Heat and Mass Transfer

, Volume 46, Issue 11–12, pp 1411–1418 | Cite as

Mixed convection boundary layer flow over a horizontal circular cylinder with Newtonian heating

Original

Abstract

The steady mixed convection boundary layer flow over a horizontal circular cylinder, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered in this study. The governing boundary layer equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into non-similar equations before they are solved numerically using a numerical scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient Re 1/2 C f and the local wall temperature θ w (x) as well as the velocity and temperature profiles with two parameters, namely the mixed convection parameter λ and the Prandtl number Pr.

List of symbols

a

Radius of the cylinder

Cf

Skin friction coefficient

f

Dimensionless stream function

g

Acceleration due to gravity

Gr

Grashof number

hs

Heat transfer parameter for Newtonian heating’

Pr

Prandtl number

Re

Reynolds number

T

Fluid temperature

T

Ambient temperature

uv

Velocity components along the x and y directions, respectively

U

Free stream velocity

ue(x)

Velocity outside boundary layer

xy

Cartesian coordinates along the surface and normal to it, respectively

Greek symbols

α

Thermal diffusivity

β

Thermal expansion coefficient

γ

Conjugate parameter for Newtonian heating

δi2, δi4

Kronecker delta operator

η

Similarity variable

θ

Dimensionless temperature

λ

Mixed convection parameter

μ

Dynamic viscosity

ν

Kinematic viscosity

ψ

Stream function

Subscripts

w

Condition at the surface

Condition at infinity

Superscript

Differentiation with respect to y and η

Notes

Acknowledgments

The authors gratefully acknowledge the research grants received (UKM-ST-07-FRGSS0036-2009 & RDU090308) and the valuable comments and suggestions from the reviewers. The second author would like to acknowledge the financial support received under the Brain Gain Malaysia (BGM) Programme from the Ministry of Science, Technology and Innovation, Malaysia and the Academy of Sciences, Malaysia.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Faculty of Industrial Science and TechnologyUniversiti Malaysia PahangKuantanMalaysia
  2. 2.School of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaBangiMalaysia
  3. 3.Faculty of MathematicsUniversity of ClujClujRomania

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