Influence of optical properties on the formation of temperature fields in aluminum oxide upon heating and melting by concentrated laser radiation

A theoretical investigation and numerical calculation on the role of absorption coefficient $k_l$ for concentrated laser radiation in the formation of a temperature field during heating and melting of a plane aluminum oxide layer is carried out. A mathematical model of transient combined radiative and conductive energy transfer considers the process of heating a plane layer within a rigorous statement with allowance for the temperature dependence of thermophysical properties of the solid phase and melt (as well as the dependence of optical properties on temperature and wavelength), includes a generalized approach to the problem of phase transition upon melting with allowance for the formation of an extended two-phase region, and takes into account ablation from the melt surface. The maximum heating time is $100$ s. The parameter kl varies from $200$ cm$^{–1}$ to $1000$ cm$^{–1}$. The results are obtained for a heat flux density of $600$ W/cm$^2$. The formation of a two-phase region, which exists for a very short time, is observed at the initial stage of melting. Maxima is found in the time dependences of the heating surface temperature and the melt thickness. These maxima do not arise simultaneously, and the time of their occurrence depends on $k_l$. It is shown that the specific features of the formation of temperature fields are due to, on the one hand, the contribution of the volume radiation and absorption of the external and intrinsic radiation fluxes inherent in all semitransparent materials at high temperatures and, on the other hand, the specificity of aluminum oxide, the absorption coefficients of the melt and solid phases of which in the energetically important spectral range differ by up to two orders of magnitude.