Mathematical modeling of high-temperature nonlinear processes of heat transfer - Слесаренко, Анатолий Павлович; Венгеров, Игорь Романович (Eastern-European Journal of Enterprise Technologies, 2013)
Mathematical modeling of thermal conditions of massifs during underground fires is the theoretical basis for engineering calculations, planning and firefighting. The article suggests approximate analytical and numerical methods of mathematical modeling of high-temperature heating of a semi-infinite massif taking into account the dependence of its thermalphysic parameters on temperature. We have examined four mathematical models based on the first and third boundary problems of nonlinear heat transfer with constant and variable temperatures of the heating medium (gas fire). We have used the method of approximation of unsteady temperature fields, the method of stratification of the decision area, and the method of chronostratification (partitioning of process on the final time intervals). We have obtained the solutions in forms, which can reduce them “to the number” with a PC; we have estimated the error of the approximate methods, which is less than 5%. The results can be used to improve the reliability, efficiency and quality of engineering calculations in mining industry.