Численно-аналитический метод расчета температурного поля полуограниченного тела с использованием показательных функций

Abstract

Background: The temperature of solid bodies participating in heat exchange with a gas or a liquid environment at Fourier's numbers below 0,05 changes only in the surface layer. The thickness of this layer changes in time, therefore, calculation of temperature fields of these bodies is rather difficult. It is quite urgent to solve the problem of calculating temperature fields of semi-limited bodies for modeling the initial stage of intensive heating (cooling) of the equipment and protections of heat power installations. Earlier, analytical or numerical methods were applied to calculation of temperature fields with a mobile border of thermal aggitation. The former ones had insufficient accuracy in solving real nonlinear problems of heat conductivity, and the latter − were extremely labor-consuming. In recent years many research teams have been developing more effective numerical and analytical methods. Materials and Methods: In order to solve the differential equation of heat conduction with boundary conditions of the IIId kind, we used the numerical method of finite differences and numerical-analytical method. Results: We have developed formulas for calculation of the parameters of the exponential function describing the distribution of the surface layer temperatures. By the initial and end conditions of heat exchange, we analytically determined the functions of estimated time end. The calculation of the temperature field dynamics was reduced to the numerical solution of the differential equation that simplifies the calculation procedure. We also improved the technique of conjugate heat exchange calculation within the estimated period of time at high temperature growth rates of the  «Вестник ИГЭУ» Вып. 2 2016 г.  ФГБОУВО «Ивановский государственный энергетический университет имени В.И. Ленина» 2 surface under heating. Calculations were made to assess the calculation method efficiency. The comparatively simple numerical-analytical method of temperature fields of semi-limited bodies was specified. Conclusions: The study of this method has shown that the addition of a mathematical description of additional conditions improves the accuracy of calculation of temperatures and their gradients.