Solution of six chemical engineering problems using the Chebyshev orthogonal collocation technique

Binous, Housam; Kaddeche, Slim; Bellagi, A.

doi:10.1002/cae.21823

Cited by 7 publications

(3 citation statements)

References 14 publications

(27 reference statements)

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“…Details of these methods can be found in the (ESM). Binous and collaborators have done previous remarkable work on the application of the Chebyshev orthogonal collocation method using Mathematica© and Matlab R on several important problems in chemical engineering, 23,24 including the Weisz and Hicks original problem. 25 Unfortunately, the OC method did not perform well for this problem, and its details will not be further explored herein.…”

Section: Numerical Methods and Parameter Spacementioning

confidence: 99%

The influence of dissociative adsorption on effectiveness factors of porous catalysts

Soares

2022

Int J of Chemical Kinetics

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The actual concentration profile of a reacting fluid inside a porous catalyst is something of a mystery. However, there are powerful models to predict the concentration distribution, and effectiveness factor as a function of the Thiele modulus. This work provides a model for the porous catalyst particle considering heterogeneous kinetics for steady‐state Langmuir‐Hinshelwood rate expressions, including the cases when adsorption stoichiometry is other than 1:1, as for dissociative adsorption (1:2), which have not been covered by the preceding literature. The isothermal and the non‐isothermal particles are considered. Numerical solutions for the concentration profile of a limiting reactant were calculated by three methods: finite differences with Newton‐Raphson recursion, Chebyshev orthogonal collocation, and integration by Adams method as done by Weisz and Hicks. The Weisz‐Hicks method outperformed the other two. Plots show the results for specific cases, which are briefly discussed. Adsorption stoichiometry and pellet geometry are of paramount importance for the assessment of effectiveness factors. The results demonstrate that the effectiveness of a catalyst pellet with prevalent dissociative adsorption of a reactant is always inferior to the effectiveness with prevalent simple adsorption.

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Section: Numerical Methods and Parameter Spacementioning

confidence: 99%

The influence of dissociative adsorption on effectiveness factors of porous catalysts

Soares

2022

Int J of Chemical Kinetics

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“…There are many works on spectral methods in Matlab, such as the book and papers of Trefethen [27,28]. Binous et al [2][3][4][5][6]24] have some studies related to the implementation of the Chebyshev collocation method. In particular, they use packages like Mathematica or Matlab to perform the solution of problems generally related to heat transfer and chemical transport.…”

Section: Introductionmentioning

confidence: 99%

On the solutions of fluid flow problems with a Chebyshev collocation method using Mathematica

Acosta‐Zamora

Núñez

2022

Comp Applic In Engineering

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Fluid flow problems are important in engineering applications like heat exchangers, renewable energy sources, and electromagnetic processing of materials, among other applications. Some examples related to a computational fluid dynamics (CFD) course are explored in this study. A CFD course provides tools for the numerical solution of fluid flows where an analytical cannot be found. Flows can be described by numerically solving the mass, momentum, and energy conservation equations for incompressible fluids.A Chebyshev collocation spectral method has been used to solve the governing equations. A high-level functional programming language strategy was implemented in Mathematica including readability and adaptability. The programs are built by applying and composing functions, mappings, iterators, and pattern matching. It was noted that students can achieve a better comprehension of the algorithms using this programming approach.

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“…Then, one needs to solve the resulting algebraic system of equations for the problem at hand. Details for the generation of the node grid and the implementation of the method of resolution can be found in previous works [1,3,4] as well as in the Supporting Information.…”

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confidence: 99%

Solving boundary value problems in heterogeneous catalysis with orthogonal collocation and arc‐length continuation

Von‐Held Soares,

Binous,

Peixoto

et al. 2023

Comp Applic In Engineering

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An important part of the education of chemical engineers involves the design and assessment of heterogeneous catalytic reactions. They pose fundamental phenomena and constitute invaluable industrial processes. Progressing in this field, especially in graduate‐level courses, entails solving nonlinear differential equations systems, which can only be achieved by using efficient and reliable numerical techniques. In this work, we solve nonisothermal one‐dimensional reaction‐diffusion BVP considering convection in the boundary conditions, by applying orthogonal collocation and arc‐length continuation. Particularly, we predict the effectiveness factor as a function of the Thiele modulus for the main three particle geometries: plane slab, cylinder, and sphere. For chemical engineering students, such problems are at the zenith of the discipline, and the results of such calculations can elucidate basic and advanced concepts of mass and heat transfer as well as chemical reaction engineering. Both Chebyshev and shifted Legendre polynomials were used to transform the boundary value problem into a set of algebraic nonlinear equations. In addition, we also compare our findings against the available analytic solutions whenever possible. Codes in Scilab, Matlab®, and Mathematica© were developed for the solution of such problems and are available in the Supporting Information. There are two possible approaches to compute effectiveness factors: (a) integration as per definition versus (b) differentiation and nonlinear system. It is demonstrable that software performance is dependent on the approach, and that the differentiation approach yields better results.

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Solution of six chemical engineering problems using the Chebyshev orthogonal collocation technique

Cited by 7 publications

References 14 publications

The influence of dissociative adsorption on effectiveness factors of porous catalysts

The influence of dissociative adsorption on effectiveness factors of porous catalysts

On the solutions of fluid flow problems with a Chebyshev collocation method using Mathematica

Solving boundary value problems in heterogeneous catalysis with orthogonal collocation and arc‐length continuation

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