Engineering Transactions, 25, 2, pp. 349-368, 1977

Zastosowanie Zasady Gaussa do Przybliżonego Rozwiązywania Równań Różniczkowych Przewodzenia Ciepła

J. Taler
Politechnika Krakowska, Kraków
Poland

W pracy przedstawiono metodę przybliżonego rozwiązywania zagadnień nieustalonego przewodzenia ciepła w ciałach stałych opartą na zasadzie najmniejszego działania (Gaussa), którą zastosowano do przekształconego przez Biota równania przewodzenia ciepła. Przedstawiono również praktycznie zastosowanie metody, rozważając nieustalone pole temperatury w półprzestrzeni, na granicy której dany jest strumień cieplny zależny od czasu i temperatury powierzchni.

Full Text: PDF

References

R. S. SCHECHTER, The variational method in engineering, Mc Graw-Hill Book Company, New York 1967.

M. A. BIOT, Variational principles in heat transfer, A unified Lagrangian analysis of dissipative phenomena, Clarendon Press, Oxford 1970.

P. GLANSDORFE, I. PRIGOGINE, Thermodynamic theory of structure, stability and flucutations, Wiley Interscience, London 1971.

I. GYARMATI, Non-equilibrium thermodynamics, field theory and variational principles, Springer-Verlag, Berlin-Heidelberg-New York 1970.

B. VUJANOVIC, An approach to linear and nonlinear heat transfer problem using a Lagrangian, AIAA Journal, 9, 1, 1971.

B. VUJANOVIC, Heat transfer with nonlinear boundary conditions via a variational principle, PAIAA Journal, 9, 2, 197

D. DJUKIC, B. VUJANOVIC, On a new variational principle of Hamiltonian type for classica field theory, ZAMM, 51, 611-616, 1971.

B. VUJANOVIC, D. DJUKIC, On one variational principle of Hamilton's type for nonlinear heat transfer problem, Int. J. Heat Mass Transfer, 15, 5, 1972.

B. VUJANOVIC, B. BACLIC, Applications of Gauss's principle of least constraint to the nonlinear heat transfer problem, Int. J. Heat Mass Transfer, 19, 7, 1976.

C. LANCZO The variational principles of mechanics, University of Toronto Press, Toronto 1962.

R. GUTOWSKI, Mechanika analityczna, PWN, Warszawa 1971.

L. OUSAGER, Reciprocal relations in irreversible processes, I. Phys. Rev., 37, 405-426, 1931.

A. STARK, Approximation methods for the solution of heat conduction problems using Gyamati's principle, Annalen der Physik, 7, 31, 1, 53-75, 1974.

B.A. FINLAYSON, The method od weighted residuals and variational principles, Academic Press, New York 1972.

B. KRAJEWSKI, On a direct variational method for nonlinear heat transfer, Int. J. Heat Mass Transfer, 18, 495-502, 1975.

M.A. BIOT, New methods in heat flow analysis with application to flight structures, J. Aeronaut. Sci., 24, 857-873, 1957.

T.R. GOODMAN, Application of integral methods to transient nonlinear heat transfer in: Advances in Heat Transfer, 1, Academic Press, New York 1964.

J. TALER, K. RUP, Zastosowanie metody bilansu cieplnego do określenia nieustalonego pola temperatur i napreżeń w ściance płaskiej, Inżyn. Chem., 3, 1976.

T.J. LARDNER, F.V. POHLE, Application of the heat balance integral to problems of cylindrical geometry, J. Appl. Mech., 28, 310-312, 1961.

T.J. LARDNER, Approximate heat conduction solutions for nonpianar geometric, J. Heat Transfer, 3, 423-425, 1965.

C. W. BOWMAN, D. M. WARD, A. I. JOHNSON, O. TRASS, Mass transfer from fluid and solid spheres at low Reynolds numbers, Can J. Chem. Eng., 39, 9-13, 1961.

T.J. LARDNER, Biot's variational principle in heat conduction, AIAA Journal, 1, 1, 1963.

P. RAFALSKI, W. ŻYSZKOWSKI, Lagrangian approach to the nonlinear boundary heat transfer-problem, AIAA Journal, 6, 8, 1968.

P. RAFALSKI, W. ŻYSZKOWSKI, On the variational principles for hea conduction problem, AIAA Journal, 7, 606-609, 1969.

W. ŻYSZKOWSKI, The transient temperature distribution in one-dimensional heat conduction problems with nonlinear boundary conditions, J. Heat Transfer, 2, 77-82, 1969.

W. ŻYSZKOWSKI, The transient temperature distribution in a slab subjected to radiative and convective heating calculuted by variational method, Int. J. Heat Mass Transfer, 16, 917-932, 1973.

E. VALLERANI, Integral technique solutions to a class of simple ablation problems, Meccanica, 2, 1974.

G. LEBON, J. CASAS-VAZQUEZ, Lagrangian formulation of unsteady non-linear heat transfer problems, J. Eng. Mathematics, 8, 1, 1974.

H. S. CARSLAW, J.C. JAEGER, Conduction of heat in solids, Clarendon Press, Oxford 1959.

P. RAZELOT, Methods of obtaining approximate solutions, in: Handbook of heat transfer. W. M. ROHSENOWA, J. P. HARTNETT'A, Mc Graw-Hill Book Company, New York 1973.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland