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Heat Treatment
ArticleName MathConnex mathematical package for calculating the equivalent thermal conductivity of a strip coil
DOI 10.17580/chm.2021.02.08
ArticleAuthor O. B. Kryuchkov, A. V. Krokhalev, P. I. Malenko, L. G. Saranin

Volgograd State Technical University (Volgograd, Russia):

O. B. Kryuchkov, Cand. Eng., Associate Prof., Deputy Dean, E-mail:
A. V. Krokhalev, Dr. Eng., Associate Prof., E-mail:


Tula State University (Tula, Russia):
P. I. Malenko, Cand. Eng., Associate Prof., E-mail:
L. G. Saranin, Graduate Student, E-mail:


When heating complex metal loads (layered, fibrous, granular), the gas gaps in them increase the temperature difference across the charge section and lead to an increase in the duration of its heating. Optimizing the time of complex loads heating, which helps to reduce fuel consumption and improve the heated metal quality, requires knowledge of temperature fields in them, which, in turn, depend on the equivalent thermal conductivity of the complex load. For their calculations mathematical modeling can be used, which requires a highly qualified researcher. Carrying out of laboratory and experimental researches takes a lot of time and demands big material expenses, thus the received results are applicable only to a concrete charge. A number of authors give formulas for calculating the equivalent thermal conductivity of the strip coil. However, the practical use of such formulas is difficult due to the presence of difficult to determine parameters: the degree of the strip layers contact, thermal conductivity of different layers of strip and gas gaps between them, heat transfer coefficients by radiation in the gaps between layers. In this case, different formulas for calculating the equivalent thermal conductivity give signifi cantly different results. In the present work, for 20 steel strip coils with height, inner and outer diameters, respectively, 1; 0.4–0.966 m; with a strip thickness of 0.001; 0.003; 0.006 m, the number of layers per side 17; 25 and 50, for the coefficients of strip coil filling 0.70; 0.75; 0.80; 0.85; 0.90; 0.95; 0.97; 0.99, 0.999, the degrees of the strip layers contact 2.8–3.0% and different heated media (air, nitrogen, hydrogen), the reduced thermal conductivity coefficients were calculated according to various formulas using the MathConnex mathematical package (part of MathCadPro). On the basis of the conducted researches the formula for calculation of equivalent thermal conductivity of strip coils is chosen. The results of the calculation are in good agreement with the literature data, it can be used to calculate temperature fields and thermophysical parameters in layered metal loads, as well as to calculate their heating time and furnace performance.

keywords Layered metal loading, equivalent thermal conductivity, heating in atmospheres of air, nitrogen, hydrogen, heat treatment, MathConnex mathematical package (part of MathCadPro)

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