Solving two-dimensional chemical engineering problems using the chebyshev orthogonal collocation technique

Housam Binous; Slim Kaddeche; Ahmed Bellagi

doi:10.1002/cae.21680

Solving two-dimensional chemical engineering problems using the chebyshev orthogonal collocation technique

Housam Binous^*
, Slim Kaddeche
, Ahmed Bellagi

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English
Pages (from-to)	144-155
Number of pages	12
Journal	Computer Applications in Engineering Education
Volume	24
Issue number	1
DOIs	https://doi.org/10.1002/cae.21680
State	Published - 1 Jan 2016

Bibliographical note

Publisher Copyright:
© 2015 Wiley Periodicals, Inc.

Keywords

M ATHEMATICA
chebyshev polynomials
graduate-level education
momentum - heat - mass transfer
numerical methods
orthogonal collocation

ASJC Scopus subject areas

General Computer Science
Education
General Engineering

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10.1002/cae.21680

Cite this

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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.",

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author = "Housam Binous and Slim Kaddeche and Ahmed Bellagi",

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AU - Binous, Housam

AU - Kaddeche, Slim

AU - Bellagi, Ahmed

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N2 - 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.

AB - 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.

KW - M ATHEMATICA

KW - chebyshev polynomials

KW - graduate-level education

KW - momentum - heat - mass transfer

KW - numerical methods

KW - orthogonal collocation

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DO - 10.1002/cae.21680

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SN - 1061-3773

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IS - 1

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Solving two-dimensional chemical engineering problems using the chebyshev orthogonal collocation technique

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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