transfer rate at the surface decreases in the presence of radiation. Comparison with known results for certain particular cases is excellent.

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Abbreviations

a,b:

constants

c p :

specific heat at constant pressure

f :

dimensionless stream function

h :

dimensionless microrotation

j :

microinertia density

k :

thermal conductivity

k * :

mean absorption coefficient

K :

material parameter

m :

boundary parameter

N :

microrotation or angular velocity

N R :

radiation parameter

Pr :

Prandtl number

q r :

radiative heat flux

T :

fluid temperature

T w :

surface temperature

T ∞ :

ambient temperature

u,v:

velocity components in the x- and y-directions, respectively

U w :

velocity of the stretching sheet

x,y:

Cartesian coordinates along the sheet and normal to it, respectively

α :

thermal diffusivity

β :

thermal expansion coefficient

γ :

spin gradient viscosity

η :

similarity variable

θ :

dimensionless temperature

κ :

vortex viscosity

ν :

kinematic viscosity

μ :

dynamic viscosity

ρ :

fluid density

σ * :

Stefan-Boltzmann constant

ψ :

stream function

w :

condition at the solid surface

∞:

ambient condition

′:

differentiation with respect to η

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Authors and Affiliations

  1. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor, Malaysia

    Anuar Ishak

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  1. Anuar Ishak
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Ishak, A. Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica 45, 367–373 (2010). https://doi.org/10.1007/s11012-009-9257-4

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  • DOI: https://doi.org/10.1007/s11012-009-9257-4

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