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

## 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

*C*_{f}Skin friction coefficient

*f*Dimensionless stream function

*g*Acceleration due to gravity

*Gr*Grashof number

*h*_{s}Heat transfer parameter for Newtonian heating’

*Pr*Prandtl number

*Re*Reynolds number

*T*Fluid temperature

*T*_{∞}Ambient temperature

*u*,*v*Velocity components along the

*x*and*y*directions, respectively*U*_{∞}Free stream velocity

*u*_{e}(*x*)Velocity outside boundary layer

*x*,*y*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

- δ
_{i2}, δ_{i4} 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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