Heat polynomials and their applications

• Autorzy: Grysa K.
• Języki publikacji: EN

Abstrakty

EN

A brief review of heat polynomials is presented. Two methods of deriving the heat polynomials arew shown. One of them is used in order to derive the heat polynomials for a homogeneous rod with lateral heat transfer. A general method of finding an approximate solution of the initialboundary problem is described. Next, the heat polynomials are presented as a tool for finding unknown boundary temperature or thermo-physical properties of the considered body. Numerical examples illustrate application of the heat polynomials for solving the initial-boundary problems as well as the problems of Biot number identification.

Słowa kluczowe

EN

heat conduction; heat polynomial; inverse problem

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2003
• Tom: Vol. 24, no 2
• Strony: 107--124
• Opis fizyczny: Bibliogr. 8 poz.,

Twórcy

autor

Grysa K.

• Prof. dr hab. inż. ; automatyka i robotyka, termosprężystość, mechanika manipulatorów ; Politech. Świętokrzyska.

Bibliografia

• [1] Ciałkowski M., Treffz functions as basis functions of FEM in application to solution of inverse heat conduction problem, Computer Assisted Mechanics and Engineering Sciences, 8(2001), 247-260.
• [2] Rosenbloom P.C., Widder D.V., Expansions in terms of heat polynomials and associated functions, Trans. Am. Math. Soc., 1956, Vol. 92, 220-266.
• [3] Yano H., Fukutani S., Kieda A., A boundary residual metod with heat polynomials for solving usteady heat conduction problems, J. of the Franklin Inst., Vol. 316, No.4, 1983, 219-298
• [4] Hożejowski L., Heat Polynomials and Their Applications in the direct and inverse heat conduction problems, Ph.D. Thesis, Kielce University of Technology, Kielce 1999 (in Polish).
• [5] Futakiewicz S., Heat Function Method in Solving the Direct and Inverse Heat conduction problems, Ph.D. Thesis, Poznań University of Technology, Poznań 1999 (in Polish).
• [6] Ciałkowski M., Frackowiak A., Heat Functions and Their Application to Solving Heat Conduction and Mechanical Problems, Wyd. Politechniki Poznańskiej, Poznań, 2000 (in Polish).
• [7] Carslaw H.S., Jaeger J.C., Conduction of Heat in Solids, 2nd ed., Oxford at the Clarendon Press, 1959.
• [8] Grysa K., On the Exact and Aapproximate Methods of Solving the Inverse Problems of Temperature Fields, Politechnika Poznańska, Rozprawy Nr 204, Poznań 1989 (in Polish).