Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering

This contribution aims at emphasizing the importance of ideal reactors in the field of environmental engineering and in the education of the corresponding engineers. The exposition presents the mass flow governing equations of the ideal reactors (batch, completely mixed flow, and plug flow reactors)...

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Autores:
Laín Beatove, Santiago
Gandini Ayerbe, Mario Andrés
Tipo de recurso:
Article of journal
Fecha de publicación:
2023
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/15522
Acceso en línea:
https://hdl.handle.net/10614/15522
https://doi.org/10.3390/fluids8020058
https://red.uao.edu.co/
Palabra clave:
Problem-solving in engineering
Ideal reactors
Mass conservation integral equation
Riccati equation
Second-order kinetics
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openAccess
License
Derechos reservados - MDPI, 2023
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oai_identifier_str oai:red.uao.edu.co:10614/15522
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
title Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
spellingShingle Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
Problem-solving in engineering
Ideal reactors
Mass conservation integral equation
Riccati equation
Second-order kinetics
title_short Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
title_full Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
title_fullStr Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
title_full_unstemmed Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
title_sort Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering
dc.creator.fl_str_mv Laín Beatove, Santiago
Gandini Ayerbe, Mario Andrés
dc.contributor.author.none.fl_str_mv Laín Beatove, Santiago
Gandini Ayerbe, Mario Andrés
dc.contributor.corporatename.spa.fl_str_mv MDPI
dc.subject.proposal.eng.fl_str_mv Problem-solving in engineering
Ideal reactors
Mass conservation integral equation
Riccati equation
Second-order kinetics
topic Problem-solving in engineering
Ideal reactors
Mass conservation integral equation
Riccati equation
Second-order kinetics
description This contribution aims at emphasizing the importance of ideal reactors in the field of environmental engineering and in the education of the corresponding engineers. The exposition presents the mass flow governing equations of the ideal reactors (batch, completely mixed flow, and plug flow reactors) as particular cases derived from the integral version of the conservation of mass of a chemical/biological species. In the case of transient problems and simple kinetics, such expressions result in first-order ordinary differential equations amenable to be solved analytically when they are linear. In this article, it is shown that when they are non-linear, due to the presence of a second-order kinetics reaction, an analytical solution is also possible, a situation not dealt with in the textbooks. Finally, the previous findings are integrated into a teaching proposal addressed to help undergraduate students to solve more efficiently ideal reactor problems
publishDate 2023
dc.date.issued.none.fl_str_mv 2023-02-08
dc.date.accessioned.none.fl_str_mv 2024-04-10T13:41:51Z
dc.date.available.none.fl_str_mv 2024-04-10T13:41:51Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
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dc.type.content.eng.fl_str_mv Text
dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/article
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dc.type.version.eng.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.citation.spa.fl_str_mv Laín Beatove, S.; Gandini Ayerbe, M. A. (2023). Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering. Fluids. 8(2). 16 p. https://doi.org/10.3390/fluids8020058
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/15522
dc.identifier.doi.none.fl_str_mv https://doi.org/10.3390/fluids8020058
dc.identifier.eissn.none.fl_str_mv EISSN 2311-5521
dc.identifier.instname.spa.fl_str_mv Universidad Autónoma de Occidente
dc.identifier.reponame.spa.fl_str_mv Respositorio Educativo Digital UAO
dc.identifier.repourl.none.fl_str_mv https://red.uao.edu.co/
identifier_str_mv Laín Beatove, S.; Gandini Ayerbe, M. A. (2023). Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering. Fluids. 8(2). 16 p. https://doi.org/10.3390/fluids8020058
EISSN 2311-5521
Universidad Autónoma de Occidente
Respositorio Educativo Digital UAO
url https://hdl.handle.net/10614/15522
https://doi.org/10.3390/fluids8020058
https://red.uao.edu.co/
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.none.fl_str_mv 16
dc.relation.citationissue.none.fl_str_mv 2
dc.relation.citationstartpage.none.fl_str_mv 1
dc.relation.citationvolume.none.fl_str_mv 8
dc.relation.ispartofjournal.eng.fl_str_mv Fluids
dc.relation.references.none.fl_str_mv 1. Lewins, J. Entropy pollution of the environment: A teaching approach to the Second Law. Int. J. Mech. Eng. Educ. 2011, 39, 60–67.
2. Alvarez Cuenca, M.; Reza, M. The multi-stage vertical bioreactor in water engineering. Can. J. Chem. Eng. 2020, 98, 172–185.
3. Wendling, L.; Dumitru, A.; Arnbjerg-Nielsen, K.; Baldacchini, C.; Connop, S.; Dubovik, M.; zu-Castell Rüdenhausen, M. Indicators of NBS performance and impact. In Evaluating the Impact of Nature-Based Solutions: A Handbook for Practitioners; European Union: Maastricht, The Netherlands, 2021.
4. Mihelcic, J.R.; Zimmerman, J.B. Environmental Engineering. Fundamentals, Sustainability, Design, 3rd ed.; Chapter 4 Physical Processes; Wiley: Hoboken, NJ, USA, 2021.
5. Sanz, J.L.; Köchling, K. Next-generation sequencing and waste/wastewater treatment: A comprehensive overview. Rev. Environ. Sci. Bio/Technol. 2019, 18, 635–680.
6. Shah, M.P.; Rodriguez-Couto, S. (Eds.) Wastewater Treatment Reactors: Microbial Community Structure, 1st ed.; Elsevier: Berlin/Heidelberg, Germany, 2021.
7. Muddemann, T.; Haupt, D.; Sievers, M.; Kunz, U. Electrochemical reactors for wastewater treatment. ChemBioEng Rev. 2019, 6, 142–156.
8. Rostam, A.B.; Taghizadeh, M. Advanced oxidation processes integrated by membrane reactors and bioreactors for various wastewater treatments: A critical review. J. Environ. Chem. Eng. 2020, 8, 104566. [CrossRef]
9. Patiño, P.; Cruz, C.; Torres, P.; Lain, S. Hydrodynamic evaluation of a hydraulic clarifier through hydraulic behaviour indicators and simplified flow models. Ing. E Investig. 2012, 32, 77–82.
10. Lain, S.; Aliod, R. Study on the Eulerian Dispersed Phase Equations in Non-Uniform Turbulent Two-Phase Flows: Discussion and Comparison with Experiments. Int. J. Heat Fluid Flow 2000, 21, 374–380.
11. Montoya, C.; Lain, S.; Torres, P.; Cruz, C.; Escobar, J.C. Effects of water inlet configuration in a service reservoir applying CFD modelling. Ing. E Investig. 2016, 36, 21–40.
12. Li, M.; Zhang, H.; Lemckert, C.; Roiko, A.; Stratton, H. On the hydrodynamics and treatment efficiency of waste stabilization ponds: From a literature review to a strategic evaluation framework. J. Clean. Prod. 2018, 183, 495–514. [CrossRef]
13. Rizzo, A.; Tondera, T.; Pálfy, T.G.; Dittmer, U.; Meyer, D.; Schreiber, C.; Masi, F. Constructed wetlands for combined sewer overflow treatment: A state-of-the-art review. Sci. Total Environ. 2020, 727, 138618. [CrossRef]
14. Boano, F.; Caruso, A.; Costamagna, E.; Ridolfi, L.; Fiore, S.; Demichelis, F.; Masi, F. A review of nature-based solutions for greywater treatment: Applications, hydraulic design, and environmental benefits. Sci. Total Environ. 2020, 711, 134731. [CrossRef]
15. Uthirakrishnan, U.; Sharmila, V.G.; Merrylin, J.; Kumar, S.A.; Dharmadhas, J.S.; Varjani, S.; Banu, J.R. Current advances and future outlook on pretreatment techniques to enhance biosolids disintegration and anaerobic digestion: A critical review. Chemosphere 2022, 288, 132553. [CrossRef]
16. Ahmed, A.; Li, W.; Varjani, S.; You, S. Waste-to-energy technologies for sustainability: Life-cycle assessment and economic analysis. In Biomass, Biofuels, Biochemicals, 1st ed.; Elsevier: Berlin/Heidelberg, Germany, 2022; pp. 599–612.
17. Uddin, M.N.; Siddiki, S.Y.A.; Mofijur, M.; Djavanroodi, F.; Hazrat, M.A.; Show, P.I.; Chu, Y.M. Prospects of bioenergy production from organic waste using anaerobic digestion technology: A mini review. Front. Energy Res. 2021, 9, 627093.
18. Townsend, T.G. Landfill Bioreactor Design and Operation, 1st ed.; Routledge: New York, NY, USA, 2018.
19. Cerminara, G.; Raga, R.; Hirata, O.; Pivato, A. Denitrification of low C/N landfill leachate in lab-scale landfill simulation bioreactors. Waste Manag. 2020, 113, 236–243.
20. Janse, J.H.; Van Dam, A.A.; Hes, E.M.; de Klein, J.J.; Finlayson, C.M.; Janssen, A.B.; Verhoeven, J.T. Towards a global model for wetlands ecosystem services. Curr. Opin. Environ. Sustain. 2019, 36, 11–19. [CrossRef]
21. Beven, K. How to make advances in hydrological modelling. Hydrol. Res. 2019, 50, 1481–1494.
22. Vinçon-Leite, B.; Casenave, C. Modelling eutrophication in lake ecosystems: A review. Sci. Total Environ. 2019, 651, 2985–3001.
23. Streeter, H.W.; Phelps, E.B. A study of the pollution and natural purification of the Ohio River. US Public Health Service. Public Health Bull. 1925, 146, 75.
24. Ejigu, M.T. Overview of water quality modeling. Cogent Eng. 2021, 8, 1891711.
25. Costa, C.M.D.S.B.; Leite, L.R.; Almeida, A.K.; de Almeida, I.K. Choosing an appropriate water quality model—A review. Environ. Monit. Assess. 2021, 193, 38.
26. Hauke, G. An Introduction to Fluid Mechanics and Transport Phenomena, 1st ed.; Springer: Berlin/Heidelberg, Germany, 2008.
27. Nazaroff, W.W.; Alvarez-Cohen, L. Environmental Engineering Science, 1st ed.; Wiley: New York, NY, USA, 2000.
28. Spiegel, M.R. Mathematical Handbook of Formulas and Tables. Schaum’s Outline Series, 1st ed.; McGraw-Hill: New York, NY, USA, 1968.
29. Bittanti, S.; Laub, A.J.; Willems, J.C. The Riccati Equation, 1st ed.; Springer: Berlin/Heidelberg, Germany, 1991.
30. Masters, G.M.; Ela, W.P. Introduction to Environmental Engineering and Science, 3rd ed.; Pearson: London, UK, 2014.
31. Masdem, S.J.; Davies, M.L. Principles of Environmental Engineering and Science, 4th ed.; Mc Graw Hill: New York, NY, USA, 2020.
32. Rawlings, J.B.; Eckerdt, J.G. Chemical Reactor Analysis and Design Fundamentals, 1st ed.; Nob Hill Publishing: Madison, WI, USA, 2002.
33. López, O.; Meneses, D.; Quintero, B.; Laín, S. Computational study of transient flow around Darrieus type Cross Flow Water Turbines. J. Renew. Sustain. Energy 2016, 8, 014501. [CrossRef]
34. Laín, S.; Taborda, M.A.; López, O.D. Numerical study of the effect of winglets on the performance of a straight blade Darrieus water turbine. Energies 2018, 11, 297. [CrossRef]
dc.rights.spa.fl_str_mv Derechos reservados - MDPI, 2023
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spelling Laín Beatove, Santiagovirtual::5318-1Gandini Ayerbe, Mario Andrésvirtual::5319-1MDPI2024-04-10T13:41:51Z2024-04-10T13:41:51Z2023-02-08Laín Beatove, S.; Gandini Ayerbe, M. A. (2023). Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in Engineering. Fluids. 8(2). 16 p. https://doi.org/10.3390/fluids8020058https://hdl.handle.net/10614/15522https://doi.org/10.3390/fluids8020058EISSN 2311-5521Universidad Autónoma de OccidenteRespositorio Educativo Digital UAOhttps://red.uao.edu.co/This contribution aims at emphasizing the importance of ideal reactors in the field of environmental engineering and in the education of the corresponding engineers. The exposition presents the mass flow governing equations of the ideal reactors (batch, completely mixed flow, and plug flow reactors) as particular cases derived from the integral version of the conservation of mass of a chemical/biological species. In the case of transient problems and simple kinetics, such expressions result in first-order ordinary differential equations amenable to be solved analytically when they are linear. In this article, it is shown that when they are non-linear, due to the presence of a second-order kinetics reaction, an analytical solution is also possible, a situation not dealt with in the textbooks. Finally, the previous findings are integrated into a teaching proposal addressed to help undergraduate students to solve more efficiently ideal reactor problems16 páginasapplication/pdfengMDPIBasel, SwitzerlandDerechos reservados - MDPI, 2023https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2https://www.mdpi.com/2311-5521/8/2/58Ideal Reactors as an Illustration of Solving Transport Phenomena Problems in EngineeringArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a8516218Fluids1. Lewins, J. Entropy pollution of the environment: A teaching approach to the Second Law. Int. J. Mech. Eng. Educ. 2011, 39, 60–67.2. Alvarez Cuenca, M.; Reza, M. The multi-stage vertical bioreactor in water engineering. Can. J. Chem. Eng. 2020, 98, 172–185.3. Wendling, L.; Dumitru, A.; Arnbjerg-Nielsen, K.; Baldacchini, C.; Connop, S.; Dubovik, M.; zu-Castell Rüdenhausen, M. Indicators of NBS performance and impact. In Evaluating the Impact of Nature-Based Solutions: A Handbook for Practitioners; European Union: Maastricht, The Netherlands, 2021.4. Mihelcic, J.R.; Zimmerman, J.B. Environmental Engineering. Fundamentals, Sustainability, Design, 3rd ed.; Chapter 4 Physical Processes; Wiley: Hoboken, NJ, USA, 2021.5. Sanz, J.L.; Köchling, K. Next-generation sequencing and waste/wastewater treatment: A comprehensive overview. Rev. Environ. Sci. Bio/Technol. 2019, 18, 635–680.6. Shah, M.P.; Rodriguez-Couto, S. (Eds.) Wastewater Treatment Reactors: Microbial Community Structure, 1st ed.; Elsevier: Berlin/Heidelberg, Germany, 2021.7. Muddemann, T.; Haupt, D.; Sievers, M.; Kunz, U. Electrochemical reactors for wastewater treatment. ChemBioEng Rev. 2019, 6, 142–156.8. Rostam, A.B.; Taghizadeh, M. Advanced oxidation processes integrated by membrane reactors and bioreactors for various wastewater treatments: A critical review. J. Environ. Chem. Eng. 2020, 8, 104566. [CrossRef]9. Patiño, P.; Cruz, C.; Torres, P.; Lain, S. Hydrodynamic evaluation of a hydraulic clarifier through hydraulic behaviour indicators and simplified flow models. Ing. E Investig. 2012, 32, 77–82.10. Lain, S.; Aliod, R. Study on the Eulerian Dispersed Phase Equations in Non-Uniform Turbulent Two-Phase Flows: Discussion and Comparison with Experiments. Int. J. Heat Fluid Flow 2000, 21, 374–380.11. Montoya, C.; Lain, S.; Torres, P.; Cruz, C.; Escobar, J.C. Effects of water inlet configuration in a service reservoir applying CFD modelling. Ing. E Investig. 2016, 36, 21–40.12. Li, M.; Zhang, H.; Lemckert, C.; Roiko, A.; Stratton, H. On the hydrodynamics and treatment efficiency of waste stabilization ponds: From a literature review to a strategic evaluation framework. J. Clean. Prod. 2018, 183, 495–514. [CrossRef]13. Rizzo, A.; Tondera, T.; Pálfy, T.G.; Dittmer, U.; Meyer, D.; Schreiber, C.; Masi, F. Constructed wetlands for combined sewer overflow treatment: A state-of-the-art review. Sci. Total Environ. 2020, 727, 138618. [CrossRef]14. Boano, F.; Caruso, A.; Costamagna, E.; Ridolfi, L.; Fiore, S.; Demichelis, F.; Masi, F. A review of nature-based solutions for greywater treatment: Applications, hydraulic design, and environmental benefits. Sci. Total Environ. 2020, 711, 134731. [CrossRef]15. Uthirakrishnan, U.; Sharmila, V.G.; Merrylin, J.; Kumar, S.A.; Dharmadhas, J.S.; Varjani, S.; Banu, J.R. Current advances and future outlook on pretreatment techniques to enhance biosolids disintegration and anaerobic digestion: A critical review. Chemosphere 2022, 288, 132553. [CrossRef]16. Ahmed, A.; Li, W.; Varjani, S.; You, S. Waste-to-energy technologies for sustainability: Life-cycle assessment and economic analysis. In Biomass, Biofuels, Biochemicals, 1st ed.; Elsevier: Berlin/Heidelberg, Germany, 2022; pp. 599–612.17. Uddin, M.N.; Siddiki, S.Y.A.; Mofijur, M.; Djavanroodi, F.; Hazrat, M.A.; Show, P.I.; Chu, Y.M. Prospects of bioenergy production from organic waste using anaerobic digestion technology: A mini review. Front. Energy Res. 2021, 9, 627093.18. Townsend, T.G. Landfill Bioreactor Design and Operation, 1st ed.; Routledge: New York, NY, USA, 2018.19. Cerminara, G.; Raga, R.; Hirata, O.; Pivato, A. Denitrification of low C/N landfill leachate in lab-scale landfill simulation bioreactors. Waste Manag. 2020, 113, 236–243.20. Janse, J.H.; Van Dam, A.A.; Hes, E.M.; de Klein, J.J.; Finlayson, C.M.; Janssen, A.B.; Verhoeven, J.T. Towards a global model for wetlands ecosystem services. Curr. Opin. Environ. Sustain. 2019, 36, 11–19. [CrossRef]21. Beven, K. How to make advances in hydrological modelling. Hydrol. Res. 2019, 50, 1481–1494.22. Vinçon-Leite, B.; Casenave, C. Modelling eutrophication in lake ecosystems: A review. Sci. Total Environ. 2019, 651, 2985–3001.23. Streeter, H.W.; Phelps, E.B. A study of the pollution and natural purification of the Ohio River. US Public Health Service. Public Health Bull. 1925, 146, 75.24. Ejigu, M.T. Overview of water quality modeling. Cogent Eng. 2021, 8, 1891711.25. Costa, C.M.D.S.B.; Leite, L.R.; Almeida, A.K.; de Almeida, I.K. Choosing an appropriate water quality model—A review. Environ. Monit. Assess. 2021, 193, 38.26. Hauke, G. An Introduction to Fluid Mechanics and Transport Phenomena, 1st ed.; Springer: Berlin/Heidelberg, Germany, 2008.27. Nazaroff, W.W.; Alvarez-Cohen, L. Environmental Engineering Science, 1st ed.; Wiley: New York, NY, USA, 2000.28. Spiegel, M.R. Mathematical Handbook of Formulas and Tables. Schaum’s Outline Series, 1st ed.; McGraw-Hill: New York, NY, USA, 1968.29. Bittanti, S.; Laub, A.J.; Willems, J.C. The Riccati Equation, 1st ed.; Springer: Berlin/Heidelberg, Germany, 1991.30. Masters, G.M.; Ela, W.P. Introduction to Environmental Engineering and Science, 3rd ed.; Pearson: London, UK, 2014.31. Masdem, S.J.; Davies, M.L. Principles of Environmental Engineering and Science, 4th ed.; Mc Graw Hill: New York, NY, USA, 2020.32. Rawlings, J.B.; Eckerdt, J.G. Chemical Reactor Analysis and Design Fundamentals, 1st ed.; Nob Hill Publishing: Madison, WI, USA, 2002.33. López, O.; Meneses, D.; Quintero, B.; Laín, S. Computational study of transient flow around Darrieus type Cross Flow Water Turbines. J. Renew. Sustain. Energy 2016, 8, 014501. [CrossRef]34. Laín, S.; Taborda, M.A.; López, O.D. Numerical study of the effect of winglets on the performance of a straight blade Darrieus water turbine. Energies 2018, 11, 297. [CrossRef]Problem-solving in engineeringIdeal reactorsMass conservation integral equationRiccati equationSecond-order kineticsComunidad generalPublication082b0926-3385-4188-9c6a-bbbed7484a95virtual::5318-11b7ae0bb-d40b-4d15-94ee-5d8949aad3c5virtual::5319-1082b0926-3385-4188-9c6a-bbbed7484a95virtual::5318-11b7ae0bb-d40b-4d15-94ee-5d8949aad3c5virtual::5319-1https://scholar.google.com/citations?user=g-iBdUkAAAAJ&hl=esvirtual::5318-10000-0002-0269-2608virtual::5318-10000-0002-6430-2601virtual::5319-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000262129virtual::5318-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000952028virtual::5319-1ORIGINALIdeal_Reactors_as_an_Illustration_of_Solving_Transport_Phenomena_Problems_in_Engineering.pdfIdeal_Reactors_as_an_Illustration_of_Solving_Transport_Phenomena_Problems_in_Engineering.pdfArchivo texto completo del artículo de revista, PDFapplication/pdf329481https://red.uao.edu.co/bitstreams/a5285da2-9179-4b3e-87c0-a0cde4a27626/download5a2df27a37c1d6365a1b6615cea52eacMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81672https://red.uao.edu.co/bitstreams/fb5033d9-908c-48bf-be5a-710bbe85d99a/download6987b791264a2b5525252450f99b10d1MD52TEXTIdeal_Reactors_as_an_Illustration_of_Solving_Transport_Phenomena_Problems_in_Engineering.pdf.txtIdeal_Reactors_as_an_Illustration_of_Solving_Transport_Phenomena_Problems_in_Engineering.pdf.txtExtracted texttext/plain57262https://red.uao.edu.co/bitstreams/7d0738bb-b47e-4312-942b-4dae0d3efd1d/download7d37d1f22a2a02adfbe2bd13d44d53a4MD53THUMBNAILIdeal_Reactors_as_an_Illustration_of_Solving_Transport_Phenomena_Problems_in_Engineering.pdf.jpgIdeal_Reactors_as_an_Illustration_of_Solving_Transport_Phenomena_Problems_in_Engineering.pdf.jpgGenerated Thumbnailimage/jpeg15464https://red.uao.edu.co/bitstreams/5ad15b09-8fda-42a9-8c73-92632654a5f1/downloade1a3cd750b0da66a5cd1ed29259560efMD5410614/15522oai:red.uao.edu.co:10614/155222024-04-12 09:29:59.937https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - MDPI, 2023open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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