By Vyacheslav S. Vikhrenko
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Extra info for HEAT CONDUCTION – BASIC RESEARCH
In the case of the first subinterval an initial condition is known. For the next subintervals initial condition is understood as the temperature distribution in the subdomain j at the final moment of time in the previous subinterval. The mean-square method is used to minimize the inaccuracy of the approximate solution on the boundary, at the initial moment of time and on the borders between elements. This way the unknown coefficients of the combination, cmj , can be calculated. Generally, the coefficients cmj depend on the time subinterval number, (Grysa & Lesniewska, 2009).
1, pp. 111-134, ISSN 1429-2955 Inverse Heat Conduction Problems 33 Ciałkowski, M. J. & Grysa, K. 6, pp. 595–616, ISSN 09280219 Dennis, B. , Dulikravich, G. S. Egorov, I. , Yoshimura, S. & Herceg, D. 256–266, ISSN 0918-6654 Dennis, J. & Schnabel, R. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, ISBN 0-89871-364-1 Duda, P. & Taler, J. (2006), Solving Direct and Inverse Heat Conduction Problems, Springer, ISBN 354033470X Fan, Y. -G. 27, pp. 1317–1323, ISSN 1312-8876 Golub, G.
The other points with the same value of the coordinate s for the outer and inner surface generally do not correspond to each other (in the case of peaks the difference is about 0,02). Fig. 6. Heat transfer coefficient over inner (dark blue squares) and outer (red dots — given; brown dots — calculated) surfaces of the blade. 2 Direct solution of a heat transfer coefficient identification problem Consider a 1D dimensionless problem of heat conduction in a thermally isotropic flat slab (Grysa, 1982): 2T / x 2 T / t for x (0,1) and t(0, tf], 31 Inverse Heat Conduction Problems T / x 0 for x = 0 and t(0, tf], kT / x Bi T 1, t T f t T 0 for (74) for x = 1 and t(0, tf], x (0,1) and t = 0 .
HEAT CONDUCTION – BASIC RESEARCH by Vyacheslav S. Vikhrenko