Analysis of heating time and of temperature distributions for cylindrical geometry with the use of solution to the inverse problem

Institute of Thermal Engineering, Poznan University of Technology, 60-965 Poznan, Poland

^* Corresponding author: magda.joachimiak@put.poznan.pl

Abstract

Changes in heating time of a cylinder in the furnace for thermal and thermochemical treatments depending on the given heating rate is analysed in this paper. Temperature distributions from the axis to the boundary of the cylinder were determined based on solving non-stationary and non-linear inverse problem for the heat equation. Differences between the temperature on the boundary and along the cylinder axis for processes with the given heating rates from 5 to 10ᵒC/min were calculated. Twofold increase in the heating rate allowed the heating time to be reduced significantly. Increase in the heating rate had no impact on the difference between the temperature on the boundary and on the axis of the cylinder and on the quantity of energy being consumed by heating elements.