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Research Papers: Forced Convection

Heat Flux Vector Potential in Convective Heat Transfer

[+] Author and Article Information
Peter Vadasz

Professor
Fellow ASME
Department of Mechanical Engineering,
Northern Arizona University,
P.O. Box 15600,
Flagstaff, AZ 86011-5600
e-mail: peter.vadasz@nau.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 1, 2016; final manuscript received August 24, 2017; published online January 17, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(5), 051701 (Jan 17, 2018) (2 pages) Paper No: HT-16-1241; doi: 10.1115/1.4038553 History: Received May 01, 2016; Revised August 24, 2017

The heat function concept introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) for two-dimensional (2D) heat transfer is being extended in this note to three dimensions. It is shown that a heat flux vector potential exists and can be used in three-dimensional (3D) heat convection problems. It is further shown that this heat flux vector potential degenerates to the heat function introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) when the heat convection is two-dimensional.

Copyright © 2018 by ASME
Topics: Convection , Heat flux , Heat
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References

Kimura, S. , and Bejan, A. , 1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919. [CrossRef]
Morega, A. L. M. , and Bejan, A. , 1993, “Heatline Visualization of Forced Convection Laminar Boundary Layers,” Int. J. Heat Mass Transfer, 36(16), pp. 3957–3966. [CrossRef]
Kaluri, R. S. , Basak, T. , and Roy, S. , 2009, “Bejan's Heatlines and Numerical Visualization of Heat Flow and Thermal Mixing in Various Differentially Heated Porous Square Cavities,” Numer. Heat Transfer, Part A, 55(5), pp. 487–516. [CrossRef]
Costa, V. A. F. , 2006, “Bejan's Heatlines and Masslines for Convection Visualization and Analysis,” ASME J. Heat Transfer, 59(3), pp. 126–145.
Brosa, U. , and Grossmann, S. , 2002, “Hydrodynamic Vector Potentials,” Eur. Phys. J. B, 26(1), pp. 121–132.

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