Mathematical model and methods for solving heat-transfer problem during underground coal gasification

Purpose. A mathematical model development for heat transfer during underground coal gasification based on the transcendental equation solution by Newton-Raphson method. Methods. The heat-transfer is research into a temperature field with variable size of zone when passing through phase transformation boundary, which changes abruptly. seam T(x, t) and displacement length transition boundary S(t) integration differential fulfillment one-phase Stefan problem conditions. proportionality factor (?), characterizing ratio “generator gas – coal” to time gasification, determined substituting Boltzmann using method solving obtained equation. Findings. main problems related laboratory process have been identified. closed georeactor system has developed, taking account effective change in its active zones. Originality. at under conditions are fulfilled. Dependences generator temperature, zones chemical reactions along combustion face column, revealed. In addition, dependences heterogeneous determined, characterize reveal relationship between thermal conductivity coefficient, specific capacity, as well bulk density calorific value. Practical implications. developed determine process. This makes it possible predict future column.