Analysis of the heat transfer for processes of the cylinder heating in the heat-treating furnace on the basis of solving the inverse problem

Abstract

Abstract This paper presents results of experimental test concerning heating of a cylinder in the furnace for heat and thermochemical treatment. Tests were conducted for heating up to temperature of 550\u202f°C, what corresponds to nitriding processes. Calculation model including Chebyshev polynomials enabling determination of temperature distribution in the cylinder is presented. Two variants of calculation model were examined; they differ in terms of the assumed boundary condition. Analysis of regularization of the solution to the inverse problem done by the change of time step (self-regularization) was made. Based on the solution of the non-linear inverse problem for the heat equation and on the gas temperature measurement read from the furnace retort, temperature distributions on the boundary of the cylinder, combined radiation convection heat transfer coefficients (CHTC) and heat flux on the surface of the cylinder were calculated. Due to a great variability of temperature for the processes under consideration, the calculation model includes the variation of the heat conduction coefficient and of the specific heat of the material the cylinder is made of depending on temperature change. Five heating processes differing in parameters of heating rate were analysed. Impact of measurement errors on distributions of temperature on the edge of the cylinder and of the CHTC was determined. Obtained temperature distributions in the element were verified by a check measurement. Maximal error of the obtained results did not exceed 0.5%. Data presented herein give practical knowledge enabling supervising the temperature distribution in the cylindrical element being processed. These problems are of crucial meaning for processes of heat and thermochemical treatment due to formation of proper surface and subsurface layers.