Home – Home – Jornals – Russian Geology and Geophysics 2013 number 1

Remote-sensing, cosmogeological, tectonic, geophysical, structural, compositional, isotopic, and geochronological criteria permit identifying the Kotuikan ring structure in the northern Siberian Platform as a Paleoproterozoic large astrobleme, close in age to the Vredefort and Sudbury impact structures. Also, indirect evidence for two more large impact structures was obtained here. This confirms widely hypothesized massive bombardment of the early Earth by asteroids and a possible effect of large impact events on the Earth’s mantle dynamics and rotation regime, that is, the tectonic evolution of our planet, including plate tectonics.

The structure, composition, and age of Vendian–Early Cambrian plagiogranitoid associations composing the Kshta and Taraskyr massifs of the Yenisei pluton in the Altai–North Sayan island-arc belt are considered. We have established that these associations formed within 550–520 Ma and differ in petrographic composition and sources. Two stages of island-arc plagiogranitoid magmatism are recognized: early (550–540 Ma, formation of plagiogranitoids of the Kshta (545 ± 8 Ma) and Taraskyr (545 ± 7 Ma) massifs) and late (525–520 Ma, formation of plagiogranitoids of the Maina complex of the Yenisei (524 ± 2 Ma) and Tabat plutons). By petrochemical composition and geochemical characteristics, the rocks of the Kshta massif are high-alumina plagiogranitoids similar to adakites. They might have been produced through the melting of metabasites compositionally similar to N-MORB in equilibrium with garnet-containing restite during the subduction of oceanic slab at ≥15 kbar. The rocks of the Taraskyr massif are low-alumina plagiogranites. They formed through the melting of metabasites located in the lower layers and(or) the basement of the island-arc system in equilibrium with plagioclase-bearing restite at 3–8 kbar. The low-alumina plagiogranitoids of the Yenisei pluton melted out under the same conditions. Isotope-geochemical studies showed that the Vendian–Early Cambrian plagiogranitoids formed at the early stage are characterized by high positive ε_Nd(T) values (7.5–4.9), Late Riphean model Nd-age (T_Nd(DM) = 0.64–0.98 Ga), and Sr isotope ratio varying from 0.7040 to 0.7053. These data point to the juvenile parental melts of the rocks and the varying content of ancient crustal material in the magma generation zone.

Two island arcs of different ages have been reconstructed in the Neoproterozoic history of southeastern East Sayan: Dunzhugur and Shishkhid. According to earlier concepts, the Dunzhugur arc formed at ~1020 Ma and underwent collision with the Siberian(?) continent at ~810 Ma. The Shishkhid arc formed somewhat earlier than 800 Ma and existed till the end of the Late Baikalian (~600 Ma, from indirect data). This primitive geologic history, when each arc existed for 200 Myr, was suggested because of the deficit of direct data, and its reconstruction cast doubt. In this work we present results of preliminary dating of detrital zircons extracted from the volcaniclastic rocks composing the above arcs. We analyzed 12 zircon crystals from the Dunzhugur volcanic clastics, whose ²⁰⁶Pb/²³⁸U age varies from 844 ± 8 to 1048 ± 12 Ma (1σ). Five most ancient zircons form a concordant cluster with an age of 1034 ± 9 Ma (2σ). Hence, the arc formed earlier than it was assumed and existed for a long time, most likely, till its collision with the continent. We also studied two zircon samples from the volcaniclastic rocks of the Oka accretionary prism, which probably formed in the Shishkhid arc. All ten crystals of the first sample form a concordant cluster with an age of 813 ± 7 Ma (2σ). The analyzed zircons of the second sample arrange in two clusters, with an age of 775 ± 8 Ma (2σ, nine crystals) and 819 ± 17 Ma (three crystals). Thus, the Shishkhid arc formed earlier than it was assumed, at the end of the Early Baikalian, and underwent active volcanism at least till 775 Ma. Dating of detrital zircons from the volcaniclastic rocks generated at the mature stage of the Shishkhid-arc evolution will help to reconstruct partly or completely its history in the period 775–600 Ma.

New data are presented on the petrogeochemical composition, age, and formation conditions of the Late Neoproterozoic metarhyolite–basalt association of the Glushikha trough (Yenisei Ridge). The association is localized within the subaerial and shallow-water terrigenous-carbonate sediments of the Orlovka Group, which overlies Proterozoic rocks with unconformity. The felsic volcanics are essentially potassic and enriched in Rb, U, Th, and Fe. They show a weakly fractionated REE pattern with a prominent negative Eu anomaly. The basalts and picrite basalts have higher contents of Ti, Fe, P, HFSE, REE, U, Th, Ba, and Sr, and their spidergrams show no Nb or Ta depletion with respect to Th and LREE. These rocks have the petrochemical parameters of intraplate magmatic associations in continental rift zones. New geochronological data (SHRIMP II) on single zircon grains from the felsite porphyry of the metarhyolite–basalt association (717 ± 15 Ma) indicate Late Neoproterozoic volcanism in the Yenisei part of the Central block of the Trans-Angara region. According to Sm–Nd isotopic data, the rhyolites originate from Paleoproterozoic crust (T_Nd(DM) = 1757 Ma; T_Nd(DM-2st) = 1651 Ma; ε_Nd(T) = –2.7). The Orlovka volcanosedimentary rocks are rift-related, as evidenced by the following facts: (1) localization of the volcanosedimentary rocks in a narrow fault-line trough; (2) bimodal rhyolite-basaltic composition of the volcanics; and (3) petrology and geochemistry of the picrite basalts and basalts, typical of intraplate environments. The studies show that Late Neoproterozoic rifting and intraplate plume magmatism took place not only in the Tatarka–Ishimba fault zone but also in the Yenisei fault zone of the Yenisei Ridge.

We present results of study of Holocene and Late Pleistocene deposits recovered on the underwater Akademicheskii Ridge in Lake Baikal. The change in mineral composition and grain size in the bottom sediment core is closely consistent with the change of major diatom complexes marking the Holocene–Late Pleistocene boundary. A high content of chloritoid (up to 14.6 %) has been found among the heavy minerals of the sand fraction of Late Pleistocene clays. The concentration of chloritoid in Holocene mud is no higher than 1.2 %. The source of chloritoid is chloritoid shales of the Anaya Formation (Upper Proterozoic), widespread in the watershed of the Primorskii Ridge in the upper reaches of the Lena and Anaya Rivers. Chloritoid was transported to the area of the Akademicheskii Ridge by predominant western and northwestern winds, which is also evidenced from the absence of mechanical impacts on the surface of its grains. The high contents of chloritoid in the Late Pleistocene sediments are due to the more intense eolian transportation at that time as compared with the Holocene.

Kuh-e Mond Field is a conventional heavy-oil resource in the Zagros Foreland Basin, Iran, produced from the fractured carbonates partially filled with dolomite, calcite, and anhydrite cement. Vitrinite reflectance data from carbonate reservoir suggest low-maturation levels corresponding to paleotemperatures as low as 50ºC. The observed maturation level (<0.5% R_max) does not exceed values for simple burial maturation based on the estimated burial history. Oil inclusions within fracture-filled calcite and dolomite cement indicate the key role of these fractures in oil migration.
Fluid inclusion temperature profiles constructed from the available data revealed the occurrence of petroleum in dolomite, calcite, and anhydrite and characterize the distinct variations in the homogenization temperatures (T_h). Fluid inclusions in syntectonic calcite veins homogenize between 22ºC and 90ºC, showing a salinity decrease from 22 to 18 eq. wt.% NaCl. Fluid inclusions in anhydrite homogenize at 50ºC, showing that the pore fluids became warmer and more saline during burial. The T_h range in calcite-dolomite cement depicts a change in water composition; therefore, we infer these cements precipitated from petroleum-derived fluids. The petroleum fluid inclusions microthermometry data suggest that the reservoir became filled with heavy black oils and high-salinity waters and indicate that undersaturated oil was present in a hydrostatically pressured reservoir.
The T_h data do not support vertical migration of hot fluids throughout the section, but extensive lateral fluid migration, most likely, drove tectonically dewatering in the south or west of the pool.

The role of fracture and faulting zones in the filtration inhomogeneity of productive formations in oil and gas fields has been considered. The absence of fracture or faulting zones from geological and, consequently, hydrodynamical models reduces the flooding efficiency and the oil recovery factor in general.
The current situation results from the underdevelopment of methods for the mapping and classification of fracture zones based on seismic-prospecting data. For example, the use of the seismic-horizon gradient method makes it possible to describe only complete rock fracturing at tectonic-block boundaries.
We propose to use the structural inhomogeneity of the deformation field of seismic horizonts for a more complete description and classification of fracture zones by the faulting regime. This parameter is suitable not only for late but also for early stages of faulting and describes block-boundary deformations more accurately than gradients. The example of a West Siberian field showed that the production wells from the J₁ productive formation in the faulting zones with the calculated post-Cenomanian structural inhomogeneity of the deformation field have considerably higher discharges owing to fracture permeability.

Local tectonic stress field has been calculated based on aftershock focal mechanisms, using materials of epicentral studies with temporary networks of stations in the epicentral area of the 2003 Chuya earthquake. The originality of this work is that the stress state is studied invoking earthquakes with large differences in energy and using highly accurate data on the location and depth in the analysis of events. The main result is the selection of two hierarchical levels of the stress field. It is shown that the stress state determined from data on large earthquakes is homogeneous (horizontal shear) throughout the aftershock zone, and the stress state determined from data on small events varies according to the block structure of the aftershock region.

Magnetotelluric sounding (MT) measurements are conducted, as a rule, along a single profile or mutiple profiles, and data are interpreted using 1D and 2D earth models. In a real situation, the earth is three-dimensional, and the primary field may vary laterally. This implies that 1D and 2D inversions of MT data contain some error, up to the appearance of false structures. In this study, analytical methods are used to obtain expressions for the effect of small deviations of the earth and the primary field from the Tikhonov–Cagniard model on the impedance and tipper tensor components (sensitivity functions determining the size of the zone near the sounding point within which the perturbations affect the impedance and tipper at this point).

We propose a heuristic method for the analytical solution of electrical-prospecting problems for direct currents and 3D isotropic media. The corresponding parameters of the medium (conductivity, magnetic permeability) are determined from Maxwell’s equations by the assignment of electric-or magnetic-field intensity in the analytical form. The application of this method is illustrated with examples.

Stability of the flow of the heated liquid film is studied in the presence of the thermocapillary effect. To describe the waves in the film, the integral model is used. According to results of linear analysis of stability, the thermocapillary effect expands the area of instability only at low Peclet values Pe, and at high values of Pe, the instability area narrows. Wave evolution in the film on a substrate with the fixed temperature was simulated numerically. Results of numerical simulations agree with the linear theory of stability.

The problem of stabilized combined motion of the gas flow and liquid film in a microchannel under the action of local heating with consideration of evaporation processes was set in selected variables. The exact solutions to the linearized problem were derived. The analytical formulas for calculation of the film thickness stabilized below the heater and the total rate of liquid evaporation were obtained. The technique of approximate calculation of total heat transfer is shown. Exemplary calculations are presented.

The solutions of the Laplace equation involving the diverging infinite series are used in the classical works at the analysis of the problem of the gravitational rise of a gas bubble in a tube filled with ideal fluid (the Taylor bubble). In the present work, an approximate method is proposed for a correct analysis of the above problem. The ideal fluid flow around a body of revolution in a tube is constructed by the method of the superposition of elementary solutions. The satisfaction of the free surface condition in the critical point neighborhood and the passage of the main parameter to the limit lead to the sought expression for the dimensionless velocity of the gas bubble — Froude number.

Experimental values of complexes of aerodynamic derivatives were obtained in a wind tunnel and analyzed for subsonic flow of a passenger aircraft model with harmonic oscillations on the rolling and yawing angles. It was demonstrated that for near-critical angles of attack, the complexes of aerodynamic derivatives taken for rolling and yawing have a string dependency on the normalized oscillation frequency. It was proven that this dependency is driven by derivatives with respect to angular velocities and angular acceleration. A mathematical model for aerodynamic loads was developed; it can be applied for aircraft flight dynamic problems and has satisfactory approximation to experimental aerodynamic characteristics.

In the present paper, we discuss results of an experimental study of performance characteristics of a 3D inlet with a flow-metering device at free-stream Mach numbers М = 1.75 and 2. The inlet was designed using gas-dynamic design methods. The initial external compression in the inlet is achieved using a V-shaped body called a waverider. The inlet is provided with a special device for its starting, also permitting regulation of the internal channel cross-sectional area in the throat region with the help of paired rotary panels, throat doors. The flow-rate and total-pressure loss characteristics in the throat of the model inlet were determined as functions of the degree of opening of the throat doors.

In the present paper, we discuss a procedure for designing of cylindrical air inlets for high flight speeds with the use of V-shaped bodies for forming a plane flow with an initial oblique compression shock. In design regime, characteristics of such air inlets can be obtained by means of simple calculations performed in a broad range of governing parameters. The difference between the performance characteristics of a typical cylindrical inlet in design and off-design flow conditions was elucidated with the help of 3D numerical calculations.

The work deals with the two-phase flow investigation. The computations were done for a continuous coagulation model within the framework of the phenomenological multi-fluid model of the medium. A conclusion was drawn that the diminution of the particles size leads to a reduction of two-phase losses in the nozzle unit of the solid-fuel engine.

The temperature dependence of the density of eutectic alloy of lead–potassium system (90.7 at. % Pb) was investigated using gamma-ray attenuation technique over the temperature range 293–950 K of solid and liquid states. The density changes during solid–liquid phase transition were directly measured for the first time. The approximating dependences for the density have been obtained, and a comparison of the data of this work with previously published results has been carried out. The reference tables for the temperature dependences of thermal properties of the alloy have been compiled in the entire examined range, and their errors have been estimated.

A molecular dynamics method was used to calculate the pressure p* and the internal energy e* of a liquid and a crystal in stable and metastable states in a system of 2048 particles, which interaction is described by a modified Lennard—Jones potential. For the liquid phase, calculations were performed along 13 isotherms from the range of reduced temperature T*=0.35-3.0, and for the crystal phase, along 16 isotherms from the range T*=0.1-3.0. The thermal p*=p*(ρ*, T*) and caloric e*=e*(ρ*, T*) equations of state for liquids and crystals have been constructed. The parameters of crystal–liquid phase equilibrium have been determined from the conditions of phases coexistence at positive pressures and in the region of negative pressures, where the coexistent phases are metastable. The spinodal of a stretched liquid has been approximated. It has been found that with a temperature decrease the metastable extension of the melting line meets the spinodal of the liquid phase. The point of their meeting, the endpoint of the melting curve, is the point of termination of crystal–liquid phase equilibrium without the onset of identity of the phases.

Results of mathematical simulation of the ceramics molding process by the hot casting method are presented. The mathematical model describes the motion of beryllia liquid thermoplastic slurry in a form-building cavity subject to solidification. Velocity and temperature profiles providing homogeneous properties of the beryllia ceramics in the process of molding by the hot casting method are obtained.

Measuring results for axial distribution of gas temperature of high-frequency torch discharge burning in the air at atmospheric pressure are presented. The distribution of electric field over the discharge axis was calculated based on the model of discharge in the form of heterogeneous electric line of finite length. It is shown that the experimentally observed linear character of electric field change along the discharge axis is conditioned by its axial heterogeneity.

Possibilities and limitations of the optical diagnostic methods for small-size (about 1 μm) droplets in the gas-droplet flows are discussed. Here we show the possibility for restoration of the functions of droplet distribution and droplet average size on the basis of measurements of ultradispersed particle parameters formed from microdroplet flows after droplet evaporation.

Speed of sound in the gaseous refrigerant R-409A has been measured by ultrasonic interferometer in the tem-perature range from 293 to 373 K and at pressures from 0.05 to 0.58 MPa. The experimental uncertainties of the temperature, pressure, and speed of sound measurements were estimated to be within 20 mK, 4 kPa, and 0.1–0.2 %, respectively. On the basis of the obtained data, the isobaric molar heat capacity was calculated for the ideal-gas state. A comparison of the obtained results with the calculated speed of sound on the basis of REFPROP program was carried out.

This work summarizes the cycle of investigations devoted to determination of the character of superheated liquid boiling-up in a glass capillary at the boundary of the attainable superheating. The brief history of studies is followed by a brief introduction into the theory of homogeneous nucleation. The result of the targeted experiments determining stationarity of a random process of a supercritical embryo generation is considered. From the experiments it may be concluded that the process is unsteady. Based on a large selection of life spans of superheated liquids, the authors have made parametric and nonparametric evaluations of the functions of distribution and dependence of boiling-up frequency on time. The comparison of the obtained results with exponential distribution shows significant differences that also prove the nonstationarity of the studied random process. Special experiments and calculations for evaluation of homogeneity of the superheated liquid boiling-up at the boundary of attainable superheating are considered. It is shown that in the experiments with glass capillary, the boiling-up occurs on the wall. As the most convincing evidence of heterogeneity of the superheated liquid boiling-up in a glass capillary the authors provide the results of high-speed video filming in a silylated and clean capillaries.

Р-ρ-Т data of SF₆ were approximated by the combined equation of state within the ranges of reduced densities (0 < ρ /ρ_c < 2.5) and temperatures (225 < Т < 340 K). The equation of state, which has the form of explicit dependence of pressure Р on r and T, includes a new regular part for approximation of Р-ρ-Т data in liquid an gaseous ranges of states beyond the critical region, nonparametrical scaling equation of state valid near the critical point of evaporation, and new crossover function for combination of these equations. The regular part of combined equation of state includes 8 simple terms of equation with eight adjustable parameters, three of which are determined by the conditions at the critical point. The total number of system-dependent constants is 14, including the critical values of Р, ρ, and Т. For the scaling part of state equation, the critical indices of 3D Ising model are used. At approximation of high-accuracy Р-ρ-Т data of SF₆ by the new combined equation their description with the pressure error below ± 0.35 % was obtained in the whole range of gas and liquid states. Heat capacity C_ν was calculated on the critical isochore using constants of combined equation. Calculation results coincide with the known experimental data within their error limit. The behavior of C_ν on isotherms was predicted in a wide range of densities, and these data were compared with predictions of other modern equations of state.

In the present paper, we discuss various approaches to measurement of velocity fields and velocity fluctuations in incompressible turbulent boundary layer by digital particle flow visualization methods. In particular, performing measurements in the vicinity of streamlined surface is considered. A description of the optical measuring system and methods to seed the flow with tracer particles is presented. Measured data for flow velocity fields and turbulent velocity pulsations in boundary layer on a flat impermeable plate are analyzed. Comparative data illustrating the efficiency of various algorithms for treating PTV images are presented.

A two-dimensional inlet of external compression with the increased flow rate factor at high supersonic velocities is constructed by the method of gasdynamic design. Its feature is that a flow with the initial oblique shock wave and the subsequent centered isentropic compression wave is formed over the external compression ramp of the inlet. These waves interact with one another so that a resulting stronger oblique shock wave and a velocity discontinuity arise in front of the entrance to the inlet internal duct. An example of an inlet configuration with the design flow regime corresponding to the Mach number M_d = 7 is considered. The characteristics of this inlet were obtained in the range of the free-stream Mach numbers M = 4−7 with the use of a Navier-Stokes code for turbulent flow. They are compared with characteristics of an equivalent conventional shocked inlet. As computations have shown, the inlet with the isentropic compression wave has much higher values of flow rate factor ϕ at Mach numbers М < M_d. So, for example, at М = 4 the value ϕ ≈ 0.72 for it is by 33 % higher in comparison with ϕ ≈ 0.54 for the equivalent shocked inlet.

When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl⎯Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl-Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air.

In the present work, the regimes of the flow and mixing of fluids in a T-shaped micromixer in the range of the Reynolds numbers from 1 to 1000 are investigated systematically with the aid of numerical modeling. The flow and mixing regimes are shown to alter substantially with increasing Reynolds numbers. Five different flow regimes have been identified in the total. The dependencies of the friction coefficient and mixing efficiency on the Reynolds number are obtained. A sharp increase in the mixing efficiency at a flow transition from the symmetric to asymmetric steady regime is shown. On the other hand, the mixing efficiency slightly drops in the laminar-turbulent transition region. A substantial influence of the slip presence on walls on flow structure in the channel and mixing efficiency has been revealed.

This paper presents physical modeling of thermal tornado under lab conditions. For the tested range of 0÷300 Hz, selective frequencies were discovered which facilitate the tornado decay. Data analysis was comp-lemented by velocity profile measurement using LDV system LD-05M. The results on velocity pulsation at selected points were recalculated into coefficient of correlation between velocities and function cos(2π f Δt_i) describing the acoustic oscillations. In the theoretical part of this paper, we present solution of dispersive equation of Euler's model and resulting boundary of stability for tornado existence. Satisfactory agreement between experiment and calculation has been observed.

The authors have formulated the problem of joint optimization of pressure and temperature of combustion products before gas turbine, profiles of nozzle and rotor blades of gas turbine, and cooling air flow rates through nozzle and rotor blades. The article offers an original approach to optimization of profiles of gas turbine blades where the optimized profiles are presented as linear combinations of preliminarily formed basic profiles. The given examples relate to optimization of the gas turbine unit on the criterion of power efficiency at preliminary heat removal from air flows supplied for the air-gas channel cooling and without such removal.

Numerical technique was developed for simulation of cavitating flows through the flow passage of a hydraulic turbine. The technique is based on solution of steady 3D Navier-Stokes equations with a liquid phase transfer equation. The approch for setting boundary conditions meeting the requirements of cavitation testing standard was suggested. Four different models of evaporation and condensation were compared. Numerical simulations for turbines of different specific speed were compared with experiment.

It was confirmed in experiments that during contact between cool and hot liquids, the lower subcooling of the cool liquid below the saturation temperature changes the characteristics of a vapor layer covering the fragments of hot liquid. This factor also decreases the probability of spontaneous direct contact between two kinds of liquid, explosive incipience of the cool liquid, and pressure pulse generation (the latter triggers fine fragmentation of hot coolant and vapor explosion). The mechanism that describes this trend in vapor layer behavior has been described.

The work presents calculation of Ag₂ dimers emission from the substrate into the vapor medium in case of joint deposition of silver and water vapors on ideal substrate formally modeling the crystal of water ice in terms of energy properties. It is assumed that the dimers are formed on the condensation surface as a result of random collisions of atoms at their surface migration, and the dimers emission is conditioned by thermal fluctuations of crystal lattice of water ice. The calculations based on the modified Langmuir adsorption model allowed concluding that emission of silver and water dimers takes place in the entire range of the studied water vapor pressure, binding energy of silver-water, and crystal temperature. Dynamics of emission from the beginning of deposition and dependence of dimers emission on micro-roughness of the condensate surface have been investigated. Statistical processing of results has shown that the probability of dimers emission from the condensate surface is determined not only by the value of the binding energy between the dimer and condensate but by configuration of the nearest dimer environment on the condensation surface. It has been found that there is a certain value of micro-roughness of condensation surface providing the maximal intensity of dimer emission. Dimers emission from the surfaces bordering on the flows of vapor mixtures contaminates the flows with unsuspected admixtures. The latter one makes investigation of this phenomenon important for aeromechanics of vapor and gas mixtures.

Results on conjugate convective heat transfer in a system geometrically similar to the system crystal-gas-growing vessel shell of a growing vessel obtained by the Czochralski method are presented. Equations of thermal gravitation convection in Boussinesq approximation are solved by the finite element method in the following variables: temperature, stream function, and vorticity in cylindrical coordinates. Heat transfer from the crystal was studied within the range of Grashof number 100 ≤ Gr ≤ 10⁴ for the fixed configuration of calculation domain. Dependence of the temperature field in the silicon crystal on convection intensity in gas (argon) was examined.

The article presents the results of studying the thermal expansion of MPG-6 and AXF-5Q graphites and graphite composite based on ¹³С isotope in the temperature range 293−1650 K. Measurements were performed with dilatometric method in DIL-402C unit manufactured by NETZSCH (Germany), with the accuracy of (1÷4)×10⁻⁷ K⁻¹. Approximation dependences of average integral coefficient of linear expansion on temperature have been obtained and reference tables calculated. It is shown that the coefficient of thermal expansion of ¹³С composite is much lesser than for MPG-6 and AXF-5Q. The explanation of this phenomenon is provided in the paper.

Results of computer simulation of reflective properties of the oxide film-metal system in the process of oxidation in the air environment are presented. The complex refractive indices for oxide film and metal were used as the initial data. Thin films (the thickness is comparable with the wavelength of incident radiation) and thick films (thickness is much larger than the wavelength of incident radiation) are considered. The parameter characterizing the cyclic character of system reflectivity during the growth of film thickness was derived for the thin film. It is shown that the cyclic parameter does not depend on optical properties of a metal substrate. In the air environment, this parameter is determined by a complex refractive index of the film, its thickness, and direction of incident radiation. Relationships for the estimate of system reflectivity in the process of oxide film growth are presented for the thick film.

The radiation network method has been applied to calculate the net radiation heat transfer between two concentric hemispheres separated by two hemispherical radiation shields with temperature-dependent surface emissivities. Three different materials are chosen for radiation shields: aluminum oxide, silicon carbide, and tungsten. The reduction in heat transfer with shields depends not only on the surface characteristics of the two shields, but also on the locations of the shields. Three illustrative examples are presented to illustrate the effects of temperature dependent emissivities and shield locations on the percentage heat transfer reduction. The analysis can be used to study other cases as warranted.

In the present analysis, a numerical study is performed to examine the heat transfer characteristics of a convective flow over a vertical plate under the combined effects of magnetic field and thermal radiation in the presence of heat source/sink. The surface of the plate is subjected to a variable surface temperature. The boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime using the suitable non-dimensional parameters. The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, more accurate and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, local and average Nusselt number in air. The present results are compared with the results available in the literature and are found to be in a excellent agreement.

The furnace processes of the combustion of poly-fraction high-ashes Ekibastuz coal in the furnace chamber of the boiler aggregate PK-39 and of the combustion of highly humid brown Berezov's coal in the furnace of the BKZ-210-140 boiler are investigated by mathematical modeling using the package of applied programs FIRE 3D [1-3]. Results of the numerical modeling of the processes of aerodynamics, heat exchange, and combustion in the furnace volume and their comparison with the results of nature tests are presented.