WEIGHTED TEMPERATURE FUNCTION METHOD FOR SOLUTION OF UNSTEADY-STATE HEAT CONDUCTION PROBLEMS
Abstract
An approximate integral method based on constructing integral identical equalities for the weighted temperature function is proposed for solution of unsteady-state heat conduction boundary-value problems. This method is simple in use and allows one to obtain much more exact solutions as compared to the known approximate methods.
About the Author
V. A. Kot
A. V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus, Minsk
Belarus
Ph. D. (Engineering), Senior researcher
Belarus
Ph. D. (Engineering), Senior researcher
References
1. Vlasova E. A., Zarubin V. S., Kuvyrkin G. N. Approximate methods of mathematical physics. Moscow, Publishing house of the Moscow State Technical University N. E. Bauman, 2001. 700 p. (in Russian).
2. Zarubin V. S. Mathematical modeling in technology. Moscow, Publishing house of the Moscow State Technical University N. E. Bauman, 2003. 496 p. (in Russian).
3. Fletcher K. Numerical Methods Based on the Galerkin Method. Moscow, Mir Publ., 1988. 352 p. (in Russian).
4. Mikhlin S. G. Variational methods in mathematical physics. Moscow, Nauka Publ., 1970. 512 p. (in Russian).
5. Wood A. S. A new look at the heat balance integral method. Applied Mathematical Modelling, 2001, vol. 25, no. 10, pp. 815–824. doi.org/10.1016/s0307-904x(01)00016-6.
6. Mitchell S. L., Myers T. G. Application of standard and refined heat balance integral methods to one-dimensional Stefan problems. SIAM Review, 2010, vol. 52, no. 1, pp. 57–86. doi.org/10.1137/080733036.
7. Myers T. G. Optimizing the exponent in the heat balance and refined integral methods. International Communications in Heat and Mass Transfer, 2009, vol. 36, no. 2, pp. 143–147. doi.org/10.1016/j.icheatmasstransfer.2008.10.013.
8. Layeni O. P., Johnson J. V. Hybrids of the heat balance integral method. Applied Mathematics and Computation, 2012, vol. 218, no. 14, pp. 7431–7444. doi.org/10.1016/j.amc.2012.01.001.
9. Mitchell S. L., Myers T. G. Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions. International Journal of Heat and Mass Transfer, 2010, vol. 53, no. 17/18, pp. 3540– 3551. doi.org/10.1016/j.ijheatmasstransfer.2010.04.015.
10. Kot V. A. Weighted temperature identities. Journal of Engineering Physics and Thermophysics, 2015, vol. 88, no. 2, pp. 423–438. doi.org/10.1007/s10891-015-1207-5.
11. Lykov V. A. Theory of heat conduction. Moscow, Vysshaya shkola, 1967. 600 p. (in Russian).
12. Carslow H. S., Jaeger J. C. Conduction of Heat in Solids. Oxford, UK, Oxford University Press, 1992. 510 p
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