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Design of continuous contacting countercurrent unit operations: An approach based on the usage of orthogonal collocation and Matlab
Author(s) -
Garma Raoudha,
Binous Housam,
Dhaouadi Hatem,
Bellagi Ahmed
Publication year - 2019
Publication title -
computer applications in engineering education
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.478
H-Index - 29
eISSN - 1099-0542
pISSN - 1061-3773
DOI - 10.1002/cae.22153
Subject(s) - countercurrent exchange , orthogonal collocation , discretization , algebraic equation , ordinary differential equation , matlab , collocation method , collocation (remote sensing) , differential equation , nonlinear system , current (fluid) , computer science , control theory (sociology) , mathematics , mathematical analysis , thermodynamics , physics , machine learning , control (management) , quantum mechanics , artificial intelligence , operating system
A counter‐current set‐up is preferred to its co‐current counterpart because substantial improvement in the performance of the unit operation is achieved. Hence, proper design of countercurrent unit operations is a fundamental part of any undergraduate chemical engineering curriculum. The governing equations, derived from material and/or energy balance equations around a continuous‐contact counter‐current unit consist of at least two coupled differential equations where the independent variable is either position or area. Such problems also involve limit conditions at both edges of the unit. In the present paper, we demonstrate that these mathematical problems are readily solved by the orthogonal collocation technique despite their seemingly mathematical complexity especially to undergraduate chemical engineering students. Our approach is applied to following four case studies: (a) countercurrent heat exchanger, (b) gas‐liquid absorption in a packed column, (c) water cooling tower and finally (d) gas permeation using dense membranes. One advantage of the method lays in the fact that both (a) the size of the equipment (eg, height of the gas‐liquid contactor, area of the separation membrane or heat exchanger…) and (b) the compositions and/or temperature profiles are obtained simultaneously in a single fast and easy calculation. These computations always involve a discretization step based on collocation points. This discretization transforms the differential equations into a set of nonlinear algebraic equation, which is readily solved using the ubiquitous command (ie, fsolve ) of Matlab® .