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

First Online: 16 October 2009 Received: 09 December 2008 Accepted: 02 October 2009 DOI :
10.1007/s11012-009-9257-4

Cite this article as: Ishak, A. Meccanica (2010) 45: 367. doi:10.1007/s11012-009-9257-4
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.

Keywords Boundary layer Heat transfer Micropolar fluid Radiation Stretching sheet Fluids mechanics Nomenclature 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

Greek Letters 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

Subscripts w condition at the solid surface

∞ ambient condition

Superscript ′ 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 UKM Bangi, Selangor Malaysia