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Research Papers: Forced Convection

Power Law Velocity and Temperature Profiles in a Fully Developed Turbulent Channel Flow

[+] Author and Article Information
Abu Seena

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Koreaabuseena@kaist.ac.kr

Noor Afzal

Faculty of Engineering, Aligarh Muslim University, Aligarh 202002, Indianoor.afzal@yahoo.com

J. Heat Transfer 130(9), 091701 (Jul 03, 2008) (11 pages) doi:10.1115/1.2944239 History: Received April 14, 2007; Revised November 07, 2007; Published July 03, 2008

The power law temperature distribution in a fully developed turbulent channel flow for large Peclet numbers has been proposed in the present work. The analysis of the power law velocity profile in a fully developed mean turbulent channel flow would be used for carrying out the analysis of the power law temperature profile. The Reynolds mean thermal energy equation in a fully developed mean turbulent channel flow has been analyzed. The mean turbulent thermal flow is divided in the inner and outer thermal layers that have been matched by Izakson–Millikan–Kolmogorov hypothesis to get the power law temperature profiles and the power law heat transfer law in the overlap region, in addition to traditional log laws for temperature profiles and heat transfer. It has been shown that the envelope of the heat transfer power law gives the heat transfer log law. Further, it is shown that the temperature power law index and prefactor are functions of the friction Peclet number, as well as function of an alternate variable, the nondimensional friction temperature. It is shown that for large Peclet numbers the power law temperature profile is equivalent to the log law temperature profile. The direct numerical simulation velocity profile data of fully developed turbulent flow provide good support for the power law temperature profile theory.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Log law. The velocity profiles for fully developed channel flow in the inner and outer layers’ variables in the semilog plot from the DNS data of Iwamoto , Abe , and Hoyas and Jimenez, and experimental data of Zanoun for various values of Reynolds numbers

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Figure 2

Power law. The velocity profiles for fully developed channel flow in the inner and outer layers’ variables in the log-log plot from the DNS data of Iwamoto , Abe , and Hoyas and Jimenez, and experimental data of Zanoun for various values of Reynolds numbers

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Figure 3

The dependence of the power law constants α and C for power law velocity profile on the Reynolds numbers from the data of Iwamoto , Abe , Hoyas and Jimenez, and Zanoun

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Figure 4

Log law. The temperature profile of the DNS data of Abe for various Reynolds numbers

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Figure 5

Power law. The temperature profile of the DNS data of Abe for various Reynolds numbers

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Figure 6

The dependence of the power law constants αt and Ct for power law temperature profile on Reynolds numbers from the data of Abe

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