1 DOI: THERMAL CONDUCTIVITY OF OXIDE SCALE AND ITS COMPONENTS IN THE RANGE FROM 0 ºC TO 1300 ºC: GENERALIZED ESTIMATES WITH ACCOUNT FOR MOVABILITY OF PHASE TRANSITIONS Emmanuil Beygelzimer 1 , Yan Beygelzimer 2 1 OMD-Engineering LLC, Dnipro, Ukraine 2 Donetsk Institute for Physics and Engineering named after A.A. Galkin, National Academy of Sciences of Ukraine, Kyiv, Ukraine *Corresponding author: emmanuilomd@gmail.com, tel.: +380 (50) 368-63-42, 49000, Volodymyr Monomakh Street, 6 of. 303, Dnipro, Ukraine. ABSTRACT The data of different authors on the thermal conductivity of wüstite Fe1-xO, magnetite Fe3O4, hematite Fe2O3 and pure iron are systematized. The generalized values are described by piecewise smooth functions containing as varying parameters the temperatures of magnetic and polymorphic (for iron) transformations as well as the thermodynamic stability boundary (for wüstite). At polymorphic transformation a finite break of the thermal conductivity function is envisaged, at other critical points only a break of its temperature derivative is acceptable. The proposed formulas are presented in two forms: the general form that allow varying the values of critical temperatures and the particular form corresponding to their basic values: the boundary of thermodynamic stability of wüstite - 570 ºС, the Curie points of magnetite - 575 ºС, of hematite - 677 ºС, of iron – 770 ºС and polymorphic transformation temperature of iron - 912ºС. To calculate the thermal conductivity of oxide scale as a whole, it is proposed to take into account separately metallic iron and composite matrix of iron oxides. Model computations using the proposed formulas shows that the true thermal conductivity of oxide scale (without pores), depending on the temperature may be from 3 to 6 W·m -1 ·K -1 in the absence of metallic iron and up to 15 W·m -1 ·K -1 if free iron is released in the eutectoid decay of wüstite. The effective thermal conductivity of oxide scale, taking into account its real porosity, may be lower by 15-35%. The obtained dependencies are recommended for use in mathematical simulation of production and processing of steel products in the presence of oxide scale on their surface. Keywords: thermal conductivity; wüstite; magnetite; hematite; oxide scale; Curie point INTRODUCTION This report completes a series of publications of the authors on the mathematical description of the thermophysical properties of wüstite Fe1-xO (x ≈ 0.05...0.15), magnetite Fe3O4, hematite Fe2O3, and metallic iron Fe, as well as oxide scale in general in the temperature range from 0 °С to 1300 °С. The thermal expansion coefficient [1], density [2] and heat capacity [3] have been described earlier. In this paper, we look at the thermal conductivity coefficient, which, as usual, is understood as the coefficient of proportionality between the vector of heat flux density and the temperature gradient. When approximating the known data on thermophysical properties, the authors set themselves two main tasks (see [1]): 1) to consider the movability of phase transitions in order to use it for adaptation of mathematical models, and 2) to generalize the results of various studies in order to recommend the most characteristic values of the properties at different temperatures for a given substance. The first task was solved by including the temperatures of phase transitions in the approximating functions as varying parameters. The second problem (generalization) was solved by choosing the type of approximating function and the coordinates of the reference points through which the graph of this function should pass. In this respect, an essential feature of the studies of thermal conductivity presented in this article is related to the fact that the empirical data on this characteristic have the largest scatter among all thermophysical properties. For example, for any of the considered iron oxides, the data of different authors on the thermal conductivity may differ by 2-4 times. In this regard, the choice of coordinates of reference points for the thermal conductivity coefficient is to a large extent conditional, because it is possible that new empirical data that will be obtained in the future, or the thermal conductivity values in some specific conditions may not correspond to the choice made by the authors. However, the authors hope that for each of the considered substances the chosen type of approximating functions correctly reflects the nature of the dependence of thermal conductivity on temperature, and the accumulation of new empirical data may require only a correction of the coordinates of reference points, but not a revision of the approximating functions. METHODS Approximation of data on the thermal conductivity of the structural components of oxide scale was carried out according to the general methods described in detail in the first part [1]. In accordance with these methods, the critical temperatures are included in the approximating functions in the form of formal parameters. Such critical temperatures are taken as: Curie points (for Fe3O4, Fe2O3, Fe), polymorphic transformation temperature (for Fe), thermodynamic stability boundary (Chaudron point for Fe1-xO). The real ranges of movability of these critical temperatures and their basic values, adopted for a particular form of approximating formulas, are given in [1]. As a key assumption, it is considered that if the critical temperature changes within the real range of its movability, the values of thermal conductivity at this critical point and at two distant reference points on different sides of it remain unchanged. In other words, it is assumed that as the critical point changes, the temperature dependence graph of the thermal conductivity shifts parallel to the temperature axis, remaining fixed at the extreme reference points. Accordingly, when the critical temperature varies, the other parameters of the approximating functions change automatically. Conjugation of approximating formulas between intervals separated by critical points was performed taking into account the accepted "behavior model" of thermal conductivity in critical states [1]: with a break of the function during the polymorphic transformation and with a break of the first derivative function (but without breaking the thermal conductivity coefficient itself) at the Curie points and at the boundary of thermodynamic stability. The type of approximating formulas was chosen according to the value of specific thermal resistance k [m‧K·W -1 ], the inverse of the thermal conductivity coefficient λ [W·m -1 ·K -1 ] (it turned out to be more convenient, the idea was borrowed from [5].): = 1  (1) Therefore, the data on the thermal conductivity coefficient known from the technical literature was first converted into the values of specific thermal resistance and only then approximated. Accordingly, the ordinates of all reference points for the approximating function were expressed in terms of the thermal resistance. The reverse recalculation into the thermal conductivity coefficient was performed at the very end after obtaining the approximating function for the resistivity. Taking into account the large scatter of currently available empirical data (see Introduction), the coordinates of the reference points chosen by the authors should be considered as "basic". In the case of new data, the values of these coordinates can be adjusted without changing the general formulas proposed. When processing the information on iron oxides we focused on the data obtained on polycrystalline samples, and with minimal porosity (or recalculated to zero porosity, as, for example, in [4]). Data on single crystals were used as additional information.