Applied Scientific Research

, Volume 44, Issue 3, pp 287–302 | Cite as

A turbulence model for the heat transfer near stagnation point of a circular cylinder

  • Mounir B. Ibrahim


A one-equation low-Reynolds number turbulence model has been applied successfully to the flow and heat transfer over a circular cylinder in turbulent cross flow. The turbulence length-scale was found to be equal 3.7y up to a distance 0.05δ and then constant equal to 0.185δ up to the edge of the boundary layer (wherey is the distance from the surface and δ is the boundary layer thickness).

The model predictions for heat transfer coefficient, skin friction factor, velocity and kinetic energy profiles were in good agreement with the data. The model was applied for Re ≤250,000 and Tu≤0.07.


Heat Transfer Boundary Layer Transfer Coefficient Heat Transfer Coefficient Turbulence Model 
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Constants in the turbulence kinetic energy equation


Constants in the turbulence length-scale equation

\(C_{f_x } \)

Skin friction coefficient\(\frac{{\tau _w }}{{\tfrac{1}{2}\varrho u_\infty ^2 }}\) atx


Cylinder diameter


Dimensionless flow streamwise velocityu/u e


Turbulence kinetic energy =1/2 the sum of the squared three fluctuating velocities


Dimensionless turbulence kinetic energyk/u e /2


Dimensionless temperature (T−T w )/(TT w )


Turbulence length-scale


Turbulence length-scale at outer region


Nusselt number




Prandtl number


Turbulent Prandtl number


Constant in the turbulence kinetic energy equation


Cylinder radius


Reynolds number ϱuD


Reynolds number ϱux


Reynolds number of turbulence


Mean temperature


Mean temperature at ambient


Mean temperature at surface


Cross flow turbulence intensity,\(\sqrt {u'^2 /u_\infty } \)


Mean flow streamwise velocity


Fluctuating streamwise velocity


Mean flow velocity at far field distance


Mean flow velocity at ambient


Friction velocity\( = \sqrt {\tau _w /\varrho } \)


Mean velocity normal to surface


Dimensionless mean velocity normal to surface


Distance along the surface


Distance normal to surface


Dimensionless pressure gradient parameter\( = - \frac{{x_1 }}{{\varrho u_e^2 }}\left( {\frac{{dp}}{{dx_1 }}} \right)\)


Boundary layer thickness atu=0.9995u e


Transformed coordinate iny direction


Fluid molecular viscosity


Turbulent viscosity


μ+μ t


Fluid molecular viscosity at ambient


Kinematic viscosityμ/ϱ




Density at ambient


Wall shear stress


Wall shear stress at zero free stream turbulence


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Copyright information

© Martinus Nijhoff Publishers 1987

Authors and Affiliations

  • Mounir B. Ibrahim
    • 1
  1. 1.Mechanical Engineering Department, Fenn College of EngineeringCleveland State UniversityClevelandUSA

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