A mathematical model for calculating the temperature field in a semitransparent composite material that in- cludes a polymethyl methacrylate matrix and quartz microspheres is suggested. In calculating the optical properties of the composite material, use was made of the optical properties of the matrix and of the inter- acting quartz microspheres at different filling factors which characterize the volume concentration of particles in the matrix. Allowance for the interaction between the composite components is made following the Max- well-Garnett approximation. Data on the complex refractive index of the composite were used for calculating the coefficients of absorption, scattering, and attenuation of packed particles by the Mie theory. The tempera- ture fields in a layer of the material are found from solving the boundary-value problem for the energy equa- tion and a system of radiation transfer equations with the use of these coefficients. perature. Introduction. Semitransparent composites are found in number of promising modern materials. Such materials assume a particular significance in articles in which an important role is played by energy transfer by heat conduction and radiation. Therefore investigations of the parameters of the composite components that influence thermal processes are very pressing. One of the means of increasing the thermoprotective properties is the use of materials involving fine particles that scatter thermal radiation. The composite material considered in the present work consists of hollow and solid quartz microspheres with a characteristic dimension of 3-50 μm introduced into a semitransparent binding matrix; the material is the means of heat shielding under the conditions of radiative-conductive transfer of thermal energy only at a high volume concentration of microspheres. To calculate the thermal fields in such a material, it is necessary to have data on the absorption and scattering coefficients with account for the interaction between particles. The problem of the influence of the proximity of particles on these coefficients remains as yet unsolved. Heat losses from the composite material surface include conductive and radiative components. Account for the indicated losses is possible at the known temperature distribution in a layer of this material. Solution of the problem is performed in the approximation of a continuous medium with effective thermophysical and optical properties. Dur- ing the passage of a radiative energy flux, the interaction between particles appears in the case of a high concentration of particles in the composite. It is known that if the distance between particles greatly exceeds that of their size and of the radiation wavelength, then the interaction between them is absent, and the absorption and scattering coefficients can be calculated by the classical Mie theory with the use of complex refractive indices of the particles and matrix (1). For the majority of optical problems, such an approach turns out to be justifiable. Since the composite material considered in the present work is an effective heat shield only at a high volume concentration of microspheres, the condition of the absence of interaction of particles that scatter and absorb radiation does not hold. Therefore the use of the classical Mie theory can lead in this case to considerable errors in calculating the radiative characteristics of a composite material and, as a consequence, of the temperature fields in it. To determine the attenuating and scattering
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Feb 1, 2012
Karlis Birgelis + 1
Open Access
