Wave concepts in the theory of heat
Abstract
The incompleteness of the fundamental solution to the heatconduction equation is discussed along with the paradox of an infinite heat propagation velocity. Analysis of the isotherm behaviour and use of Green's theorem lead to a general nonlinear wave equation in which the speed of isotherm propagation along the normal is used as an experimental parameter. The relationship between this speed and thermal diffusivity is identified. The different particular cases of this wave equation are studied. Some wave equation solutions are shown to correspond to those of the nonlinear parabolic equation. The derivation of the wave heat conduction equation is given from the point of view of molecular kinetic considerations. The concept of time relaxation is generalized using the Maxwell method and taking into account the correlation between components of a heat velocity of atoms of molecules.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 February 1976
 DOI:
 10.1016/00179310(76)901101
 Bibcode:
 1976IJHMT..19..175B
 Keywords:

 Conductive Heat Transfer;
 Isotherms;
 Propagation Velocity;
 Wave Equations;
 Wave Propagation;
 Kinetic Theory;
 Nonlinear Equations;
 Parabolic Differential Equations;
 Temperature Distribution;
 Thermal Diffusivity;
 Fluid Mechanics and Heat Transfer