This article discusses the possibility of using an unconventional method of heat treatment of a wall structure in winter. The methods of introducing concrete work at a negative outside temperature are analyzed. The basis of the article is the derivation of systems of differential equations characterizing thermal processes during concreting of a wall fragment to previously constructed sections and floor slabs. A mathematical model has been developed that describes heat transfer processes based on the differential heat equation. In compiling the mathematical model, the classical equations of thermophysics are used, which do not require proof of reliability. The article also discusses the classical boundary conditions of the first, second, third, and fourth genera. The reliability of the calculation results was estimated by the experimental method on a fragment of a concrete wall with a given shape thickness. Processing of experimental data was performed using standard methods of mathematical statistics.

The article discusses the development of a mathematical model of the thermodynamic system during winter concreting of bored piles. The processes of heat transfer based on the differential heat equation and the Stefan problem are described. A method for calculating the rationale for the parameters of the energy-saving and gentle thermal treatment of concrete using non-traditional sources of thermal energy is proposed. The solutions for using two-phase thermosyphons as heating elements are considered.

In this paper we present a mathematical model of a three-dimensional non-stationary temperature field for concrete that hardens in winter conditions. The developed mathematical model describes heat transfer processes basing on the differential heat equation. We also consider the classical boundary conditions of the I, II, III and IV kinds. We compiled a computer interpolation of the family of nomograms in the second order regression equation in order to calculate the relative theoretical strength of concrete after heat treatment.

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