Determination of thermal conductivity and emissivity of electromagnetically levitated high-temperature droplet based on the periodic laser-heating method: Theory

Recently, a novel method of measuring the thermophysical properties, especially thermal conductivity, of high-temperature molten materials using the electromagnetic levitation technique has been developed by [H. Fukuyama, H. Kobatake, I. Minato, K. Takahashi, T. Tsukada, S. Awaji, Establishment of noncontact AC calorimetry of high-temperature melts using solid platinum spheres as a reference, in: Proceedings of 16th Symposium on Thermophysical Properties, CD-ROM, 2006, p. 937; H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji, Noncontact AC calorimetry of liquid silicon with suppressing convections in a static magnetic field, in: Proceedings of 16th Symposium on Thermophysical Properties, CD-ROM, 2006, p. 625], where the method was based on periodic laser-heating, and a static magnetic field was superimposed to suppress convection in an electromagnetically levitated droplet. In the present work, the periodic laser-heating method was modeled to estimate the thermal conductivity and emissivity of the electromagnetically levitated droplet using a measured parameter, i.e., the phase lag between the modulated light and the temperature variations detected by a pyrometer, Δϕs, at various frequencies of the modulated light ω. Here, the unsteady-state heat conduction equation for the droplet accompanying radiative heat transfer to the ambient was simplified and transformed to steady-state linear equations. The experimental relation between Δϕs and ω was fitted by the mathematical model proposed here to estimate simultaneously the thermal conductivity and emissivity of molten silicon. Also, the numerical simulations for unsteady thermal field in the electromagnetically levitated droplet which was periodically laser-heated were carried out to demonstrate the validity of the proposed simplified model, and then to investigate the sensitivity of the thermophysical properties to the relation between Δϕs and ω.