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

Wróblewska A., Frąckowiak A., Ciałkowski M.

Archives of Thermodynamics

2008

Vol. 29, no. 1

3-18

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.