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

1
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, 31982 Hofuf, Al Ahsa, Saudi Arabia
2
Department of Mathematics & Statistics, Bacha Khan University, 24461 Palosa, Charsadda Khyber Pakhtunkhwa, Pakistan
*
Author to whom correspondence should be addressed.
Processes 2019, 7(7), 453; https://doi.org/10.3390/pr7070453
Received: 11 June 2019 / Revised: 10 July 2019 / Accepted: 12 July 2019 / Published: 15 July 2019
(This article belongs to the Special Issue Chemical Process Design, Simulation and Optimization)
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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 efficiency 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. View Full-Text
Keywords: volume-based population balance model with fines dissolution; quadrature method of moments; orthogonal polynomials volume-based population balance model with fines dissolution; quadrature method of moments; orthogonal polynomials
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Mukhtar, S.; Sohaib, M.; Ahmad, I. A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit. Processes 2019, 7, 453.

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