THE FINITE ELEMENT METHOD (FEM): AN APPLICATION TO FLUID MECHANICS AND HEAT TRANSFER
https://doi.org/10.32362/2410-6593-2018-13-4-17-25
Abstract
In this paper the finite element method (FEM) is used to solve three problems that are of the paramount importance in Chemical Engineering. The first problem is related with the bidimensional flow of an ideal fluid around a cylindrical body, and the objective is to determine the velocity distribution of the flow. To model the flow, the potential formulation is used to obtain an analytical solution, and then, the approximated solution obtained by using FEM is compared with the analytical solution. From this comparison, it is deduced that both solutions have a good agreement. The second problem is the calculation of the temperature profile in a two-dimensional body with specified boundary conditions. This problem is modeled by the two-dimensional Laplace equation, and from the problem data and using variables separation, an analytical solution was obtained. Then, FEM was used to obtain an approximate solution and compared with analytical ones. Besides, from this comparison, it is concluded that both solutions agree. Finally, in the third problem the temperature distribution in a bidimensional body with internal heat generation is studied. This problem is modeled by Poisson equation in two dimensions, but due to the boundary conditions and the complications that arise by adding some heat sources in the final FEM discretization, the problem does not have an analytical solution. However, the analysis of FEM solution indicates that this solution is correct.
About the Authors
L. A. Toro
National University of Colombia, headquarters Manizales
Colombia
Colombia
Ph.D., Associate Professor
headquarters Manizales, Cra 23 # 64-60, Colombia
Full Professor
Manizales, Cra 21 #38-52, Caldas, Colombia
C. A. Cardona
National University of Colombia, headquarters Manizales; Autonomous University of Manizales
Colombia
Colombia
Ph.D. (Eng.), Professor of the Chair of Chemical Engineering
headquarters Manizales, Manizales-Caldas, Colombia
Yu. A. Pisarenko
MIREA - Russian Technological University (M.V. Lomonosov Institute of Fine Chemical Technologies)
Russian Federation
Russian Federation
D.Sc. (Eng.), Professor of the Chair of Chemistry and Technology of Basic Organic Synthesis
86, Vernadskogo Pr., Moscow 119571, Russia
A. V. Frolkova
MIREA - Russian Technological University (M.V. Lomonosov Institute of Fine Chemical Technologies)
Russian Federation
Russian Federation
Ph.D. (Eng.), Associate Professor of the Chair of Chemistry and Technology of Basic Organic Synthesis
86, Vernadskogo Pr., Moscow 119571, Russia
Researcher ID N-4517-2014
References
1. Hughes T.J.R. The finite element method. New York: Dover Publ., Inc., 2000. 704 p.
2. Lewis R.W., Nithiarasu P., Seettharamu K. Fundamental of the finite element method for heat and fluid flow. John Wiley & Sons, Ltd., 2004. 358 p.
3. Zienkiewicz O.C., Taylor R.L. El método de los elementos finitos. Vol. 1. Cuarta Edición. CIMME. Madrid, McGraw-Hill, 1994. 649 p. (in Span.) (Zienkiewicz О.C., Taylor R.L. The Finite Element Method, volume 1. McGraw-Hill, London, 4th edition, 1989].
4. Zienkiewicz O.C., Taylor R.L. El método de los elementos finitos. Vol. 2. Cuarta Edición. CIMME. Madrid, McGraw-Hill, 1994. 446 p. (in Span.) [Zienkiewicz О.C., Taylor R.L. The Finite Element Method, volume 2. McGraw-Hill, London, 4th edition, 1991].
5. Ciarlet P. The finite element method for elliptic problems. North-Holland Publishing Company, 1980. 529 p.
6. Kwon Young W., Bang Hyochoong. The finite element method. CRC Press, 2000. 590 p.
7. Chen Zhanxin. Finite element methods and their applications. New York: Springer, 2005. 424 p. 8. Gelfand I.M., Fomin S.V. Calculus of variations. Mineola, New York: Dover Publ., 2000. 240 p.
8. Weinstock R. Calculus of variations, with applications to physics and engineering. New York: Dover Publ., 1974. 334 p.
9. Hutton D.V. Fundamentals of finite element method. Mc Gaw Hill Higher Education, 2004. 494 p.
10. Bhatti M.A. Fundamentals of finite element analyis and applications. John Wiley and Sons, Inc., 2005. 720 p.
11. Chandrupatla T.R., Belegundu A.D. Introducción al estudio del elemento finito en ingeniería, segunda edición. Prentice Hall, 1999. 462 p. (in Span.)
12. Evans L.C. Partial differential equations. Berkeley Mathematics, 1994. 662 p.
13. Cengel Y.A., Cimbala J.M. Mecánica de fluidos: Fundamentos y aplicaciones. McGraw Hill, 2006. 997 p. (in Span.)
14. Reddy J.N. An Introduction to the finite element method. McGraw Hill, Inc., 1993. 672 p.
15. Edwards H.C., Penny D.E. Ecuaciones diferenciales y problemas con valores en la frontera. Cómputo y modelado. Cuarta edición. Prentice Hall, 2009. 827 p. (in Span.)
16. Asmar N. Partial differential equations and boundary value problems. Upper Saddle River, Jeersey, 2000. 816 p.
Review
For citations:
Toro L.A., Cardona C.A., Pisarenko Yu.A., Frolkova A.V. THE FINITE ELEMENT METHOD (FEM): AN APPLICATION TO FLUID MECHANICS AND HEAT TRANSFER. Fine Chemical Technologies. 2018;13(4):17-25. https://doi.org/10.32362/2410-6593-2018-13-4-17-25
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