A potential‐theory formulation of radiant‐heat transfer

Abstract The radiant‐heat flux in a homogeneous atmosphere constitutes an irrotational vector field. As a consequence, the flux can be represented as the gradient of a suitably‐defined radiant‐heat potential. This potential is shown to be a functional of the product of the radiant‐source function at all points in the atmosphere and an attenuation factor to allow for the absorption of the intervening medium. The formalism is independent of the choice of coordinate system. The familiar equations of radiant transfer, such as the Milne‐Schwarzschild equilibrium equation, are deducible as special cases for the particular geometry of the plane‐parallel atmosphere. Most importantly, the radiant heating at an arbitrary point is expressed as a functional of the second derivative of the Planck intensity. This radiant‐heat flow equation will form the basis for the construction of a new atmospheric radiation chart.