The physical and mathematical models of heat and mass transfer at the heating of a water droplet with carbonic inclusion in a high-temperature (more than 800 K) gas area in a flaming field of combustion are presented in the work. The physical and mathematical formulations of the heat and mass transfer problems under conditions of phase transformations are reduced. The methods of numerical solution of the set problem are described. The numerical investigations for the wide range of parameters of the system "heterogeneous water droplet with a solid inclusion - high-temperature gas area" were conducted. Two modes of phase transformations were indicated in the concerned system: the mode of formation of "flash" vaporization centers in a field of the contact between solid inclusion and liquid (at a temperature of gas area Tf > 1050 K and a radius of heterogeneous droplet r₂ > 0.3 10³ m) and the mode of liquid evaporation from the free droplet surface into the field of high-temperature gases (at Tf < 1050 K and r₂ < 0.3-10^-3m). The distributions of temperature corresponding to each of revealed modes of phase transformations were presented. The comparison of numerical simulation results with the results of conducted before experimental investigations of evaporation of water droplets with solid inclusions during motions in a "flame" combustion field was carried out. A good agreement with the results of numerical calculation using the developed model and the results of experimental investigations was revealed.

Analytic solution of the problem of stationary spherically symmetric double-front diffusion combustion around a particle boiling fuel (with infinite density to ensure the stationarity of combustion) in a hybrid atmosphere was derived. Under the hybrid atmosphere was understood to be a mixture of air and combustible gas, present in a quantity smaller than the lower concentration limit of the flat flame propagation through gas-air mixture (LEL_g). The nearest to particle flame front (A) has the same nature as the single diffusion flame front around the particle burning in clean air (Varshavsky, 1945). In the second flame front (B) there is a stable diffusion combustion of gas-air mixture. Main assumptions facilitate the representation of results in analytical form, was to neglect the influence of gravity, heat loss by radiation, the real thickness of the diffusion flame, the dependence of the thermophysical parameters on the temperature. It was assumed that the temperature of the flame at the limit of diffusion combustion in front B coincides with the temperature of the flat flame in the gasair mixture at LEL_g. The Lewis number equal to 1 for all components of the gas phase apart from the combustible gas, in which this parameter (Le₃) can take different values. The results are illustrated on two variants of the original data. In the first variant, all combustible gaseous components identical to typical hydrocarbon (ethane). The difference between the second variant of the modeling from the first variant was only the fuel gas for which diffusion capacity, LEL_g and the burning temperature, borrowed from hydrogen. Dependencies of the size and temperature of the diffusion flames on the content of combustible gas in the air and the particle radius shown in the graphic form for both versions. The geometric similarity of the fields of temperature distribution in space was absent for particles with radius of the order of and less than 20 |im. As in the case of unstable stationary diffusion flame in a homogeneous combustible mixture (Zeldovich, 1944) when Le₃ > 1 in the area bounded by the front surface B, it was noted superadiabatic temperature. The stationary solution of the task was absent when the concentration of combustible gas exceeds LEL_g /Le₃. The function of the temperature distribution in the space between the fronts A and B linearly increased with the increase of the content of combustible gas. The last rule was used for the quantitative explanation of the dependence of the lower concentration limits of flame propagation in dispersive component (HKIIP_s) on the content of combustible gas in the turbulent hybrid dust - combustible gas-air mixture, including an explanation of the particular case, when the combustible gas is hydrogen. Due to the lack of a theory of turbulent combustion of dust-air mixture in this application used reasonable assumptions and known experimental dependence HKIIP_s of dust-air mixture on the initial temperature.

On June, 1^st, 1976 at the company "Nipro" in Flixborough of Great Britain there was an explosion of cyclohexane which has entered into ten of major accidents of 20^th century. Despite the conducted numerous investigations of this industrial explosion a number of the technical moments of failure at the company "Nipro" are remained unknown. In particular, TNT-equivalent forecasts fluctuates largely from 15 to 55 tons. In this connection it is found that the high bound of theoretically possible weight of cyclohexane in a vapor cloud is able to make 37,9 tons. On the basis of mathematical processing of the Sadee's data it is positioned that for considered failure dependence of excessive pressure of explosion AP on distance R is described by equation AP = 94970R^-1,526 with factor of correlation 0,990. This circumstance allows to use the Sadee's data as the standard for verification of techniques of forecasting of consequences of vapor cloud explosions. As a result of the made verification of methods of RB G-05-039-96, RD 03-409-01, the SP 12.13130.2009, GOST P 12.3.047-2012, Dorofeev, TNO and BST2 is positioned that consequences of real explosion in Flixborough is better are described TNT-method from RD 03-409-01 and the Dorofeev's equation for the detonation mode.

This paper presents a modeling of fire and explosive properties of strained cyclic hydrocarbons - cyclopropene, cyclopropane, tetrahedrane, bicyclo[[1.1.0]butane, cyclobutane, propellan, bicyclopentane, spiro[2.2]pentane, prismane, cubane, 3-rotan and perspirocyclopropane[3]rotan. Calculations of concentration flammability limits (CFL) are made in two models - interpolation and molecular. It is shown, that the calculations of CFL made by interpolation model are unacceptable for the strained molecular structures. Substances of strained molecular structure with the enthalpy of formation greater than zero have wide concentration flammability limits. In detonation regime collapse of compounds of cyclopropene, tetrahedrane, propellan, prismane and cubane with the formation of graphite and hydrogen specific energy decay characteristics (decay enthalpy and velocity of the detonation wave) exceed specific energy characteristics of trinitrotoluene (TNT). We propose a parameter that characterizes the explosive properties of strained compounds - the minimum pressure at which the substance can decay in the absence of an oxidizing agent in the system.

Every year the number of forest fires considerably increases and along with this also increase the burned-out areas of forests. The main tasks of fire protection of forests are prevention of forest fires, optimum suppression and elimination of their consequences. Important aspects from the point of view of fire prevention are technologies and methods of prognostication. Basic methods of mathematical research of the probability of occurrence of forest fires are considered in this article. It is find out that the scientific researches related to the mathematical modeling of the probability of occurrence of fires taking into account thunderstorm activity and anthropogenic load have mainly applied value and are aimed at providing of fire safety of forests and elimination of the landscape fires. Creation of mathematical model and methods of solving of a task of optimization of fire safety system using simulation modeling is considered. After investigation of the numerical data and after analysis of results of computing experiment it is possible to say that if thunderstorm activity will remain at the same (high) level and the level of influence of the anthropogenous factor will be reduced from 0.95 to 0.55, the area of forest fires will be reduced nearly by 10 times. In this regard it is possible to conclude that researches which purpose is optimization of mathematical model and software package for monitoring and prognosis the occurrence of wildfires on the basis of simulation modeling are relevant.

Efficiency of smoke removal systems may be reduced due to the phenomenon of "plugholing", which lies in the fact that the clean air out under ceiling smoke layer due to the action of lift forces passes through the smoke ejection hole. Amodified zone model for calculation of thermal and gas dynamics of fire under action of a smoke removal system with artificial impulse during "plugholing" is proposed. Reducing the flow rate of a mixture of gases and smoke leaving from under ceiling layer outside the room is taken into account by introducing the rate coefficient. A numerical study of thermal dynamics picture of fire in the model room with model combustible load by using the modified zone model and a three-dimensional field model is made. It is considered the room in the form of a parallelepiped with dimensions of 30x25x15 m. Combustible material is turbine oil. Volumetric flow rate of fan of smoke removal system are 30000, 60000 and 90000 m³/h. Dependencies between velocity of lowering the bottom border of the under ceiling layer and the time of fire, that obtained with the use of the modified zone model and a three-dimensional field model, are compared. It is shown that the smoke removal system efficiency is significantly reduced when "plugholing" is occurred. The flow rate of a mixture of gases and smoke leaving from under ceiling layer outside the room is 2 times less than in the case of the absence of "plugholing". It is found that to prevent "plugholing" in the case of smoke removal system with artificial impulse for each fan there is critical minimum square of the hole of smoke removal system, which essentially depends on the thickness of under ceiling layer at the time of the beginning of system work.

It is shown that in case of accidental explosions inside volumes of production area the propagation rate of flame front on a gas-air mixture (GAM) can increase due to the flame inherent phenomena of hydrodynamic instability, continuous movement of air and combustible mixture, presence of obstacles on the way of flame and bays flights in cladding structures. It is also shown that intensification of explosive combustion which appear in acceleration of flame propagation which result in increase of pressure rise rate and as a result has material effect on a choice of method of explosion protection of constructions from destruction. Equations determining the numerical values of intensification coefficients taking into account the type of GAM, number of objects on the way of flame propagation, ratio of their total area blocking free volume to the area of its cross section and distance between obstacles are given. The mathematical expressions describing process of discharge of explosion products directly into atmosphere based on law of conservation of mass, volume and energy for open system using baric and temperature dependence of normal speed of flame propagation, and also equations of gas efflux for subsonic and sonic modes are presented.

With consider regulation process of evacuation of people in emergency situations program computer systems which have to give the chance to analyse different settlement situations at the solution of problems of ensuring fire safety in buildings of different classes of functional fire danger are developed now. Compliance of results of the calculations perfromed by these program computer systems, to data of natural supervision of the movement of human flows in actual practice has to be an indispensable condition of possibility of their application in rationing. Therefore paramount criterion of applicability of any of such program complexes is the validity of model of evacuation which they use. It is shown that simplified the analytical and imitating and stochastic models based on extensive statistical material of researches of human streams in buildings of various functional purpose with their various structure of the main contingent of people and on the determined consistent patterns of communication between parameters of flows ofpeople of any psychophysiological state are correctly described by program computer systems ADLPV-2.0, "Floutek VD". These models reflect also the kinematic dependences of change of parameters of a flow occurring upon its transition through the borders of adjacent sites of an evacuation way described by a graphic-analytical method. The comparative analysis with these results of results of the individual and line model given in "A technique of determination of settlement sizes of fire risk in buildings, constructions and structures of various classes of functional fire danger" demonstrates a dissonance of this model. The analysis of results of the program of the individual flow movement "Evatek" model shows their convergence with the results close to the lower bound of a confidential interval of an estimated time of evacuation. The model demands completion of reproduction of kinematics of individual behavior of people. The analysis of foreign models of the individual flow movement of people which is carried out on the example of the program "PathFinder" and "FDS+Evac" complexes shows that they use dependences between parameters of streams not corresponding to human streams. As a result of the carried-out analysis comes to light that for modeling of process of evacuation it is necessary to use imitating and stochastic model of the movement of human flows which most precisely reflects dynamics of process in different exploitation conditions of the building.