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.
Issue Section:
Forced Convection
References
1.
Kimura
, S.
, and Bejan
, A.
, 1983
, “The Heatline Visualization of Convective Heat Transfer
,” ASME J. Heat Transfer
, 105
(4
), pp. 916
–919
.2.
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
.3.
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
.4.
Costa
, V. A. F.
, 2006
, “Bejan's Heatlines and Masslines for Convection Visualization and Analysis
,” ASME J. Heat Transfer
, 59
(3
), pp. 126
–145
.5.
Brosa
, U.
, and Grossmann
, S.
, 2002
, “Hydrodynamic Vector Potentials
,” Eur. Phys. J. B
, 26
(1
), pp. 121
–132
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