Published
Las matemáticas y la ingeniería química, una relación sinérgica
DOI:
https://doi.org/10.15446/ing.investig.n45.21315Keywords:
Matemáticas aplicadas, Modelos matemáticos (es)Applied mathematics, Mathematical models (en)
Downloads
Las matemáticas han estado incluidas en los pensums de ingeniería química desde sus comienzos inicialmente como un aspecto formativo, en la aplicación de la lógica deductiva y su carácter formal, y posteriormente como una herramienta para el diseño, el análisis y optimización de procesos químicos. El modelo matemático trajo una mayor relación entre las dos disciplinas, pues la solución de los modelos requirió de técnicas más exactas y rápidas. Numerosos libros sobre matemáticas aplicadas han sido escritos por ingenieros químicos especializados en matemáticas o matemáticos con especialidad en Ingeniería Química, lo cual demuestra la dualidad que debe darse en la enseñanza de esta asignatura.
Since first pensums Mathematics have been in Chemical Engineering programs. They were formative assignature with application of deductive logic and formal character.
Now they are a tool to project, to analysis and to optimization of chemical processes. The mathematical models brought about heavy relation between Mathematics and Chemical Engineering. Many books, about Applied Mathematics, were wrote by Chemical Engineers with mathematical specialization or mathematician with chemical engineering specialization. This aspect demonstrate that the mathematics teaching in chemical engineering requires this duality.
References
Amundson, N.R. “Mathematical Methods in Chemical Engineering: matrices and their Applications”, Prentice Hall, 1966.
____. “Applications of Matrices and Finite Difference Equations to Binary Distillation”. En: Trans. AIChE, 42, 939 -46, 1946.
Aris, R. “Studies in Optimization”. En: Chem. Eng. Sci, 12, 243-52, 1960.
____. “The Optimum Design Chemical Reactors”. Tesis Presentada a la Universidad de Minessota, 1960.
Aris, R. and Amundson, N.R. “Mathematical Methods in Chemical Engineering: First Order Partial Differential Equations with Applications”, Prentice Hall, 1973.
Avnix, D. (Ed). “The Fractal Approach to Heterogeneous Chemistry”. J. Wiley.
Bilous, O and Amundson, N.R. “Chemical Reactor Stability and Sensitivity”, AIchE J. 1, 513 - 211, 1955.
Bird, R.B., Stewar, W.E. y Ligtfoot, E.N. “Transport Phenomena”, Wiley, 1960.
Bischoff, K.R. “Effectiveness Factors for General Reaction Rate Forms”. En: AIChE, J, 11, 351, 1965.
Bogoya, D, “Naturaleza de la Simulación” En: Ingeniería e Investigación No.29, pp 45, Bogotá, 1996.
Broadbent, S.R. y Hammersley, J.M. En: Proc. Camb. Phil. Soc., 53, 629, 1957.
Brodshaw, B.C. "Relations of Mathematics to Chemistry" En: J. Chem Educ. 3, pp. 1293, 1926.
Caicedo, L. Presentación Oral Seminario de Biotecnología, Universidad Nacional de Colombia, 1987.
Carnaham - Luther and Wilkee. “Applied Numerical Methods”, J. Wiley, New York, 1969.
Carslaw, H.S. “Fourier Series and Integrals, and the Mathematical Theory of the Conduction of Heat”. Macmillan, 1906.
Carslaw, H.S. y Jaeger, J.C. “Conduction of Heat in Solids”. Oxford, 1959.
Churchill, R.V. “Modern Operational Mathematics in Engineering”. McGraw Hill, 1944.
Crank, J. “Mathematics of Diffusion”. Oxford University Press, London, 1956.
Crank, J. and Park, G.S. “Diffusion in Polymers”. Academic Press, Londres, 1968.
Damkohler, G. “Influence of Diffusion, Fluid Flow and Heat Transport on Yield in Chemical Reactors”. International Chemical Engineering, 28, 132 - 98, 1988, Traducido del original de 1938.
Douglas, J.M. “Process Dynamics and Control” Cols 1,2. Prentice Hall, 1972.
Durmeister, L.C., “A Monte Carlo Procedure for Straight Convecting Boundaries”. Int. J. Heat and Mass Transfer, 28, 717-20, 1985.
Finlayson, B.A. “The Method of Weighed Residuals and Variational Principles”. En: Academic Press, New York, 1972.
____. “Nonlinear Analysis in Chemical Engineering”. McGraw Hill, New York, 1980.
Frazer, Jones and Skan, S.W. “Approximations to Functions and the Solutions of Differential Equations”. Gt. Brit. Air Ministry Aero. Res. Comm. Tech. Rept., 11, 517-49, 1937.
Fredrickson, A.G., En: Chem. Eng. Sci, 21, 687, 1966.
Gupta, S.K. “Momentum Transfer Operations”, Tata McGraw Hill, New Delhi, 1979.
Henley and Rosen. “Material and Energy Balance Computations”. McGraw Hill, New York, 1969.
Hernandez, G.J., Torres, L.G. and Nino, L.F. “Fundamentos de Neurocomputación”. En: Ingenieria e Investigación. No. 30, 63-78.
Himmenblau, D.M. “Chemical Process Optimization”. McGraw Hill, New York, 1970.
Hulburt, H.M. “Chemical Reactions in continuous Flow Systems: Reaction Kinetics”. En: Ind. Eng. Chem., 36, 1012 - 17, 1944.
____. “Chemical Reactions in continuous Flow Systems: Heterogeneous Reactions”. En: Ind. Eng. Chem., 37, 1063-69, 1945.
Ithara, S. and Stiel, L.I. “Optimal Design of Multiple - Effect Evaporators with Vapor Bleed Streams”. En: I&EC Proc. Design and Develop. 7, 6, 1968.
Kantorovich, L.V. “Métodos Matemáticos y Planificación de la Industria”, Universidad Estatal de Leningrado, 1939, en Barsov A.S., "Qué es la programación lineal", Editorial Mir, Mosc, 1977.
Kreyszig, E. Matemáticas Avanzadas para Ingeniería.
Lanczos, C.J. En: Math. Phys., 17, 123, 1938.
____. Applied Analysis. Prentice Hall, 1956.
Langhaar, H.L. “Dimensional Analysis and Theory of Models”. Wiley, New York, 1951.
Lapidus, L. “Digital Computation for Chemical Engineering”, McGraw Hill, New York, 1962.
Lewis, W.K. “The efficiency and design of Rectifying Columns for Binary Mixtures”. En: Ind. Eng. Chem., 14, 492-7, 1922.
____. “The Rate of Drying of Solids Materials”. En: Ind. Eng. Chem., 113, 427-32, 1921.
Liapunov, M.A. “Probleme général de la stabilité de movement”, 1882. En: Ann Math. Studies, 17, Princenton University Press, 1947.
Liljenroth, F.G. “Starting and Stability Phenomena of Ammonia - Oxidation and Similar Reactions”. En: Chem. Met. Eng., 19, 287, 1918.
Luyben, W.L. “Process Modeling, Simulation and Control for Chemical Engineers”. McGraw Hill, New York, 1973.
____. “Process Modeling, Simulation and Control for Chemical Engineers”, 2nd Ed. McGraw Hill, New York, 1994.
Marshall, W.R. and Pigford R.L. “The Application of Differential Equations to Chemical Engineering Problems”. University of Delaware Press, 1947.
Mc Adams, W. “Heat Transmission”. McGraw Hill, New York, 1993.
Mellor, J.W. “Higher Mathematics for Students of Chemistry and Physicswith Special Reference to Practical Work”. Longmans, Green, 1902.
____. “A Comprehensive Treatise on Inorganic & Theorical Chemistry”. Longman, 1922
Metropolis, N and Ulam, S. “The Monte Carlo Method”. En: J. Amer. Statistical Assoc, 44, (247), 335-41, 1949.
Nassar, R.A, et al. En: Chem. Eng. Sci., 36,1307, 1981.
Nassar, R., Too, J.R. and Fan, L.T. En: J. Appl. Polym. Sci, 26, 3745, 1981.
Nielsen, J. “Editorial in Honor of J. Villadsen”. En: Chem. Eng. Sci. 52, pp V-V1, 1997.
Perlmutter, J. “Introduction to Chemical Engineering Control”, J Wiley, New York, 1965.
Phillips, H.B. “Differential Equations”, John Wiley, 1922.
Ray, W.H. y Szately, J. “Process Optimization: With Applications in Metallurgy and Chemical Engineer” J. Wiley. 1973.
Reklaitis, Radvidran y Ragsdell. “Engineering Optimization”, 1983.
Resnick. “Process Analysis and Design for Chemical Engineers”. McGraw Hill, New York, 1981.
Rice, E.L. The J. of Ind. & Eng. Chemistry, 14, 1032 - 36, 1921.
Rud y Watson. “Strategy of Process Engineering”, 1968.
Sahimi, Muhammad. “Applications of Percolation Theory” Taylor and Francis Publ., London, 1994.
Sherwood, T.K. “The Drying of Solids”. En: Ind. Eng. Chem., 21, 12-6, 1929.
____. “The Drying of Solids - Application of Diffusion Equations”. En: Ind. Eng. Chem., 24, 307-110, 1932.
Sherwood, T.K. y Reed, C.E., “Applied Mathematics in Chemical Engineering”, McGraw Hill, 1939.
Smith, N.L. y Amudson, N.R. En: Ind. Eng. Chem, 43, 2156, 1951.
So, R.M., Pratt, D.T. y Nooven, M.D. “Modeling of Mass Transport in Turbulent Shear Flows”, Proc. 7. Int. Heat Transf. Conference, 3, 301 - 6, 1982.
Stephanopulos. “Chemical Process Control”. Prentice Hall, 1984.
Thiele, E. “Relation Between Catalytic Activity and Size of Particle”. En: Ind. Eng. Chem, 31, 916-20, 1939.
Tiller, F.M. y Tours, R.S. “Stagewise Operations: Application of the Calculus of Finite Differences to Chemical Engineering”. En: Trans. AIChE, 40, 317-31, 1944,
Van Heerden, C. “The Character of the Stationary State of Exothermic Processes”. En: Chem. Eng. Sci., 8, 133-45, 1958.
Villadsen, J.V. y Michelsen, M.L. “Solution of Boundary Value Problems by Orthogonal Collocation”. En: Chem. Eng. Sci, 22, 1483- 1501, 1967.
____. “Solution of Differential Equations Models by Polynomial Approximations”. Prentice Hall, 1978.
Wen and Fan. “Models for Flow Systems and Chemical Reactors”, Marcel Dekker, New York, 1975.
Wilhelm, R.H., Johnson, W.C and Acton, FS. “Conduction, Convection and Heat Release in Catalytic Converters”. En: Ind. Eng. Chem.,35, 562 - 75, 1943.
Whitt, F.R. “Early Teachers and Teaching of Chemical Engineering”. The Chemical Engineer No. 356, October, 1969.
Wylei, C.R. and Barret, L.C. “Avanced Engineering Mathematics”. McGraw Hill, 1982.
Dimensions
PlumX
Article abstract page views
Downloads
How to Cite
License
Copyright (c) 2000 Luis A. Caicedo, Gerardo Rodríguez, Armando Durán
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.
