Generalization of the Fourier problem of temperature waves in half-space

The problem of asymptotic fluctuations of temperature and moisture content in a half-space whose boundary is blown by an air flow with a temperature varying according to the harmonic law is solved by the method of complex amplitudes. The material filling the half-space consists of a solid base (capillary-porous body) and water. The well-known Fourier solution for temperature fluctuations in half-space in the absence of moisture and under the boundary conditions of heat exchange of the first kind is generalized to the case of a wet material under the boundary conditions of Newton for temperature and Dalton for moisture content. The results of the work can be used in geocryology to model seasonal changes in the thermophysical state of frozen rocks and soils, in the theory of building structures to study the thermal regime of indoor premises with fluctuations in ambient temperature, in the theory of drying by electromagnetic radiation to study the processes of heat and mass transfer in oscillating modes.