THE FINITE ELEMENT METHOD (FEM): AN APPLICATION TO FLUID MECHANICS AND HEAT TRANSFER

• Main Authors: L. A. Toro, C. A. Cardona, Yu. A. Pisarenko, A. V. Frolkova
• Format: Article
• Language: Russian
• Published: MIREA - Russian Technological University 2018-08-01
• Series: Тонкие химические технологии
• Subjects: analytical solution; approximate solution; laplace equation; poisson equation; potential formulation; the finite element method
• Online Access: https://www.finechem-mirea.ru/jour/article/view/157

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.