Based on the theory of similarity analysis and the analogy between momentum and energy transport equations, the temperature scalings have been derived for forced convection turbulent boundary layers. These scalings are shown to be able to remove the effects of Reynolds number and the pressure gradient on the temperature profile. Furthermore, using the near-asymptotic method and the scalings from the similarity analysis, a power law solution is obtained for the temperature profile in the overlap region. Subsequently, a composite temperature profile is found by further introducing the functions in the wake region and in the near-the-wall region. The proposed composite temperature profile can describe the entire boundary layer from the wall all the way to the outer edge of the turbulent boundary layer at finite Re number. The experimental data and direct numerical simulation (DNS) data with zero pressure gradient and adverse pressure gradient are used to confirm the accuracy of the scalings and the proposed composite temperature profiles. Comparison with the theoretical profiles by Kader (1981, “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 24, pp. 1541–1544; 1991, “Heat and Mass Transfer in Pressure-Gradient Boundary Layers,” Int. J. Heat Mass Transfer, 34, pp. 2837–2857) shows that the current theory yields a higher accuracy. The error in the mean temperature profile is within 5% when the present theory is compared to the experimental data. Meanwhile, the Stanton number is calculated using the energy and momentum integral equations and the newly proposed composite temperature profile. The calculated Stanton number is consistent with previous experimental results and the DNS data, and the error of the present prediction is less than 5%. In addition, the growth of the thermal boundary layer is obtained from the theory and the average error is less than 5% for the range of Reynolds numbers between and when compared with the empirical correlation for the experimental data of isothermal boundary layer conditions.
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Research Papers
Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers
Xia Wang,
Xia Wang
Department of Mechanical Engineering,
e-mail: wang@oakland.edu
Oakland University
, Rochester, MI 48309
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Luciano Castillo,
Luciano Castillo
Department of Mechanical Engineering, Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute
, Troy, NY 12180
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Guillermo Araya
Guillermo Araya
Department of Mechanical Engineering, Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute
, Troy, NY 12180
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Xia Wang
Department of Mechanical Engineering,
Oakland University
, Rochester, MI 48309e-mail: wang@oakland.edu
Luciano Castillo
Department of Mechanical Engineering, Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute
, Troy, NY 12180
Guillermo Araya
Department of Mechanical Engineering, Aerospace and Nuclear Engineering,
Rensselaer Polytechnic Institute
, Troy, NY 12180J. Heat Transfer. Feb 2008, 130(2): 021701 (17 pages)
Published Online: February 4, 2008
Article history
Received:
June 13, 2006
Revised:
May 30, 2007
Published:
February 4, 2008
Citation
Wang, X., Castillo, L., and Araya, G. (February 4, 2008). "Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers." ASME. J. Heat Transfer. February 2008; 130(2): 021701. https://doi.org/10.1115/1.2813781
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