An equilibrium thermal wake strength parameter is developed for a two-dimensional turbulent boundary layer flow and is then used in the combined thermal law of the wall and the wake to give an approximate temperature profile to insert into the integral form of the thermal energy equation. After the solution of the integral momentum equation, the integral thermal energy equation is solved for the local Stanton number as a function of position for accelerating turbulent boundary layers. A simple temperature distribution in the thermal “superlayer” is part of the present modeling. The analysis includes a dependence of the hydrodynamic and thermal wake strengths on the momentum thickness and enthalpy thickness Reynolds numbers, respectively. An approximate dependence of the turbulent Prandtl number, in the “log” region, on the strength of the favorable pressure gradient is proposed and incorporated into the solution. The resultant solution for the Stanton number distribution in accelerated turbulent flows is compared with experimental data in the literature. A comparison of the present predictions is also made to a finite difference solution, which uses the turbulent kinetic energy—turbulent dissipation model of turbulence, for a few cases of accelerating flows.
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November 2009
This article was originally published in
Journal of Heat Transfer
Research Papers
An Integral Solution for Heat Transfer in Accelerating Turbulent Boundary Layers
James Sucec
James Sucec
Department of Mechanical Engineering,
University of Maine
, Orono, ME 04469-5711
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James Sucec
Department of Mechanical Engineering,
University of Maine
, Orono, ME 04469-5711J. Heat Transfer. Nov 2009, 131(11): 111702 (8 pages)
Published Online: August 25, 2009
Article history
Received:
December 15, 2008
Revised:
April 21, 2009
Published:
August 25, 2009
Citation
Sucec, J. (August 25, 2009). "An Integral Solution for Heat Transfer in Accelerating Turbulent Boundary Layers." ASME. J. Heat Transfer. November 2009; 131(11): 111702. https://doi.org/10.1115/1.3154649
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