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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
Article

Abstract

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.

Keywords

Heat Transfer Boundary Layer Transfer Coefficient Heat Transfer Coefficient Turbulence Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

µ,CD

Constants in the turbulence kinetic energy equation

C1,C2

Constants in the turbulence length-scale equation

\(C_{f_x } \)

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

D

Cylinder diameter

F

Dimensionless flow streamwise velocityu/u e

k

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

K

Dimensionless turbulence kinetic energyk/u e /2

I

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

l

Turbulence length-scale

le

Turbulence length-scale at outer region

NuD

Nusselt number

p

Pressure

Pr

Prandtl number

Prt

Turbulent Prandtl number

Prk

Constant in the turbulence kinetic energy equation

R

Cylinder radius

ReD

Reynolds number ϱuD

Rex

Reynolds number ϱux

RK

Reynolds number of turbulence

T

Mean temperature

T

Mean temperature at ambient

Ts

Mean temperature at surface

Tu

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

u

Mean flow streamwise velocity

u

Fluctuating streamwise velocity

ue

Mean flow velocity at far field distance

u

Mean flow velocity at ambient

u*

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

v

Mean velocity normal to surface

V

Dimensionless mean velocity normal to surface

x,x1

Distance along the surface

y

Distance normal to surface

β

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

δ

Boundary layer thickness atu=0.9995u e

η

Transformed coordinate iny direction

μ

Fluid molecular viscosity

μt

Turbulent viscosity

μeff

μ+μ t

µ

Fluid molecular viscosity at ambient

ν

Kinematic viscosityμ/ϱ

ϱ

Density

ϱ

Density at ambient

τw

Wall shear stress

τw,0

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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