At the coal deposits exploitation by using underground methods, as a rule, negative factors that reduce coal production and miners' safety exhibit. These factors include, first of all, methane emitted from the broken coal and the coal dust as an inevitable result of work of headers and cleansing combines. Interacting with the atmosphere of mines, methane and coal dust generate dust- and dust-gas-aerial mixtures where thermophysical and chemical processes take place. First of all, these processes are combustion and detonation that until recently were included into the category of highly hazardous accidents.
Based on the assumptions of single-stage chemical reaction of combustion and ideal gas agents and reaction products, an attempt to construct a math model of combustion of aeromethane mixture, considering the kinetics of chemical reaction of the origin agents. Three justified simplifying suggestions are made. The first implies that the pressure derivative is negligibly small in relation to the temperature derivative. The second implies that the area of laminar combustion consists of two zones: the mixture is being heated in one of them, and the combustion chemical reaction takes place in the other. The third implies that the temperature of mixture’s ignition does not significantly differ from the end temperature of the mixture at the completion of combustion reaction.
A boundary value problem for the ordinary non-linear differential equation of the second order is set. Considering the simplifying assumptions, this was reduced to the linear equation whose solution is found in quadrature. The formulas describing combustion process have been developed. The dependences of the rate of laminar combustion on a number of mixture’s properties are established.
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