Spreadsheet for teaching reciprocating engine cycles

Kaddeche

Bellagi

2015

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 ß . 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. ß 2015 Wiley Periodicals, Inc. Comput Appl Eng Educ 24:144-155, 2016; View this article online at wileyonlinelibrary.com/journal/cae;

Section: Introductionmentioning

confidence: 99%

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

Kaddeche

Bellagi

2015

“…Here, we apply both methods for two different case studies: (1) Haber process and (2) (2) OGSF 508 or Industrial Chemical Reactions-Catalysts-R&D Trends. Several pedagogical papers have dealt with thermodynamics [3][4][5][6] and chemical reaction engineering [7,8]. Students appreciate especially the use of Mathematica © because it make difficult mathematical problems easily tractable and allow them to focus on the chemical engineering side of the problem at hand.…”

Section: Introductionmentioning

confidence: 99%

Haber process and steam‐coal gasification: Two standard thermodynamic problems elucidated using two distinct approaches

Aheed

Hossain

2015

The present study shows how the direct Gibbs free energy minimization technique is sometimes superior to the reaction coordinates-equilibrium constants method when the thermodynamic analysis of complex systems is performed. In this respect, the above two methods are applied for two different processes to determine their equilibrium compositions: (1) the Haber process: a simple problem consisting of a single gasphase reaction where both methods are expected to give the same result and (2) steam-coal gasification process which is more complex since it involves numerous reactions and solid-phase chemical species (i.e., coal or carbon). Thus, in the second case the reaction coordinates-equilibrium constants method fails to provide correct predictions of the equilibrium composition. In addition, the authors give the optimum conditions for the two processes: high pressure for Haber process and high temperature for steam-coal gasification in agreement with LeChatelier principle. In order to deal with deviation from the ideal-case assumption, the Peng-Robinson Equation of State (PR EOS) is implemented for both techniques and both case studies. All computations and figures are generated using a single computer algebra, Mathematica © .

“…Several pedagogical articles dealing with chemical engineering problems solving using mathematical and spreadsheet software such, as Maple, Matlab ® , M athematica © , and Excel, have been published. To cite only a few recent: in (1) thermodynamics , (2) separation unit operations , (3) chemical reaction engineering [9,10], and (4) numerical methods [11,12]. Except Ref.…”

Section: Introductionmentioning

confidence: 99%

Bellagi

2015

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