Математическая модель процесса обжига слоя кускового известняка
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 1
Abstract
MATHEMATICAL MODEL OF PROCESS OF BURNING OF LAYER OF LUMP LIMESTONE Ryzhov A.F., Milashenko N.S. Abstract The receipt of quantitative lime for different industries of industry requires development of the corresponding technological modes. For the choice of the rational mode of thermal treatment of limestone in kilns it is desirable to have the generalized analytical expressions qualificatory the temperature field and dynamics of decomposition of limestone depending on the terms of external heat exchange. An aim of work is analytical researches of process of heating of layer of lump limestone passing with deepening of surface of dissociation deep into material. The decision of task of non-stationary heat conductivity of flat piece of limestone is presented at the border terms of the third family with the locomotive border of phase transformation. For the decision of nonlinear task of heat conductivity the method of reduction and self-reactance indignation is used. Because of application of method of self-reactance indignation the initial nonlinear task of heat conductivity is transformed in the sequence of usual linear differential equalizations the decision of that is possible by means of well-known methods of mathematical physics. Found analytical dependences, qualificatory character of advancement of border of division of phases and distribution of temperature on a section. Presented in a criterion kind and simply enough realized at numeral calculations. Calculations show that a satisfactory accuracy for the practice provides a first approximation. Using this methodology, the generalized dependence of duration of the complete burning of piece of limestone of flat form is got on the different terms of external heat exchange. Found analytical relationships that define the character of advancement of the phase boundary and the distribution over the cross section of the heated piece of material temperatures are in the form of a criterion, and simply implemented in numerical calculations. They are obtained in an explicit form, which facilitates the analysis of the thermal state of a burnt piece of limestone in the furnace.The presented analytical methodology can be used for the choice of the rational mode of burning of lump limestone in stoves. References [1] Monastyrev, A.V. (1975), Proizvodstvo izvesti [Manufacture of lime]. - M .: Higher School, - 224 pp. [2] Lykov, A.V. (1968), Production of lime [The theory of heat conduction]. - M .: Energia, 1968. - 472 pp. [3] Lyubov, B.J. and Yalovoy, N.I.(1970), Matematicheskij analiz plavleniya [Mathematical analysis of the melting bodies] // Math. USSR Academy of Sciences. Metals. № 2. - S. 152-162pp.
Authors and Affiliations
А. Ф. Рыжов, Н. С. Милашенко
Keywords
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