Meccanica

, Volume 47, Issue 5, pp 1261–1269

Numerical solutions of free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid

Article

Abstract

In this paper, the problem of free convection boundary layer flow on a solid sphere in a micropolar fluid with Newtonian heating, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations in the form of partial differential equations are solved numerically using an implicit finite-difference scheme. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the material or micropolar parameter K, the Prandtl number Pr and the conjugate parameter γ are analyzed and discussed.

Keywords

Boundary layer Free convection Micropolar fluid Newtonian heating Sphere 

Nomenclature

a

radius of the sphere

hs

heat transfer parameter for Newtonian heating

Cf

skin friction coefficient

f

dimensionless stream function

g

acceleration due to gravity

Gr

Grashof number

H

angular velocity of micropolar fluid

j

microinertia density

K

material parameter of micropolar fluid

k

thermal conductivity

Pr

Prandtl number

Re

Reynolds number

T

fluid temperature

T

ambient temperature

U

free stream velocity

u,v

velocity components along the x and y directions, respectively

x,y

Cartesian coordinates along the sphere and normal to it, respectively

Greek Letters

β

thermal expansion coefficient

γ

conjugate parameter for Newtonian heating

μ

dynamic viscosity

ν

kinematic viscosity

θ

dimensionless temperature

κ

vortex viscosity

φ

spin gradient viscosity

ρ

fluid density

ψ

stream function

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Faculty of Industrial Science and TechnologyUniversiti Malaysia PahangUMP KuantanMalaysia
  2. 2.School of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaUKM BangiMalaysia
  3. 3.Solar Energy Research InstituteUniversiti Kebangsaan MalaysiaUKM BangiMalaysia
  4. 4.Faculty of MathematicsUniversity of ClujClujRomania

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