SOLUTION OF GEOCRYOLOGY PROBLEMS ON THE BASIS OF FORMULAS FOR DECAYING HARMONIC WAVES OF HEAT AND MASS TRANSFER IN A HOMOGENEOUS HALFSPACE

An initial boundary value problem has been formulated within the A. V. Luikov theory for calculating temperature and moisture content fi elds in a homogeneous halfspace whose boundary is in a state of heat and mass exchange with an air medium. The halfspace material is made up of a hard substrate (a capillary-porous body) and water, the heat transfer between the halfspace boundary and the air medium occurs according to the Newton law, and the mass transfer occurs according to the Dalton law. In the initial state, the air medium and the material have an identical temperature, and the densities of the heat and moisture fl ows on the boundary separating them are equal to zero. At the instant of time assumed as the computing origin, the air temperature begins to make minor harmonic oscillations near its original value. It has been shown that with the passage of time, a heat and mass transfer regime will set in inside the material, under which temperature and moisture content fi elds have the form of decaying harmonic waves. For a mathematical model of partial-type heat and mass transfer (the movement of moisture of the surface only occurs due to a moisture content diff erential, and the transformation of water into steam only occurs on the surface), a dependence of the penetration depth and phase velocity of these waves on the values assigned under the problem conditions and determining the process has been obtained. The constructed solution and the resulting conclusions are the extension of Fourier′s investigations described in the literature, that refer to a situation when the halfspace material does not contain moisture and, according to a harmonic law, there is variation in the temperature of the material′s surface rather than in the air temperature. The results of the investigation can be used in geocryology as a theoretical tool in simulating daily and annual oscillations in the soil′s thermophysical state, which is an important task for planning economic activity in the frozen rock areas
   
Author:  A. M. Afanasiev, Yu. S. Bakhracheva
Keywords:  Luikov equations, problem for halfspace, asymptotic solution, complex amplitude method, decaying harmonic waves, depth of penetration, delay time, geocryology
Page:  394