*Article* **A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit**

#### **Safyan Mukhtar 1,\*, Muhammad Sohaib 2 and Ishfaq Ahmad 2**


Received: 11 June 2019; Accepted: 12 July 2019; Published: 15 July 2019

**Abstract:** In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the e fficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

**Keywords:** volume-based population balance model with fines dissolution; quadrature method of moments; orthogonal polynomials
