Dependence of liquid metals radiation on normalized entropy in the fifth period

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Abstract

This study presents a universal approach for describing thermal radiation of molten fifth-period d-metals (yttrium, zirconium, niobium, molybdenum, rhodium, palladium) using dimensional analysis based on Buckingham’s π-theorem. The key achievement is the reduction of complex mathematical descriptions of radiant heat flux density to a single dimensionless variable – the ratio of molar entropy to the universal gas constant (S/R).Critically, this approach significantly simplifies the analysis of radiative characteristics in liquid metals.Furthermore, the proposed methodology demonstrates remarkableuniversalityandreproducibilityacross the entire group of studied elements. The methodology involves flux normalization at a fixed S/R = 14 value, corresponding to the characteristic entropy disorder level of these metal melts. To account for temperature-dependent density variations, a reduced radiation flux is introduced, compensating for melt density changes with temperature. The logarithm of the ratio between reduced radiation flux and individual scale flux (defined for each metal at S/R = 14) follows an exponential dependence. The resulting universal correlation shows excellent consistency (R² ≥ 0.98) across all period elements, confirming its statistical significance. Predicted values calculated using this correlation agree well with both experimental measurements and approximated data, showing mean deviations of ~4.3%. Notably, the normalized scale flux exhibits periodic variations with increasing atomic number, mirroring the behavior of surface tension at melting points. This suggests a common structural-energy origin for both radiative and surface properties of molten metals. The developed approach enables reliable prediction of liquid d-metals’ emissivity in the absence of experimental data and provides a foundation for modeling complex multicomponent metallic systems. These results hold significant implications for metallurgy, materials science, and thermal physics applications, including alloy development and high-temperature process optimization.

About the authors

D. V. Kosenkov

Kazan National Research Technological University, Kazan, Russia

Email: dmi-kosenkov@yandex.ru
Kazan, Russia

V. V. Sagadeev

Kazan National Research Technological University, Kazan, Russia

Author for correspondence.
Email: dmi-kosenkov@yandex.ru
Kazan, Russia

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