Determination of the Radiation Exchange Factor in the Bundle of Steel Round Bars

A method to obtain a radiation exchange factor FR in the bundle of steel round bars is presented. This parameter is required for determination of the radiative thermal conductivity krd, which is one of the basic thermal properties of the bar bundles. In the presented approach, the analyzed parameter is calculated indirectly. The initial point for calculations is the geometric model of the medium defined as a unit cell. Then, for the elements present in this cell, the thermal resistance of both conduction and radiation is determined. The radiation resistance is calculated from the radiosity balance of the surfaces enclosing the analyzed system. On this basis, the radiation thermal conductivity krd is calculated. Next, taking into account the bar diameter, the value of parameter FR is also determined. The analysis is performed at the process temperature range of 200 to 800 °C for three bar diameters: 10, 20 and 30 mm, and for the three porosities of the bundle. Different emissivity of bars in the range of 0.5 to 0.9 was also taken into account. Finally, a relationship that allows calculating the FR factor correlated with the emissivity of the bars and the bundle porosity was established. The krd obtained from the methodology presented and compared with the values calculated directly do not exceed 9%; however, after averaging over the entire temperature range of the process, the difference does not exceed 0.2%.

THERMAL RADIATION IN SPARK DISCHARGE

The work is devoted to numerical study on thermal radiation in spark discharge. The influence of radiative thermal conductivity on the expansion of the spark channel has been established. The study of the effect of value of the capacitance of the discharge capacitor on the energy emitted by the discharge has been carried out. The change in the thermodynamic state of the gas in the spark channel is considered taking into account following factors: change in the capacitance of the discharge capacitor, the length of the discharge gap and the initial gas pressure. The influence of the initial gas pressure and the gap length on the parameters of thermal radiation of a gas under conditions of a constant breakdown voltage supplied to the spark gap is investigated.

Statistical Approach to Radiative Transfer in the Heterogeneous Media of Thin-Wall Morphology—II: Applications

The statistical multiphase approach (MPA) proposed in the first part of this work to evaluate radiative properties of composite materials is applied to porous structures of opaque material and biological tissues. Radiative thermal conductivity is calculated for the bundle of circular rods, packed pebble beds, and metal foams. The results generally agree with the reference calculations by other methods. The small difference can be explained by different approaches to scattering and assumptions about the temperature distribution. Attenuation of light in skin tissues is calculated by the diffusion approximation. The attenuation coefficient generally agrees with the reference Monte Carlo simulation (MC). The difference observed at certain combination of parameters can be due to the assumption of regular arrangement of vessels at the MC simulation.

Statistical Approach to Radiative Transfer in the Heterogeneous Media of Thin-Wall Morphology—I: Theory

Foams, three-dimensional (3D)-printed cellular and honeycomb structures, and very oblate particles dispersed in a matrix are the examples of heterogeneous media with thin-wall morphology. Phase boundaries can also be considered by this approach. Statistical description is proposed to estimate the effective radiative properties of such media. Three orientation models are studied: (i) isotropic, (ii) surface elements parallel to a plane, and (iii) surface elements parallel to an axis. Radiative transfer equations (RTEs) are obtained and analyzed in the framework of the homogeneous phase approach (HPA) and the multiphase approach (MPA). Analytical expressions are obtained for the absorption, extinction, and scattering coefficients, the scattering phase function, and the radiative thermal conductivity for very oblate particles dispersed in an absorbing scattering matrix. The reflective properties of the platelets and their preferential orientation can be used to optimize the radiative thermal conductivity.