Warming of Monolithic Structures in Winter

The present work attempts to develop a mathematical model for calculating the heat transfer coefficient of the fence of monolithic structures erected in winter. The urgency and, at the same time, the practical significance of the research lies in the fact that to date no simple, effective tool has been developed to ensure the elimination of the unfavorable thermally stressed state of a structure's concrete from maximum equalization of temperatures across its cross-section. The main problem for concrete is a high temperature which leads to a sharp decrease in the quality of erected structures due to developing cracks. This paper based on the well-known Newton's law and its differential equation demonstrates the formula of concrete cooling and the analysis of its proportionality coefficient. Based on the literature analysis, it is established that the proportionality coefficient is determined by the thermophysical properties of concrete, the size and shape of the structure, and the intensity of its heat exchange with the surrounding medium. A limitation was used on the temperature gradient over the section of the monolithic structure to derive a formula for calculating the reduced heat transfer coefficient of a concrete fence. All mathematical calculations are given for cooling monolithic constructions in the form of plates. At the end of the work an example is given for the calculation of the required reduced heat transfer coefficient for the fence ensuring compliance with the permissible concrete temperature gradient. (paper)