Ballistic-Diffusive Heat Conduction in Thin Films by Phonon Monte Carlo Method: Gray Medium Approximation Versus Phonon Dispersion

The gray medium approximation treating all phonons with an averaged and representative mean-free-path (MFP) is an often used method in analyzing ballistic-diffusive heat conduction at nanoscale. However, whether there exists a reasonable value of the average MFP which effectively represents the entire spectrum of modal MFPs remains unclear. In this paper, phonon Monte Carlo (MC) method is employed to study the effects of the gray medium approximation on ballistic-diffusive heat conduction in silicon films by comparing with dispersion MC simulations. Four typical ways for calculating the average MFP with gray medium approximation are investigated. Three of them are based on the weighted average of the modal MFPs, and the remaining one is based on the weighted average of the reciprocals of the modal MFPs. The first three methods are found to be good at predicting effective thermal conductivity and heat flux distribution, but have difficulties in temperature profile, while the last one performs better for temperature profile than effective thermal conductivity and heat flux distribution. Therefore, none of the average MFPs can accurately characterize all the features of ballistic-diffusive heat conduction for the gray medium approximation. Phonon dispersion has to be considered for the accurate thermal analyses and modeling of ballistic-diffusive heat transport. Our work could be helpful for further understanding of phonon dispersion and more careful use of the gray medium approximation.

Distribution of rare earth elements in Ruska Poliana granites and accessory fluorites

Fluorite is one of the main concentrators of rare earth elements (REE) in the granites of the Ruska Polіana massif of the Korsun-Novomyrhorod pluton of the Ukrainian Shield. Despite its distribution in the granites of the massif, the geochemical features of the fluorites have not yet been investigated. The aim of this work was to determine the content of REE in the fluorites, the granites and to study the distribution of REE in the fluorites and granites containing this mineral. The content of REE in 4 samples of the granites and 4 monofraction the fluorites from these granites (well № 8568) was determined by the ICP MS method on the Element-2 device at M. P. Semenenko Institute of Geochemistry, Mineralogy and Ore Formation of the NAS of Ukraine (Kyiv). The well № 8568 was drilled in the southeastern part of the Ruska Polіana granite massif of the Korsun-Novomyrhorod pluton of the Ukrainian Shield (Ruska Polіana Village). In this part, the researchers revealed granites with rare metal mineralization. The investigated granites of well are represented by 3 types: the gray-pink fine-medium-grained granites (type I) (156,1–158,0 m), the gray-pink porphyriform granites (type II) (174,6–176,5 m), the gray medium-coarse-grained granites (type III) (225,0–227,0 m) and the pink-gray medium- coarse granites (type III) (239,6–242,0 m). According to the results of the ICP MS analysis, the highest content of lanthanides (26933 ppm) and yttrium (11 705 ppm) was observed in fluorites from the gray-pink fine-medium granites of the upper part of the well. But the gray-pink fine-medium granites have the lowest total lanthanide content (218 ppm). The lowest levels of lanthanides (692 ppm) and yttrium (831 ppm) were determined in the fluorites of the pink-gray medium-coarse grained granites of the deepest part of the well. The pink-gray medium-coarse granites are characterized by high lanthanide content (797 ppm). The fluorites from Ruska Poliana of the gray-pink fine-medium grained granites can be compared with the fluorite from Perga granite by the total content of lanthanides. Among the rock-bearing minerals in biotites from the Ruska Poliana granites of different depths of the well, there is a high content of REE, almost at the level of the granites themselves. Such a high level indicates the presence of inclusions of accessory minerals enriched with REE in the biotites, especially fluorites.

MONITORING OF THE OVERGROWING OF UNUSED AGRICULTURAL LAND BASED ON GIS TECHNOLOGY

The problem of overgrowing of fertile lands of the forest-steppe zone requires a scientific solution. In this regard, the article presents the use of technologies of geographic information systems in conjunction with field research to monitor the overgrowth of unused agricultural land. Two plots of agricultural land of Penza region with areas overgrown with weeds, young overgrown with woody vegetation and shrubs were selected. Space decoding was carried out based on the data of GPS coordinates, photos and satellite images of Landsat-8 in the spectrum of Near Infrared, Shortwave infrared, Blu. Methodological framework made recommendations for classification of Portland University. The area of distribution for 2013–2018 is defined, its speed which makes 2–3 hectares/year is calculated. Amendments to the interpretation of satellite images taking into account regional features are proposed. The Botanical composition of the undergrowth is presented, the type of soil (chernozems clay-illuvial and dark gray medium) and Geology is determined. Overgrowth, as a rule, is determined by the spread of Betula pendula R. and Pinus silvestris L. the Use of topographic index of waterlogging allowed to establish regularities of the composition of vegetation to local places of excess and lack of moisture. Thus, Alnus glutinosa L. and Salix caprea L. are found in waterlogged areas, elevated areas with pronounced aridity are occupied by Pinus silvestris L. and Picea abies L. In the conditions of weakening of anthropogenic factor dark gray medium-soils on sandy rocks of Cretaceous and Paleogene age are subject to water erosion and deflation. The interrelation between the development of processes of overgrowth and climate warming, when winters are warm and snowy, and summers are cool and humid, is shown.

Effect of radiation on the flow structure and heat transfer in a 2-D gray medium

A numerical study of combined natural convection and radiation in a square cavity filled with a gray non-scattering semi-transparent fluid is conducted. The horizontal walls are adiabatic and the vertical are differentially heated. Convection is treated by the finite volumes approach and the discrete ordinates method is used to solve radiative transfer equation using S6 order of angular quadrature. Representative results illustrating the effects of the Rayleigh number, the optical thickness and the Planck number on the flow and temperature distribution are reported. In addition, the results in terms of the average Nusselt number obtained for various parametric conditions show that radiation modifies significantly the thermal behavior of the fluid within the enclosure.

Coupled Thermal Radiation and Mixed Convection Step Flow of Nongray Gas

The main goal of this paper is to analyze the thermal and hydrodynamic behaviors of laminar mixed convection flow of a nongray radiating gas over an inclined step in an inclined duct. The fluid is considered an air mixture with 10% CO2 and 20% H2O mole fractions, which is treated as homogeneous, absorbing, emitting, and nonscattering medium. The full-spectrum k-distribution (FSK) method is used to handle the nongray part of the problem, while the radiative transfer equation (RTE) is solved using the discrete ordinate method (DOM). In addition, the results are obtained for different medium assumptions such as pure mixed convection and gray medium to compare with the nongray calculations as a real case. The results show that in many cases, neglecting the radiation part in computations and also use of gray simulations are not acceptable and lead to considerable errors, especially at high values of the Grashof number in mixed convection flow.

Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media

The evaluation of direct exchange areas (DEA) in zonal method is the most important task due to the heavy computer cost of multi-integrals together with the existing of singularities. A technique of variable transformation to reduce the fold of integrals, which was developed originally by Erkku (1959) to calculate the DEAs of uniformly zonal dividing cylindrical system, was extended by Tian and Chiu (2003) for nonuniformly zonal dividing cylindrical system with large thermal gradients. In this paper, we further extend the reduced integration scheme (RIS) to calculate the DEAs in three-dimensional rectangular system. The detail deductions of six-, five-, and fourfold integrals to threefold ones are presented; the DEAs in a rectangular system with assumption of gray medium are computed by the Gaussian quadrature integration (GQI) and the RIS comparatively. The comparisons reveal that the RIS can provide remarkable higher accuracy and efficiency than GQI. More interestingly and practicably, the singularities of DEAs can be decomposed and weakened obviously by RIS.