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Simulation of discontinuous population balance equation with integral constraint of growth rate expression
Author(s) -
Chang RongYeu,
Wang MawLing
Publication year - 1985
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450630320
Subject(s) - mathematics , legendre polynomials , partial differential equation , constraint (computer aided design) , population balance equation , population , continuous function (set theory) , first order partial differential equation , mathematical analysis , function (biology) , differential equation , partial derivative , expression (computer science) , computer science , geometry , demography , evolutionary biology , sociology , biology , programming language
An effective method based on the concept of continuous characteristics is developed to solve the continuous population equation with integral constraint of growth rate expression. This method can also be extended to solve a general form of a first order partial differential equation. A typical example of a class II MSMPR crystallization process at transient state is modelled and analyzed. The system which possesses originally a discontinuous population density function is transformed into a continuous one by appropriate treatment of the initial condition. The partial differential equation of the continuous population density function is solved by the shifted Legendre polynomials approximation and moments method simultaneously. The original discontinuous population density function is then transformed back from the calculated continuous one by the system characteristics. Very satisfactory computational results are obtained.