- Tytuł:
- Application of Rank Controlled Differential Quadrature Method for Solving an Infinite Steel Plate Cooling Problem
- Autorzy:
-
Żak, P. L.
Suchy, J. S.
Lelito, J.
Gracz, B. - Powiązania:
- https://bibliotekanauki.pl/articles/381994.pdf
- Data publikacji:
- 2013
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
information technology
foundry industry
solidification process
exact solution
rank controlled differential quadrature
numerical modelling
technologia informatyczna
przemysł odlewniczy
proces krzepnięcia
dokładne rozwiązanie
kwadratura różniczkowa sterowanego rzędu
modelowanie numeryczne - Opis:
- Rank Controlled Differential Quadrature method is a numerical method that allows to approximate the partial derivatives that appears in partial differential equations. Those equations with proper geometrical, physical, initial and boundary conditions make mathematical models of physical process. The heat transfer process is governed by Fourier–Kirchhoff equation, which is parabolic Partial Differential Equation. In this paper authors present the steel plate cooling problem. At the beginning of the process plate is heated up to 450 °C and is cooled to ambient temperature. The cooling of the plate is basic heat transfer problem. If the plates dimensions has proper proportions such problem may be described as one dimensional and solved exactly. The mathematical model and exact solution is given in the work. Authors apply the Rank Controlled Differential Quadrature to approximate derivatives in Fourier–Kirchhoff equation and in boundary conditions. After changing derivatives into quadrature formulation set of algebraic equations is obtained. Substituting thermo-physical parameters numerical model is obtained. The computer program was prepared to solve the problem numerically. Results of simulation are confronted with the exact ones. Error value at each time step as well as error value increase rate for examined numerical method is analyzed.
- Źródło:
-
Archives of Foundry Engineering; 2013, 13, 3 spec.; 201-206
1897-3310
2299-2944 - Pojawia się w:
- Archives of Foundry Engineering
- Dostawca treści:
- Biblioteka Nauki
Artykuł