The concept of retardation of phase and energy propagation, borrowed from analyses used in physical optics, is applied to the analysis of heat conduction in solids. Analogies between physical optics and heat conduction in solids are pointed out and these are given a general interpretation in terms of a superposition of traveling waves. It is shown that interference effects may occur in the propagation of heat in a solid. Some of the notions of physical optics are then applied to the analysis of heat conduction in solids. A simple experiment demonstrating interference of traveling waves in heat conduction is analyzed. An analog to the Kirchhoff formula, exhibiting the role of diffraction effects in the conduction of heat in solids, is derived.
Sommerfeld's multiple -valued solution of Maxwell's equations is applied to the diffraction of a plane wave by a flat conducting strip and a circular conducting channel. Solutions are derived valid for any given wavelength and in closed form. The method of applying Sommerfeld's procedure indicates how Sommerfeld's solution can be generalized.
This paper shows how Sommerfeld's multiple -valued function method can be extended to solve Fresnel three -dimensional diffraction problems for a point radiation source and perfect conductors in two different configurations: a semi-infinite plane and a circular disc. Characteristically, the solutions are in closed form, can be directly calculated and are without any restriction on the relative sizes of radiation wavelength and scatterer.
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