Heat Flux Vector Potential in Convective Heat Transfer

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.