Fluid Dynamics

, Volume 6, Issue 5, pp 778–785 | Cite as

Solution of the heat-transfer equation for equilibrium turbulent boundary layers when the temperature distribution of the streamlined surface is arbitrary

  • A. Sh. Dorfman


We give an approximate solution of the heat-transfer equation for equilibrium turbulent boundary layers for which the velocity distribution and the coefficient of turbulent viscosity can be described by functions of two parameters. In [1–4] equilibrium turbulent boundary layers characterized by a constant dimensionless pressure gradient were investigated. The
$$\beta = \frac{{\delta ^{* \circ } }}{{\tau _w ^ \circ }}\left( {\frac{{dP}}{{dx^ \circ }}} \right)$$
profile of the velocity defect was calculated in [4] for such layers throughout the whole range −0.5≤β≤∞, while a method was indicated in [5] for combining the defect velocity profiles with the universal profiles of the wall law, and a composite function defining the coefficient of turbulent viscosity was proposed. In this paper we construct the solution of the heat-transfer equation for equilibrium boundary layers under the assumption that the velocity distribution in the layer and the coefficient of turbulent viscosity are described by functions, obtained in [4, 5], of the dimensionless coordinateη=y/Δ, depending on two parametersβ and Re*, while the turbulent Prandtl number Prt is either constant or is also a known function of η and the parametersβ and Re*. The temperature of the surface Tw(x) is assumed to be an arbitrary function of the longitudinal coordinate and the solution is constructed in the form of series in the form parameters containing the derivatives of Tw(x). These form parameters are similar to those used in [6–9] to construct exact solutions of the equations of the laminar boundary layer.


Boundary Layer Velocity Distribution Prandtl Number Form Parameter Turbulent Viscosity 
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Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • A. Sh. Dorfman
    • 1
  1. 1.Kiev

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