Numerical solution of a direct and inverse stationary problem of heat transfer with a modified method of elementary balances

• Autorzy: Wróblewska A. , Frąckowiak A. , Ciałkowski M.
• Języki publikacji: EN

Abstrakty

EN

The paper presents solution of a direct and inverse problem of circular infinite hollow cylinder cooling with a modified method of elementary balances. The idea of the method consists in division of the considered area into sub-domains. In each of the elements the solution is interpolated with the help of linear combination of base functions. The energy is subject to balancing around each of the mesh nodes. The idea is similar to CVFEM (Control Volume Finite Element Method); nevertheless, the base functions applied here in order to approximate the solution in the element are clearly specific for the method. The solution of the inverse problem with randomly disturbed boundary conditions of the flux and temperature at the outer infinite hollow cylinder boundary, with maximum error reaching 10 percent, gives very good results. The inverse problem solution is obtained in the sense of the SVD algorithm.

Słowa kluczowe

EN

inverse problem; method of elementary balances

PL

metoda elementarnej równowagi; zagadnienie odwrotne

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2008
• Tom: Vol. 29, no. 1
• Strony: 3--18
• Opis fizyczny: Bibliogr. 7 poz.,rys., tab., wykr, wz.,

Twórcy

autor

Wróblewska A.

autor

Frąckowiak A.

autor

Ciałkowski M.

• Poznań University of Technology, Chair of Thermal Engineering, Piotrowo 3, 60-965 Poznań, Poland

Bibliografia

• [1] BAUMEISTER J.: Stable Solution of Inverse Problems. Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden, 1987.
• [2] BJÖRCK Ä., DAHLQUIST G.: Numerical Methods, PWN, Warszawa 1983 (in Polish)
• [3] CIAŁKOWSKI M., FRĄCKOWIAK A. AND GRYSA K.: Solution of a stationary inverse heat conduction problem by means of Trefftz non-continous method, Intern. J. of Heat and Mass Transfer, 50 (2007) 2170-2181.
• [4] FRĄCKOWIAK A.: Base functions of the Finite Element Method and their properties, Zeszyty Naukowe Politechniki Poznańskiej, submitted for publ. (in Polish).
• [5] FRĄCKOWIAK A., CIAŁKOWSKI M., J. VON WOLFERSDORF: Numerical solution of a two-dimensional inverse heat transfer problem in gas turbine blade cooling, Archives of Thermodynamics, Vol.27, No.4, 2006, 1-8.
• [6] GRESHO P.M., SANI R.L.: Incompressible Flow and the Finite Element Method, John Wiley and Sons, LTD, 2000
• [7] TALER J.: Determination of local heat transfer coefficient from solution of the inverse heat conduction problem, Forschung im Ingenieurwesen (Engineering Research), 2007, 71, 69-78.