Thermal wave reflection and refraction at a plane interface: Twodimensional geometry
Abstract
A theoretical study of thermal waves generated by a line timeperiodic heat source in a medium composed of two halfspaces of different thermal properties is presented. The standard method of solution to this problem consists in the application of a Fourier transform with respect to the variable parallel to the interface, which is then inverted numerically. We propose to derive modified solutions using the deformation of the integration contour in the complex plane of the transform variable. The modification of the contour is adopted from the Cagniardde Hoop method which is used in elastic wave propagation. The main advantage of the obtained solutions is the feasibility of their physical interpretation. In particular, it is shown that geometrical ray propagation and Snell's law can be obtained in the highfrequency approximation, but not as a general rule. It is also found that when the heat source is located in a less heatconductive medium the structure of the temperature fields changes dramatically beyond the critical angle of incidence. This suggests a thermal analogy with the total reflection phenomenon. The analytical formulas derived for the temperature fields and the heat fluxes allow easy numerical computations, and can be used for the interpretation of experimental data.
 Publication:

Physical Review B
 Pub Date:
 April 2002
 DOI:
 10.1103/PhysRevB.65.134209
 Bibcode:
 2002PhRvB..65m4209S
 Keywords:

 66.70.+f;
 44.05.+e;
 44.10.+i;
 44.30.+v;
 Nonelectronic thermal conduction and heatpulse propagation in solids;
 thermal waves;
 Analytical and numerical techniques;
 Heat conduction;
 Heat flow in porous media