Solution of partial differential equation of population balance by shifted Legendre polynomials

Abstract

Abstract The batch crystallization processes which are described by partial differential equations of the population density function with appropriate conditions are analyzed. The key method asserts that the population density function can be expressed by a series of shifted Legendre polynomial functions. An effective method which employs a shifted Legendre integral transformation associated with its polynomial functions is applied to solve population balance equations. Making the transformation, the partial differential equation is converted to a series of ordinary differential equations of expansion coefficients. The expansion of the population balance function into shifted Legendre polynomial functions is discussed in detail. The proposed method is straightforward for digital computation and accurate. Illustrative examples are given and compared with the results obtained by the moments method.