Transfer Equation Research Articles

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Bio-optical inversion scheme based on the radiative transfer equation

An inversion algorithm based on a forward optical model based on a radiative transfer equation is developed in terms of IOPs with explicit inclusion of the volume scattering function (VSF). Key results from the analysis are: 1) the inversion retrievals perform to comparable levels as the operational configuration of the NASA’s Generalized Inherent Optical Property (GIOP) framework; 2) closure error between RT r rs and measured r rs have no significant effect on predicting the accuracy of the derived IOPs; and 3) is important to ZTT, but not explicitly included in other types of comparable semi-analytic algorithms.

Plasma-Fluid Energy Transfers in Plasma Assisted Ignition

ABSTRACT A three-dimensional model of plasma-fluid coupling is developed, including the Navier-Stokes, the drift-diffusion, and the radiative transfer equations, to investigate the energy transfers between plasma and fluid in repetitive-pulsed discharge ignition. A modal decomposition of the energy transfer is performed to determine the contributions of plasma to the mechanical coupling and pressure losses during ignition. The detailed model is validated against experiments and compared against a well-known empirical approximation. The main findings are that the modal coupling is dependent on the geometry of the electrodes and flat electrodes provide the strongest mechanical transfer into the acoustic modes. Uniform flow conditions decrease the extent of the mechanical coupling due to the decreased pressure velocity correlations in shear flows. Water vapor production reduces the entropic mode of the energy coupling.

Optimization of coupling phase-change materials and thermal screens in façade-integrated hybrid photovoltaic collectors for optimal energy production and thermal comfort in buildings

The operation of building-integrated photovoltaic (BIPV) systems gives rise to a significant proportion of the solar radiation absorbed by the cells being unable to be converted into electricity. This phenomenon consequently increases the temperature. This temperature increase impacts the cells' electrical efficiency, leading to a reduction in their performance and accelerating their degradation. The combination of phase-change materials with insulating fluid blades, situated behind photovoltaic cells, represents a passive cooling solution that optimizes the performance of hybrid photovoltaic systems when incorporated into facades. The present study assesses a system that incorporates paraffin as a PCM and an argon layer in a PV-PCM-argon layer physical model (PVT/ArPCM), in comparison with a PV-PCM system (PVT/PCM), to enhance the thermoelectric performance of photovoltaic systems mounted on façades while ensuring optimal thermal comfort within buildings. The discrete heat transfer equations were solved using the Thomas algorithm and the iterative Gauss-Seidel method in conjunction with the implicit finite difference method. The findings illustrate that the electrical efficiency experienced only a slight increase, estimated at 0.01%, while there was a notable enhancement in the indoor thermal comfort experienced by occupants, with a 65% improvement observed due to the incorporation of an argon-filled thermal screen. The incorporation of an argon layer led to a minor reduction in temperature of 0.01°C in the photovoltaic cells, resulting in a minimal improvement of 0.014% in electrical power production. The phase-changing material incorporated into PVT/ArPCM demonstrated superior thermal management capabilities in comparison to the same material employed in PVT/PCM.

Impact of the Lyα radiation force on super-Eddington accretion on to a massive black hole

Abstract The viability of super-Eddington accretion remains a topic of intense debate, crucial for understanding the formation of supermassive black holes in the early universe. However, the impact of the Ly$\alpha$ radiation force on this issue remains poorly understood. We investigate the propagation of the Ly$\alpha$ photons and evaluate the Ly$\alpha$ radiation force within a spherically symmetric accreting H i gas on to the central black hole. We solve the radiation transfer equation, incorporating the destruction processes of Ly$\alpha$ photons through two-photon decay and collisional de-excitation. We find that the Ly$\alpha$ photons, originating in the H ii region around black holes, suffer from multiple resonance scattering before being destroyed via two-photon decay and collisional de-excitation. Hence, the Ly$\alpha$ radiation force undergoes a significant amplification, surpassing gravity at the innermost section of the H i region. This amplification, quantified as the force multiplier, reaches approximately 130 and remains nearly constant, regardless of the optical depth at the line center, provided the optical thickness of the flow is within the range of $10^{10\\!-\\!14}$. The requisite lower limit of the product of gas density and black hole mass to realize super-Eddington accretion is found to be in the range $(2\\!-\\!40) \times 10^9\, M_\odot \, {\rm cm}^{-3}$, which is a few to tens of times larger than the minimum value obtained without accounting for the Ly$\alpha$ radiation force. The pronounced amplification of the Ly$\alpha$ radiation force poses a substantial challenge to the feasibility of super-Eddington accretion.

Heat and mass transfer during conductive drying of washing phosphate sludge

This study investigates the influence of drying temperature on the conductive drying behavior of washing phosphate sludge. A mathematical model, based on Fourier's Fick diffusion law and the heat transfer equation, was developed to simulate coupled heat and mass transfer during the drying process, incorporating the shrinkage effect. The sludge samples, obtained from the Khouribga phosphate plant in Morocco, were subjected to drying at temperatures of 70°C and 95°C. The experimental setup included continuous monitoring of temperature, humidity, and mass loss throughout the process. COMSOL Multiphysics software was used to solve the nonlinear equations governing heat and mass transfer. Results indicate that increasing the drying temperature significantly accelerates the drying rate. The model successfully predicts the moisture content and temperature distribution over time, aligning well with experimental data. Statistical validation, using the determination coefficient (R²) and root mean square error (RMSE), confirms that the model accurately describes the drying behavior, with R² values of 0.9957 and 0.9967 at 70°C and 95°C, respectively. The inclusion of the shrinkage effect enhances the model's precision in describing the drying kinetics under varying conditions.

Theoretical investigation of multipulse femtosecond laser processing on silicon carbide: ablation, shielding effect, and recast formation

In this study, we propose a transient multi-physics coupling model for ultrafast laser ablation based on the material point method (MPM). By employing the continuum assumption for material, heat transfer equation and particle phase change, as well as spatial discretization of the model, we achieve simulations of various coupled physical phenomena such as material temperature, phase change, stress, and recast layer formation. In terms of time, we simulate laser processing processes with up to 1000 pulses. The model is validated by comparing with experimental results on ablation morphology, recast layer formation from melted particles, and surface oxidation. The proposed model accurately captures the multi-physics aspects of ultrafast laser ablation processes in SiC ceramics. The experimental validation confirms the model’s reliability and offers valuable insights into the underlying physical phenomena.

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Modeling proppant transport and settlement in 3D fracture networks in geothermal reservoirs

In this paper, we develop an efficient proppant transport model using the Eulerian-Eulerian approach for simulating proppant transport in fractures and 3D fracture networks in geothermal reservoirs. The proposed model accounts for proppant settling, pack/bed formation, bridging/screenout, proppant concentration effect, fracture wall effect, and the transition from Poiseuille flow (fracture channel) to Darcy flow (proppant pack). Notably, the heat transfer process and its impact on proppant transport are also considered—a facet often overlooked in previous proppant transport models. A three-dimensional displacement discontinuity method (3D DDM) that incorporates the stress shadow effect is employed to generate the fracture geometry. The governing equations for slurry flow, proppant transport, and heat transfer are discretized and solved using the finite volume method (FVM). The model is verified against analytical solutions and published experimental data, demonstrating good agreement with these references. To demonstrate the proposed model, we applied it to both low-temperature (depleted hydrocarbon wells) and high-temperature (dry hot rocks) enhanced geothermal systems (EGS). The simulation results highlight the significant influence of reservoir temperature on proppant transport and settlement in a reservoir environment. Heating of the slurry by higher temperature reservoir rocks reduces fluid viscosity and accelerates proppant settling, thereby shortening the transport distance and reducing the coverage area of the proppant. Both ultra-light and micro-proppant are effective in mitigating proppant settlement in enhanced geothermal systems. However, proppant is susceptible to bridging at fracture intersections, where the fracture widths are narrower due to more pronounced stress shadow effects in these areas. Consequently, the use of micro-proppant could offer substantial benefits over ultra-light proppant in enhancing proppant coverage area in enhanced geothermal systems.

Study on radiation characteristics of multi-phase plumes containing ice crystals in orbit-control engines

In order to obtain the radiation characteristics of the multiphase plume containing ice crystals in the high-altitude orbit control engine and analyze its influence on the telemetry effect, this paper deduces the radiation characteristics parameters of gases based on Einstein radiation theory and radiation transfer equation. Based on the latest HITRAN2020 spectral line library solving gas radiation and the Mie theory of particle scattering solving particle radiation, the radiation characteristic parameters of the multi-phase plume containing ice crystals in the high-altitude orbital control engine and the radiation intensity distribution in the near-infrared and mid-long wave infrared bands are simulated, and the main influencing factors of the radiation are analyzed. The results show that, in general, the main radiation of the engine plume includes the scattered light in the near infrared band and the thermal radiation in the middle long wave infrared band. In the near-infrared band, considering solar background radiation, the total radiation amount in the calculation domain is about 10 −6 W/sr, and the thermal radiation is dominant within the axial distance of 0.5 m, while the ice crystal scattering is dominant beyond the axial distance of 0.5 m . In the mid-long wave infrared band, the total radiation amount in the calculation domain is about 10 W/sr, and the thermal radiation of gas dominates within 1 m axial distance, while the thermal radiation of ice crystal dominates beyond 1 m axial distance.

Thermal gradient-induced critical current degradation in mesoscopic superconducting thin film

Abstract Superconducting materials inevitably suffer from the sudden change of temperature in localized areas in practical applications, and the concomitant thermal gradient may be detrimental to their performance. Critical current density is a key factor affecting the performance of superconductors. However, the effect of thermal gradient on the critical current density has not been identified. Here, by combining the time-dependent Ginzburg–Landau equations and the heat transfer equation, the thermal gradient and magnetic field dependence of the critical current density are systematically investigated and rationalized by exploring the behavior of vortex and magnetization. For lower magnetic fields, it is found that the thermal gradients strongly reduce the local surface barriers, which inhibits vortex entry and movement, leading to a rapid deterioration of the current-carrying capability. Under moderate magnetic fields, the critical current density corresponding to higher thermal gradients decreases more slowly with increasing magnetic field, which results from the thermal gradient-induced entry and moving of vortices along the current direction. As the magnetic field continues to increase, the variation of the critical current density transitions into a platform period and even slightly rises. The enhanced critical current is primarily attributed to the excess entry of vortices, which increases the surface barrier of the sample. With the further increase in the magnetic field, the critical current density continues to decrease due to increased magnetic field penetration. These results unveil the fundamental interplay between thermal gradients, external magnetic field, vortex, magnetization and critical current density, and provide a theoretical basis for understanding the heat-induced quenching of mesoscopic superconducting thin films in practical applications.

Improved Fracture Permeability Evaluation Model for Granite Reservoirs in Marine Environments: A Case Study from the South China Sea

Permeability is a crucial parameter in the exploration and development of oil and gas reservoirs, particularly in unconventional ones, where fractures significantly influence storage capacity and fluid flow. This study investigates the fracture permeability of granite reservoirs in the South China Sea, introducing an enhanced evaluation model for planar fracture permeability based on Darcy’s law and Poiseuille’s law. The model incorporates factors such as fracture heterogeneity, tortuosity, angle, and aperture to improve permeability assessments. Building on a single-fracture model, this research integrates mass transfer equations and trigonometric functions to assess intersecting fractures’ permeability. Numerical simulations explore how tortuosity, angle, and aperture affect individual fracture permeability and the influence of relative positioning in intersecting fractures. The model makes key assumptions, including minimal consideration of horizontal stress and the assumption of unidirectional laminar flow in cross-fractures. Granite outcrop samples were systematically collected, followed by full-diameter core drilling. A range of planar models with varying fracture apertures were designed, and permeability measurements were conducted using the AU-TOSCAN-II multifunctional core scanner with a steady-state gas injection method. The results showed consistency between the improved model and experimental findings regarding the effects of fracture aperture and angle on permeability, confirming the model’s accuracy in reflecting the fractures’ influence on reservoir flow capacity. For intersecting fractures, a comparative analysis of core X-ray computed tomography (X-CT) scanning results and experimental outcomes highlighted discrepancies between actual permeability measurements and theoretical simulations based on tortuosity and aperture variations. Limitations exist, particularly for cross-fractures, where quantifying complexity is challenging, leading to potential discrepancies between simulation and experimental results. Further comparisons between core experiments and logging responses are necessary for model refinement. In response to the challenges associated with evaluating absolute permeability in fractured reservoirs, this study presents a novel theoretical assessment model that considers both single and intersecting fractures. The model’s validity is demonstrated through actual core experiments, confirming the effectiveness of the single-fracture model while highlighting the need for further refinement of the dual-fracture model. The findings provide scientific support for the exploration and development of granite reservoirs in the South China Sea and establish a foundation for permeability predictions in other complex fractured reservoir systems, thereby advancing the field of fracture permeability assessment.

Approximate Solution of Fuzzy Sedimentary Ocean Basin Boundary Value Problem Using Variational Iteration Method

The problem that is considered in this paper is developed from the migration of the coastline over time in sedimentary ocean basins that may be considered as a moving boundary problem with a variable latent heat transfer equation as a governing equation if one of the boundaries is unknown, with boundary and initial conditions are given. This model discusses the shoreline movement within sedimentary basins. The main objective of the paper is to use fuzzy logic to formulate this problem when modelling sand particles migration in saltwater by utilizing fuzzy numbers whenever replacing some of the problem's parameters. In reality, the proposed model is more general than the nonfuzzy or crisp models. By employing the variational iteration method, the approximate numerical solution of the proposed problem has been found, and computer software written in Mathematica 11 have been used to obtain the results.

Towards a theory of steady-state solidification process with a quasi-equilibrium two-phase region

AbstractThe process of directional crystallization in the presence of a quasi-equilibrium two-phase region located between the solid material and the liquid phase is studied theoretically. The mathematical model of the process is based on heat and mass transfer equations in the solid, liquid and two-phase regions, as well as boundary conditions at the phase interfaces “solid phase” – “two-phase region” and “two-phase region” – “liquid phase”, which are moving with a constant velocity. The process of directional crystallization is given by fixed temperature gradients in the solid and liquid phases, which determine a constant velocity of melt solidification. An exact analytical solution of the nonlinear problem with two moving boundaries of phase transformation is obtained, which is based on the transition to a new independent variable, the solid phase fraction, when integrating the nonlinear heat and mass transfer equations in the two-phase region. As a result of solving the problem, the distributions of temperature and concentration of dissolved impurity, the solid phase fraction in a two-phase region, the laws and velocities of motion of its interphase boundaries are determined. It is analytically shown that the impurity concentration and temperature in the two-phase region are only the functions of solid phase fraction, which, in turn, depends on the spatial coordinate. Analysis of the obtained solutions shows that the solid phase fraction in a two-phase region can be both a decreasing and increasing function of the spatial coordinate, which is directed from the solid material to the melt. This determines the internal structure of two-phase region, its permeability, average interdendritic spacing, distribution of dissolved impurity, crystallization velocity and laws of two-phase region boundaries.

Dynamic insights into thermal shock response of double-layer cylinders with FGM main layer and viscoelastic holder via generalized Green-Naghdi theory

This study investigates the dynamic thermoelastic response of a hollow cylinder composed of two distinct layers: a Functionally Graded Material (FGM) as the primary layer and an isotropic viscoelastic material as the supporting layer. Utilizing a power function, the material properties of the FGM layer are determined, while the viscoelastic layer follows the Kelvin-Voigt model. The research employs the generalized Green-Naghdi theory to formulate the heat transfer equation, capturing the energy dissipation and thermoelastic wave propagation within this novel configuration. Highly coupled equations governing both layers are derived, incorporating appropriate boundary and continuity conditions. The Chebyshev collocation element (CCE) method is utilized for the spatial solution, significantly reducing the computational effort by requiring only two higher-order elements. The Newmark time marching approach is employed to solve the resulting ordinary differential equations (ODEs). The model's accuracy is validated against existing literature, and parametric studies are conducted to evaluate the impact of thermal shock on the FGM layer. It has been observed that the presence of the viscoelastic barrier effectively impedes the full penetration of stress waves, thereby reducing the potential for shock-induced damage.

Two-dimensional P1 approximation (P1-2D) for the evaluation of the radiant field in annular and tubular photocatalytic reactors

The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in two dimensions using the P1 approximation approach (P1-2D) to describe the radiant field in annular and tubular photocatalytic reactors. The radiant sources employed were assumed to be periodic when applying the boundary conditions to facilitate the determination of the integration constants in the RTE solution. Three different systems were considered: S1 and S2 consisted of annular reactors, while S3 consisted of a tubular reactor. Simulations were conducted using commercial TiO2 P25 and anatase TiO2 as photocatalyst models, with their optical properties sourced from the literature. The linear source spherical emission (LSSE), Gaussian emission (GE), and uniform emission (UE) models were used as radiant sources. The LVRPA was found to decrease from the inner to the outer wall of the reactor for S1 and S2, and from the wall to the center of the reactor for S3; it was close to the values obtained using the Monte Carlo (MC) procedure in S2. The overall volumetric rate of photon absorption (OVRPA) increased exponentially with catalyst loading until a point where no significant increase was observed for each reactor. The apparent optical thickness τ App 1 ​formulated was a more reliable optimization parameter than the optical thickness.

Exact analytical solution of the equations for a quasiequilibrium two-phase domain: permeability and interdendritic spacing

This study is concerned with the theoretical description of a quasi-stationary process of directional crystallization of binary melts and solutions in the presence of a quasi-equilibrium two-phase region. The quasi-equilibrium process is ensured by the fact that the system supercooling is almost completely compensated by heat released during the phase transformation. Quasi-stationarity of the process determining constancy of the crystallization rate is ensured by given temperature gradients in the solid and liquid phases. The system of heat and mass transfer equations and boundary conditions to them under these assumptions is dependent on a single spatial variable in the reference frame moving with the crystallization rate relative to a laboratory coordinate system. Exact analytical solutions to the formulated problem in parametric form are obtained. The parameter of the solution is the solid phase fraction in a two-phase region. The distributions of temperature and impurity concentration in the solid, liquid and two-phase regions of the crystallizing system, the rate of solidification, and the spatial coordinate in the two-phase region depending on the solid phase fraction in it are found. An algebraic equation for the solid phase fraction at the interface between the solid material and the two-phase region is derived. Exact analytical solutions show that the impurity concentration in the two-phase layer increases as the solid phase fraction increases. Moreover, the solid phase fraction at the interface solid phase — two phase region and its thickness increase as the temperature gradient in the solid phase and the solidification rate increase. The developed theory allows us to determine analytically the permeability of the two-phase region and a characteristic interdendritic spacing in it. Analytical solutions show that the relative permeability in the two-phase region increases from a certain value at the interface with the solid phase to unity at the interface with the liquid phase. The selection theory of stable dendritic growth allows us to determine analytically a characteristic interdendritic distance in the two-phase layer that decreases as the temperature gradient in the solid phase increases. An increase of impurity in the molten phase gives a decrease in the interdendritic spacing within a two-phase region.

THE IMPACT OF SOLAR RADIATION ON THE TEMPERATURE REGIME OF A ROOM IN WINTER

The article is devoted to the computational studies of the air-thermal state of office premises taking into account the effect of solar radiation coming through window openings. The study was conducted for a room with two windows using two heating devices installed under them. The air-temperature regime of premises in winter, characterized by the highest thermal energy consumption for heat supply, is considered. The study is based on the solution of a three-dimensional nonlinear heat transfer problem described by a system of equations of turbulent momentum and energy transfer. The k-e turbulence model is used to close this system. The results of numarical modeling of the physical situation under study are presented. The research data on the features of the air-thermal state of the premises under solar radiation conditions are given. The results of a comparative analysis of the air-temperature conditions of office premises corresponding to the solution of the specified heat exchange problems in the presence and absence of solar radiation are presented and the effects of solar radiation on the structure of the air flow and the thermal state of the premises are established. It is shown that in the presence of solar radiation, the air flow picture and the character of the temperature fields in the premises change significantly. In particular, in these conditions, the increase in the average temperature of the premises for the studied period is 2.5 °С. The possibility of a certain reduction of the load on the heating system in the presence of solar radiation is noted. Bibl. 17, Fig. 5.

DEVELOPMENT OF THE THEORY OF GAS FUEL COMBUSTION TAKING INTO ACCOUNT MODERN KINETIC MECHANISMS OF COMBUSTION

An actuality of modernizing advancement the modern adopted combustion theory is due to a significant change in the composition of fuels at the market of developed countries by rejection of basic mineral (organic) fuels (fossil fuels), which have been used in the world for 250 years. The transformation of traditional fuels’ orientation towards an application of carbon-free fuels, primarily to hydrogen and its mixtures with natural gas. Each way of mentioned activity is connected with to ensure an environmental decarbonisation. Criteria for evaluating the CO2 emissions by fuels’ choice and selection have been proposed while numerical calculations of the specific CO2 content in the combustion products of the hydrocarbon-hydrogen mixture jʹ and j have been evaluated. It is possible to reduce these values when adding the shared H2 in the fuels (m3 CO2/ MJ; kg CO2/ MJ). Considering the combustion process in combustion systems (combustion chambers, boilers, furnaces) at constant pressure (p =const, dp =0 — isobaric process), the enthalpy of the reactants’ flow of the mixture (total (chemical) enthalpy I) can serve as a measure of the specific energy of the reacting mixture. An approach is proposed, according to which the main equations of heat and mass transfer in the torch (premixed flame) are composed basing upon the principle of conservation the total (chemical) enthalpy representing energy as basic function. The basic approach to the development of a modern combustion theory is focused on the concept of T. von Karman, according to which the combustion process is considered as “aerothermochemistry”, i.e. the description of physical and chemical processes is based on the combination of heat and mass transfer equations with chemical kinetics’ equations. At the current period, the problem of chemical kinetics (burning process) is considered through the combustion mechanisms of basic fuels, which consist of a large number of equations for molecules and particles involved in process at various stages of the combustion — from the preheating of the reaction mixture and through the stage of ignition (or self-ignition) — to the final temperature of flue gases. The laminar combustion velocity SL is a determinative characteristic of the combustible properties of gas fuels and, accordingly, of the safety restrictions by the fuel choice. Quantitative values of SL for the separate basic fuels, including the hydrogen, both the organic (fossil fuels) and alternative ones could be differed by an order of magnitude and more. The problem of estimable forecasting the SL value provides an option of the composition of the fuel-oxidant mixture in the industry, power and municipal energetics. The SL value’s prediction makes an especially important action at the current stage of modelling completion with an account of the global warming and by preventing an excess of CO2 emissions, including involvement of hydrogen-containing gases by substitution the carbon-friendly fuels, firstly the fossil fuels. The contemporary theory of combustion has been developed by extensive use the adequate kinetic mechanism GRI-Mech 3.0, the universality of which has been confirmed by our calculations of SL values for a wide range of the gas fuels — from methane CH4 to hydrogen H2 and their mixtures. An advanced modern theory of combustion using the adequate and approved GRI-Mech 3.0 combustion kinetic mechanism has been developed. The universality of this mechanism is confirmed by our calculations of SL values for a wide range of gaseous fuels — from methane CH4 to hydrogen H2 and their mixtures (mixed gases MG). For further analysis and development, the model of combustion in the reacting flow by Y.B. Zeldovich and D.A. Frank-Kamenetsky was used, considering the transfer processes of total enthalpy I as the energy characteristic of the combustible mixture. The kinetic component (on the example of natural gas) is taken into account using the combustion mechanism for GRI-Mech 3.0. The latter summarizes the combustion process of through 325 constituent reactions for 53 components. The adequacy of the combustion model proposed in the paper is confirmed by numerical examples of the coincidence of numerical SL values: ours — calculated; literary — experimental. The validity of experimental values of SL is provided by the use of different methods of measuring the SL. Calculations of the specific total enthalpy I of the reacting mixture along the length x º l (thickness of the front for a homogeneous flame in a one-dimensional formulation) have been performed as a result of researches confirmed the initial position: I(x) = const with deviations for CH4 +7 % / –2 %; for H2 +9,2 % / –2,8 % in relation to the heat of combustion. Bibl. 52, Fig. 9, Tab. 3.

Estimation and Optimization of the Radiant Field in Flat Plate Heterogeneous Photoreactors with the P1-approximation of the Radiative Transfer Equation (RTE).

In this work, the P1-approximation of the radiative transfer equation (RTE) was used for the description and optimization of the radiant field in a flat plate photoreactor under solar radiation with three commercial brands of titanium dioxide photocatalysts. The boundary layer of photon absorption (δ_abs), the average volumetric rate of photon absorption (VRPA), and a new apparent optical thickness (ζ_app1) were used as design parameters for optimization. A simple mathematical expression for the calculation of δ_abs also called the best reactor thickness was formulated. For the three catalysts, varying the reactor height (L), it was found a decrease in the local volumetric rate of photon absorption (LVRPA) from the top side until the bottom of the reactor for any value of the catalyst loading (Ccat). It was also observed that when Ccat increases the VRPA increases exponentially until a fixed value where it remains almost constant. With L= 1 cm, the optimum Ccat (Ccatop) was 0.2 g/l in 0.85 cm of thickness, 0.3 g/l in 0.82 cm of thickness, and 0.4 g/l in 0.89 cm of thickness for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. The optimum apparent optical thickness (ζ_(app1,op)) was 4.03, 4.62, and 3.7 for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. These results are in good agreement with the literature. Results found in this work give predictions on radiation absorption in flat plate photocatalytic reactors with different heights.