Approximate analytical method for calculating the heating process of concrete structures in heating formwork

Abstract

The use of electric heating of concrete during construction in winter makes it possible to create an optimal thermal regime in which the hardening process takes place, and to obtain a structure of the required quality. When developing a system for automatic control of the heating process, it is necessary to determine the law of regulating the power of heaters. This article presents a method for calculating the thermal heating regime of concrete structures in heating formwork, the essence of which is to reduce the boundary value problem of thermal conductivity to a system of equivalent integral equations. To solve this problem, a theoretical study was carried out, a theoretical study of the heat transfer process in concrete structures heated during winter concreting was carried out, and a mathematical description of this process was presented in the form of a system of differential equations. After the transformations of the above system of equations and the application of the Green function of the second kind to it for the plate and rod, an approximate solution of the equivalent equation was obtained. As a result of the application of the asymptotic method to the solution of the integral equation, an analytical solution of the problem under consideration is obtained. The resulting solution makes it possible to determine the temperature fields on the concrete surface, as well as the value of the specific heat flux from electric heaters. In order to automate the process of performing the thermal calculation of heating concrete structures with the help of heating forms, a program for calculating temperature fields in heating forms has been developed based on the solution obtained, which makes it possible to effectively solve the tasks of monitoring and controlling the concrete hardening process. The developed program makes it possible to calculate temperature fields not only at constant heater power, but also when it changes with the help of regulators. The presented method of thermal calculation with a hardware and software complex for regulating the power of electric heaters allows solving a fairly wide range of tasks related to maintaining a constant temperature field.