Calculation of convection coefficient during steel hardening of axisymmetric probes in thermal oils

Abstract

Abstract The paper presents the results of the convection coefficient during the process of two-dimensional axisymmetric steel hardening of in two different thermal oils used in the area of thermal treatment of steel. One thermal oil was Isorapid 277 HM preheated to the set temperature, and the other one was Marquench 722 also preheated to the set temperature. The experimental work setup consists of six quenches, three dimensionally different axisymmetric probes in two different thermal oils. Steel hardening was done under strictly controlled conditions: heating the sample to the tempering temperature of most steels in a nitrogen atmosphere, vertical slow immersion of the test sample in the opposite flow of thermal oil. The temperature of the thermal oil was kept constant, stopping the test sample in the sample steel hardening area and non-stationary data collection until thermal oil equilibrium temperature with interruption of data collection. The data collection rate was two probes/second in parallel from four points located within the test cylinder. Three measuring points were located directly below the surface of the cylinder distributed along the height of the cylinder, while the fourth one was in the centre of gravity of the cylinder. Time-measured temperature values in the indicated four points of each probe were written in a text file. The set mathematical model describes the non-linear two-dimensional axisymmetric non-stationary heat transfer through the cylinder. The set mathematical model requires the inverse solution of the heat conduction problem, that is, ill-conditioned problems, so the solution of the problem came down to a sufficiently accurate estimation of the unknown convection coefficient imposed on the outer surface of the probe. The chosen solution algorithm was the one from previously published works. The solution algorithm was based on a iterative combination of the finite element method (FEM), while the second part of the solution algorithm is the Levenberg Marquardt method (LMM) from the line of optimization deterministic algorithms, which takes the calculation results of the temperatures at the points of the computational domain from the FEM, and for comparison, that is, error minimization, using the experimental results of temperature measurements at the same place.