Nusselt Number Correlations for Turbulent Natural Convection Flows Using Asymptotic Analysis of the Near-Wall Region

[+] Author and Article Information
C. Balaji1

Institute of Thermo-Fluid Dynamics, Hamburg University of Technology, Denickestrasse 17, D-21073 Hamburg, Germany

M. Hölling, H. Herwig

Institute of Thermo-Fluid Dynamics, Hamburg University of Technology, Denickestrasse 17, D-21073 Hamburg, Germany


Corresponding author.

J. Heat Transfer 129(8), 1100-1105 (Dec 01, 2006) (6 pages) doi:10.1115/1.2737485 History: Received February 14, 2006; Revised December 01, 2006

In this paper, we propose a general methodology by which a universal temperature profile, derived by matching temperature gradients in the overlap region of the wall layer and the core layer, that is valid for high Rayleigh number flows, can be recast into a correlation for the Nusselt number. We then evaluate its adequacy for three types of flows: (a) fully developed flows (e.g., the infinite channel), (b) developing flows (e.g., the vertical flat plate boundary layer), and (c) complex flows (e.g., Rayleigh-Bénard convection and the differentially heated square cavity). The correlation for the Nusselt number, in general, contains a logarithmic term, usually missing in earlier studies, with which we are able to match existing direct numerical simulations or experimental data very well for both fully developed and complex flows.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Two layer structure of the near wall region of high Rayleigh number flows showing the viscous sub-layer, overlap, and the fully turbulent outer layers

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Figure 2

Schematic showing turbulent natural convection from an infinite vertical channel with the left wall being heated and the right wall being cooled. Also shown are typical velocity and temperature distributions across the channel.

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Figure 3

Schematic depicting turbulent natural convection from a hot vertical flat plate losing heat to quiescent air. Also shown are velocity and temperature profiles at an axial location x.

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Figure 4

High resolution plot demonstrating the procedure to determine the constants in the Nusselt number correlation for the vertical flat plate

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Figure 5

Nusselt-Rayleigh plot for the vertical flat plate at high Rayleigh numbers showing comparison of Eq. 23 with the results reported in the literature

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Figure 6

Comparison of Nu∕Ra1∕3 versus Ra from various studies for turbulent natural convection from a square cavity (high resolution plot)



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