Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

Modeling of Hardwood Pyrolysis Using the Convex Combination of the Mass Conversion Points

This work investigates the kinetics of a pyrolysis reactor. Pyrolysis is demarcated as a two-step process that is the primary and the secondary decomposition of hardwood in the presence of nitrogen. The qualitative aspect of the analysis is performed by allowing the heterogeneous characteristics of the initial distribution function of volatile content. The temperature inside the reactor varies from 19 °C to 363.761 °C. The pressure of producer gas changes from 6 Pa to 26.8 Pa during the pyrolysis of hardwood, which affects the conversion of biomass with respect to temperature. The weighted fraction of the Weibull and the Rayleigh models is used for modeling the mass variation of the biomass inside the rector. The dimension of the reactor used for the experimental work has a length of 400 mm and a cross-sectional area of 9498.5 mm2. The pyrolysis test rig is programed for the cubical form of thermal history [T = (at3 + bt2 + ct − d)].

A theoretical study of the changes in the statistical character of a polydisperse polymer system undergoing random degradation

The combinatorial procedure, employed in our earlier work in connexion with the problem of degradation of an initially monodisperse polymer system, is extended here to the polydisperse case. The results thus obtained are applied in order to study, stage by stage, the changes in the statistical character of the distribution in a number of typical cases. Next a scheme, based on an expansion of the initial distribution function in terms of the associated Laguerre polynomials, is developed in order to treat those cases in which the statistical information is confined only to a few low-order moments. Finally, we discuss the inverse problem of determining the characteristics of the initial distribution from a knowledge of the weight-average chain length at various stages of the degradation process.