periodic variations of the temperature distribution in a medium.
Temperature waves are due to periodic fluctuations in the heat fluxes entering the medium, that is, to the variability of the heat sources. Temperature waves experience strong attenuation during propagation. Significant dispersion—that is, a substantial frequency dependence of velocity—is characteristic of temperature waves.
The attenuation factor of temperature waves is usually approximately 2π/λ, where λ is the wavelength. For a monochromatic plane temperature wave propagating along a thermally insulated rod of constant cross section, the relation of λ to the oscillation period τ and to the thermal diffusivity K is given by the equation . Here, the velocity v of the wave crests is . Thus, the shorter the oscillation period, or the wavelength, the more rapidly temperature waves propagate and attenuate over short distances. The depth of penetration of a plane temperature wave, defined as the distance at which temperature fluctuations decrease by a factor that is, the shorter the period, the smaller the depth of penetration. For example, the depth of penetration of diurnal temperature fluctuations into the ground is smaller by a factor of nearly 20 than the depth of penetration of seasonal fluctuations.
In engineering, temperature waves are taken into account in calculations of the thermal conductivity of the walls of buildings, the protective inner linings of furnaces, the blocks of internal combustion engines, and elsewhere. In physics, the study of temperature waves is one method of determining the thermal diffusivity, specific heat, and other thermal characteristics of materials. The temperature-wave method is especially convenient for measuring the characteristics of pure substances at low temperatures.
REFERENCECarlslaw, H. S., and J. Jaeger. Teploprovodnosl’ tverdykh tel. Moscow, 1964. (Translated from English.)
I. P. KRYLOV