This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures. In these porous materials, they have periodic configurations and associated coefficients are dependent on the macro-location. Also, radiation effect at microscale has an important influence on the macroscopic temperature fields, which is our particular interest in this study. The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first. Then, the second-order multiscale formulas for solving temperature fields of the nonlinear problems are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail. Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy. They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely, and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.

This work develops a second-order two-scale (SOTS) model based on homogenization method to predict thermo-mechanical coupling performance of porous materials with quasi-periodic structures. For the kinds of porous materials, the corresponding material coefficients are dependent on the macroscopic variable and the radiation effect at microscale is considered in this paper. The quasi-periodic properties of the thermo-mechanical coupling models which consider mutual interaction between temperature and displacement fields are proposed at first. Then, the two-scale formulas for the thermo-mechanical coupling problems with radiation boundary conditions are derived successively, and the finite element algorithms based on the SOTS model are brought forward in detail. Finally, by some typical examples, the effectiveness and validity of the proposed algorithms are confirmed. The computational results demonstrate that the SOTS method is efficient and valid to predict the thermo-mechanical coupling properties, and can acquire the microscale information of the porous materials accurately.

Based on the surface morphology, a model is presented to investigate the heat transfer in anodic aluminum oxide (AAO) porous thin films. The extra thermal resistance from the micropores will inevitably cause a change in thermal properties, which can be analyzed by the Fourier law. The effect of the characteristic size on the thermal conductivity is discussed in details by means of the theory of phenomenological model of phonon scattering. Considering the effects of porosity and the distribution of micropores reflected by parameter D, the function of the effective thermal conductivity of AAO porous thin films expressed by two independent variables, εp and D. The temperature field is simulated with the effective thermal conductivity and the result demonstrates a bigger temperature rise in AAO porous thin films.

Transparent conducting aluminum-doped zinc oxide (AZO) films have been prepared on soda-lime glass substrates by radio frequency magnetron sputtering using a high density ceramic target at different substrate temperatures. The structural, morphology, electrical, and optical properties of the AZO thin films were investigated by X-ray diffraction, scanning electron microscope, Hall measurement, and optical transmission spectroscopy, and which were strongly influenced by substrate temperatures. Films with better texture, higher transmission, lower resistivity and larger carrier concentration were obtained for the samples fabricated at higher substrate temperature. The AZO film with the lowest resistivity of 4.63×10−4 Ω.cm and an average optical transmission of 92% in the visible range was deposited on the substrate heated at 450 °C. The optical bandgap depends on the deposition condition, and was in the range of 3.35~3.59 eV.

The thermal effect arisen from absorbing inclusions is the main factor which causes the damage of optical materials or component irradiated by the longer pulse duration laser. The unsteady heat conduction depends markedly on both the thermal properties of inclusions and the parameters of laser. Based on the differential equation of heat conduction, the temperature distribution caused by single absorbing inclusion is solved by use of finite difference method. The effect of the laser intensity and the pulse duration on temperature field is analyzed in detail. The result demonstrates that the smaller size inclusion and the smaller pulse duration cause relative safe thermal effect, consequently, the less probability to be damaged by thermal effect.