Derivation and solution of multifrequency radiation diffusion equations for homogeneous refractive lossy media

Abstract

Starting from the radiation transport equation for homogeneous, refractive lossy media, we derive the corresponding time-dependent multifrequency diffusion equations. Zeroth and first moments of the transport equation couple the energy density, flux and pressure tensor. The system is closed by neglecting the temporal derivative of the flux and replacing the pressure tensor by its diagonal analogue. The system is coupled to a diffusion equation for the matter temperature. We are interested in modeling annealing of silica (SiO2). We derive boundary conditions at a planar air-silica interface taking account of reflectivities. The spectral dimension is discretized into a finite number of intervals leading to a system of multigroup diffusion equations. Three simulations are presented. One models cooling of a silica slab, initially at 2500 • K, for 10 s. The other two are 1D and 2D simulations of irradiating silica with a CO2 laser, λ = 10.59 µm. In 2D, we anneal a disk (radius = 0.4, thickness = 0.4 cm) with a laser, Gaussian profile (r0 = 0.5 mm for 1/e decay.)

Determination of the intrinsic temperature dependent thermal conductivity from analysis of surface temperature of laser irradiated materials

“…For all but silica, the T increases more rapidly with power, which is consistent with both a decrease in k and a lack of significant radiation transport. 11,12 The data were well fitted with parameters A and as given in Table I. For silica, since the data in Fig.…”

Thermomechanical Modeling of Laser‐Induced Structural Relaxation and Deformation of Glass: Volume Changes in Fused Silica at High Temperatures

“…Heat transfer boundary conditions for laser‐heating problems typically include surface convection, radiation, and evaporative cooling, but are highly dependent on the temperature range of interest. However, it can be shown that the large temperature gradients associated with laser heating of highly absorbing, low thermal diffusivity media result in radiative and convective loss from the surface that are negligible . Figure compares the relative contributions of the four transport mechanisms up to 3000 K, estimated analytically for a steady‐state 1 mm beam over a range of peak powers.…”

“…However, it can be shown that the large temperature gradients associated with laser heating of highly absorbing, low thermal diffusivity media result in radiative and convective loss from the surface that are negligible. 35 Figure 2 compares the relative contributions of the four transport mechanisms up to 3000 K, estimated analytically for a steady-state 1 mm beam over a range of peak powers. As shown, until peak temperatures approach the boiling point of a-SiO 2 (2500 K), heat is lost largely through conductive cooling.…”