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Solving two‐dimensional chemical engineering problems using the chebyshev orthogonal collocation technique
Author(s) -
Binous Housam,
Kaddeche Slim,
Bellagi Ahmed
Publication year - 2016
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.21680
Subject(s) - orthogonal collocation , chebyshev polynomials , heat transfer , steady state (chemistry) , collocation (remote sensing) , chebyshev filter , thermal conduction , orthogonal polynomials , annulus (botany) , mathematics , collocation method , computer science , mechanics , mathematical analysis , thermodynamics , materials science , differential equation , physics , chemistry , ordinary differential equation , machine learning , composite material
ABSTRACT The present paper describes how to apply the Chebyshev orthogonal collocation technique to solve steady‐state and unsteady‐steady two‐dimensional problems. All problems are solved using one single computer algebra, Mathematica © . The problems include: (1) steady‐state heat transfer in a rectangular bar, (2) steady‐state flow in a rectangular duct, (2) steady‐state heat transfer in a cooling cylindrical pin fin, (4) steady‐state heat conduction in an annulus, (5) unsteady‐state heat transfer in a rectangular bar, and finally (6) unsteady‐state diffusion reaction system. Whenever possible the results obtained with orthogonal collocation are compared to the analytical solution in order to validate the applied numerical technique. © 2015 Wiley Periodicals, Inc. Comput. Appl. Eng. Educ. 24:144–155, 2016; View this article online at wileyonlinelibrary.com/journal/cae ; DOI 10.1002/cae.21680