The use of optimization techniques for numerical analysis of temperature fields in the quartz optical fiber billet

In this paper a procedure is proposed for determination of heat load under high temperatures. The procedure proposed allows finding temperature of a surface heated by a gas burner flame which is necessary to assure the accuracy of further research of temperature fields and stress-strain state of products. The discussed problem is about determining surface temperature of an optical fiber billet made of quartz glass placed within heating zone of a gas burner and also further research of temperature fields within the billet in course of a production process. Method of determining surface temperature of a billet in a gas burner heating zone includes conducting an experiment to measure temperature in a number of points away from the burner flame and subsequent solving of an optimization problem to calculate the temperature of a surface within heating zone. In the course of experiment surface temperature of a tube was measured by two thermocouples at a distance from the heating zone which was followed by solving an optimization problem. As the target function, sum of squares of deviations of calculated temperature values at given points from the observed experimental values was taken. The developed method has been tested on a series of test problems. The uniqueness of the solution of optimization problem was confirmed by ‘descending’ from a set of different initial values. Temperature fields within billet of a quartz optical fiber heated by a uniformly moving gas burner were examined. To solve a non-stationary heat conduction problem, finite elements method has been used while the optimization problem has been solved by the Golden section method.