Orthogonal collocation methods using Mathematica© in the graduate chemical engineering curriculum

Abstract

We present in this pedagogical paper several important aspects of the application of orthogonal collocation for solution of Chemical Engineering problems. These include: the Stefan-Maxwell diffusion; the startup of a Poiseuille Flow in a Newtonian Fluid; the transient heat conduction with temperature-dependent thermal conductivity; and the reaction-diffusion in a drop. The presented method of resolution (i.e., orthogonal collocation) of such problems can be easily introduced in any graduate-level chemical engineering numerical method course. Indeed, this technique has been used for the past four year at King Fahd University of Petroleum & Minerals (KFUPM) in the graduate-level core numerical methods course called CHE 560. ß

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

“…The scope of this study includes an explanation of how to solve the conservation equations for a Newtonian incompressible fluid. The Chebyshev collocation method is used to achieve this goal, but it is also necessary as a strategy for decoupling Equations ( 1) and (2). A first-order projection, first presented by Chorin [13], is a handy option.…”

“…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.…”

An interactive approach for illustrating a proof of the sampling theorem using MATHEMATICA

“…In ref. , the employment of interactive modules using M ATHEMATICA for the pedagogical introduction of a numerical method applied to problems in chemical engineering at graduate level is presented.…”

MATLAB applications for teaching Applied Thermodynamics: Thermodynamic cycles

“…This selection was supported by a previous successful experience using notebooks as teaching tools [9], and taking into account that redesigned educational strategies based on computer-aided chemical engineering can integrate courses more efficiently and upgrade the use of computational tools in future courses [26]. Moreover, the benefits of using computer-assisted tools to improve student learning are widely tested, in particular in laboratories [5,10,28,30], and e-learning teaching [1,7,8,21,22]; and computer savviness is among the top 10 skills chemical engineers [16].…”