The Diagnostics of Optical and Thermal Characteristics of Semitransparent Media at Modeling Phase Influence of Oscillating Convection and Thermoradiation

The paper suggests diagnostics method of non-stationary combined regime heating of semitransparent materials base on an evaluation of the interconnected complex of optical parameters (extinction – brad, scattering-σ and absorption κ indices) and thermophysical (thermal diffusivity aT and conductivity coefs) ones using simulation the general temperature field θ(z,ωt,Δφconvrad)=θc+r(z,ωt,bconv,Δφθc+r)+θrad(z,ωt,brad,Δφθrad) including the additive terms due to the convective and radiation fluxes with a phase shift Δφconvrad within the external oscillating (frequency ω ) heat load.A one-dimensional problem of finding the temperature for a semitransparent material in the absence of aggregative transitions, neglecting long wavelength re-emission was considered in the analytic representation. The classical solution (of the homogeneous heat equation) and the particular one (of the inhomogeneous one with an internal thermal radiant source) defined summable terms with independent phases Δφθc+r,Δφθrad and different indices respectively for attenuation bconv=ω+2aT = (conductive heatwave) and for diffraction extinction brad=κ2+κσ (radiant heatwave). In-phase production of additive term θrad(z=0,t) simultaneously with external convection impact on the exposed surface allowed for the first time to establish interconnected complex brad=ω⋅ctg(Δφconvrad)/aT⋅ The obtained formulas for specific temperature distributions allow you to use them to estimate values of optical and thermal parameters of a semitransparent material from experimentally recorded phase jumps of the temperature field during the action of alternate impact of initial phased convective and radiation components of the external heat flux. The results of the study can be used both for experimental diagnostics and to select the heat regimes for combined radial and convective processing of semitransparent ceramics, composites, and biomaterials.

( radiant heatwave). In-phase production of additive term θrad(z=0,t) simultaneously with external convection impact on the exposed surface allowed for the first time to establish interconnected complex obtained formulas for specific temperature distributions allow you to use them to estimate values of optical and thermal parameters of a semitransparent material from experimentally recorded phase jumps of the temperature field during the action of alternate impact of initial phased convective and radiation components of the external heat flux. The results of the study can be used both for experimental diagnostics and to select the heat regimes for combined radial and convective processing of semitransparent ceramics, composites, and biomaterials.

Introduction
Traditionally in thermal physics it is important to analyze the heat regimes of materials under the influence of external oscillating convective and thermoradiation heat fluxes with different phase shift  [1]. Studies on the calculated and experimental estimates of the temperature fields for technical materials and natural environments are known [2][3][4][5].
But the interpretation of numerical and experimental estimates significantly complicated when predicting the impact of phased components of convective and radiant heating on formation of general temperature regime with predominance of conductive heating or alternative volumetric radiant overheating for semitransparent materials.
Therefore, obtaining an analytical solution is an urgent task allowing to evaluate an interconnected complex of optical and thermophysical characteristics of semitransparent material will depend on experimentally recorded temperature field characteristics, produced by the action of an external nonstationary convective-thermoradiant heat flux, changing according to a harmonic law with equal frequencies ω of its components and simulated phase shift [6][7][8].

Mathematical model of combined convective heating and volumetric radiant overheating
We are guided by the theory of radiative-conductive subsurface heating of semitransparent material with thickness 0 zH  under the influence of radiant component overheating together with convective surface heating in one-dimensional approximation. Therefore the calculated temperature is determined not only by thermophysical parameters but also by optical properties.
The inhomogeneous heat equation should include the thermal source function F(z, t, ω) which is caused by penetrating radiation: where с -specific heat capacity,  -density, Boundary conditions on the exposed surface are determined by the influence of convection fluxes and long wavelength nonpenetrating radiation in the absence of aggregative transitions: where αturb -coefficient of turbulent heat exchange, 0 с -Stephan-Boltzmann coefficient, εefeffective emissivity coefficient.
Our examined samples of semitransparent material should be considered as scattering and weakly absorbing mediums and ensure the necessary reflection and transmission for fallen radiation. The methodology of calculative-theoretical estimations of the optical parameters is well known [4,5], including version developed earlier by authors [6] which is used in this work.
The penetration of radiation is defined by volumetric coefficients of reflection, transmission and absorption, depending on scattering and absorption indexes of the given optically inhomogeneous environment.
Obtained numerical values of extinction brad and scattering  indexes for example the ceramic layer are determined by experimental values of albedo A and absorption index κ. The given calculations were based on a functional relationship of these optical parameters [6]: where brad -extinction index is considered as attenuation coefficient, A -albedo is reflection coefficient of semi-infinite layer with spherical scattering indicatrix (р = 1) in two-flux approximation of solution for radiative transfer equation.
For known samples of porous ceramics (based on silica, zirconium aluminum) κ ~ 0.01-1 m -1 and  ~ 1-3000 m -1 , albedo changes in interval А ~30-99% with brad < 10-30 m -1 . It allows us to offer simple optical models for materials for solving engineering problems of complex heat transfer.
Thus it is possible to calculate the absorbed radiant energy function (2) within UV, visible and near IR spectral ranges for most artificial and natural radiant heat sources.
Considered physical and mathematical model of the radiant heat exchange is caused by technological conditions for convective (e.g. flame machining) or radiant (e.g. laser one) processing for materials. Intensive heat fluxes can exceed tens of MW/m 2 . At temperatures of aggregative transitions up to ~2000-3000K for the refractory ceramics (type Al2O3, SiO2, ZrO2) the generated fluxes of self -IR radiation from expose surface may not exceed 1 MW/m 2 .
Therefore, to obtain an analytical solution in the boundary conditions (3) authors will be neglected longwave re-emission on the external border and this thermal problem becomes linear: ), which form and model the general temperature field θ(z,t) with additive terms θc+r(z,t) and θrad(z,t) with appropriate phases index brad (4) with conductive-radiate heat transfer. Besides, for the constant components of the external temperature θA0 (1a) and the incident radiation flux qrad0 (1b) the trivial exact solution is known [1], which will not be considered in our analysis of generated oscillating temperature fields. The formulated problem (1)(2)(3)(4)(5) admits an analytical solution.
Since the heat conductivity equation (2) is inhomogeneous with the desired temperature field ( , ) zt  , then it is possible to find separate solutions in the form of independent components: 1 -conductive component of homogeneous equation with oscillating convective heating at the boundary (5) and 2 -particular solution for the inhomogeneous equation (3) with thermoradiation subsurface overheating.
Then, taking into account the initial temperature, the general solution for (1-5) is [8]: