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

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 start‐up 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. © 2015 Wiley Periodicals, Inc. Comput. Appl. Eng. Educ. 24:101–113, 2016; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21676

[1]  D. B. Clarke,et al.  Isochronous last-abundant-appearance datum (LAAD) of the diatom Hemidiscus karstenii in the sub-Antarctic , 1978 .

[2]  Sherwood W. Wise,et al.  Surface lithofacies, biofacies, and diatom diversity patterns as models for delineation of climatic change in the southeast Atlantic Ocean , 1981 .

[3]  Argimiro R. Secchi,et al.  Teaching chemical reaction engineering using EMSO simulator , 2010, Comput. Appl. Eng. Educ..

[4]  O. J. Koblentz-Mishke.  Plankton primary production of the world ocean. , 1970 .

[5]  Jeremy Bailey,et al.  Maple and the art of thermodynamics , 1998 .

[6]  E. Wood,et al.  Microbiology of Antarctic Sea-ice: Microalgae and Antarctic Sea-ice , 1963, Nature.

[7]  Grethe Rytter Hasle,et al.  Nitzschia and Fragilariopsis species studied in the light and electron microscopes. III. The genus Fragilariopsis , 1965 .

[8]  Luismar Marques Porto,et al.  Java Applets for Chemical Reaction Engineering , 1998 .

[9]  J. D. Hays,et al.  Variations in the Earth ' s Orbit : Pacemaker of the Ice Ages Author ( s ) : , 2022 .

[10]  O. G. Kozlova,et al.  Diatoms and silicoflagellates in suspension and floor sediments of the Pacific Ocean , 1967 .

[11]  L. Burckle,et al.  Late Pleistocene Eucampia antarctica abundance stratigraphy in the Atlantic sector of the Southern Ocean , 1983 .

[12]  Housam Binous,et al.  Study of the separation of simple binary and ternary mixtures of aromatic compounds , 2014, Comput. Appl. Eng. Educ..

[13]  Jaime Benitez,et al.  Principles and Modern Applications of Mass Transfer Operations , 2002 .

[14]  L. Burckle.  Diatom Evidence Bearing on the Holocene in the South Atlantic , 1972, Quaternary Research.

[15]  B. Finlayson.  Nonlinear analysis in chemical engineering , 1980 .

[16]  W. Fred Ramirez,et al.  Computational Methods for Process Simulation , 1997 .

[17]  E. Carmack,et al.  Frontal zone mixing and Antarctic Bottom water formation in the southern Weddell Sea , 1976 .

[18]  M. J. Newman,et al.  Variations in the Earth ' s Orbit : Pacemaker of the Ice Ages , 2007 .

[19]  P R Burkholder,et al.  Productivity of Microalgae in Antarctic Sea Ice , 1965, Science.

[20]  Ahmed Bellagi,et al.  Chebyshev orthogonal collocation technique to solve transport phenomena problems with Matlab® and Mathematica , 2015, Comput. Appl. Eng. Educ..

[21]  Iván D. Gil,et al.  Using process simulators in the study, design, and control of distillation columns for undergraduate chemical engineering courses , 2011, Comput. Appl. Eng. Educ..

[22]  M. Ewing,et al.  Atlantic Deep-Sea Sediment Cores , 1961 .

[23]  Ming Peng,et al.  The simulation of the simple batch distillation of multiple‐component mixtures via Rayleigh's equation , 2007, Comput. Appl. Eng. Educ..

[24]  J. Donahue.  Pleistocene Diatoms as Climatic Indicators in North Pacific Sediments , 1970 .

[25]  G. Fryxell,et al.  BIDDULPHIOID DIATOMS: RESTING SPORES IN ANTARCTIC EUCAMPIA AND ODONTELLA 1 , 1980 .

[26]  H. Schrader.  Fecal Pellets: Role in Sedimentation of Pelagic Diatoms , 1971, Science.

[27]  J. Fenner,et al.  Diatom Phytoplankton Studies in the Southern Pacific Ocean, Composition and Correlation to the Antarctic Convergence and Its Paleoecological Significance , 1976 .

[28]  R. Carty,et al.  Concentration Profiles in Ternary Gaseous Diffusion , 1975 .

[29]  D. Cooke.  Variations in the seasonal extent of Sea ice in the Antarctic during the last 140,000 years , 1978 .

[30]  F. Mccoy.  Photographic analysis of coring , 1980 .

[31]  Yucheng Liu.  Development of instructional courseware in thermodynamics education , 2011, Comput. Appl. Eng. Educ..

[32]  Rubén Dorado,et al.  Spreadsheet for teaching reciprocating engine cycles , 2012, Comput. Appl. Eng. Educ..

[33]  O. G. Kozlova.  Diatoms of the Indian and Pacific sectors of the Antarctic , 1966 .

[34]  Housam Binous,et al.  Introduction of the arc‐length continuation technique in the chemical engineering graduate program at KFUPM , 2015, Comput. Appl. Eng. Educ..

[35]  Fernando P. Bernardo,et al.  A virtual platform to teach separation processes , 2012, Comput. Appl. Eng. Educ..

[36]  G. Deacon.  The hydrology of the southern ocean , 1937 .

[37]  W. R. Taylor.  Freshwater Algae , 1933, Botanical Gazette.

[38]  T. J. Hart,et al.  Phytoplankton periodicity in Antarctic surface waters , 1945 .

[39]  R. M. Nedderman,et al.  Applied mathematics and modeling for chemical engineers , 1996 .

[40]  J. D. Hays,et al.  Reconstruction of the Atlantic and Western Indian Ocean Sectors of the 18,000 B.P. Antarctic Ocean , 1976 .

[41]  Mamdouh AlHarthi,et al.  Simple batch distillation of a binary mixture , 2014, Comput. Appl. Eng. Educ..

[42]  J. Frenguelli,et al.  Diatomeas y silicoflagelados del sector antártico sudamericano , 1958 .