DIRECT INTEGRATION OF THE HEAT CONDUCTION EQUATION FOR A SEMI-BOUNDED SPACE
Abstract
On the basis of direct integration of the generalized equation of heat transfer in a semi-bounded space, the sequences of identical integral equalities defining the features of a differential equation and boundary conditions were obtained for the first time. On the basis of power polynomials with an exponential factor, this made it possible to construct approximate solutions with high convergence. The error in determining parameters over a wide range is hundredths and thousandths of a percent.
About the Author
V. A. Kot
A. V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus
Russian Federation
Ph. D. (Engineering), Senior researcher
Russian Federation
Ph. D. (Engineering), Senior researcher
References
1. Koshlyakov N. S., Gliner E. B., Smirnov M. M. Equations of partial derivatives of mathematical physics. Moscow, 1970. 767 p. (in Russian)
2. Lykov A. V. Heat conduction theory. Moscow, 1967. 600 p. (in Russian)
3. Kartashov E. M. Analytical methods in heat conduction theory of solids. Мoscow, 2001. 480 p. (in Russian)
4. Carslow H. S., Jaeger J. C. Conduction of Heat in Solids. Oxford, UK, Oxford University Press, 1992. 510 p.
5. Özisic M. N. Heat Conduction. New York: John Wiley & Sons, Inc., 1993. 692 p.
6. Barenblatt G. I., Levitan B. M. On some boundary-value tasks for the turbulent heat conduction equation. Izvestiia Akademii nauk SSSR. Seriia matematicheskaia [Mathematics of the USSR – Izvestija], 1952, vol. 16, pp. 253–280. (in Russian)
7. Kartashov E. M. A class of integral transformations for the generalized equation of nonstationary heat conduction. Journal of Engineering Physics and Thermophysics, 2008, vol. 81, no. 1, pp. 129–137. doi.org/10.1007/s10891-008-0023-6.
8. Sneddon I. Fourier transforms. New York, Mc Graw-Hill Book Co., 1951. 542 p.
9. Beitmen G., Ardeji A. Tables of Integral Transformations. V. 1. Transformations of Fourier, Laplace, Mellin. Мoscow, 1969. 344 p. (in Russian)
10. Volkov I. K., Kanatnikov A. N. Integral transformations and operational calculus. Мoscow, 2002. 228 p. (in Russian)
11. Alhasov A. B., Ramazanov M. M. Radial Model of Steam Extraction from a High-Temperature Bed by Means of a Single Well. Journal of Engineering Physics and Thermophysics, 2014, vol. 87, no. 3, pp. 556–565. doi.org/10.1007/s10891-014-1045-x.
12. Mundry, E. Über die lösung der wärmeleitungsgleichung für den aussenraum eines zylinders mit kreisförmigem querschnitt. International Journal of Heat and Mass Transfer, 1966, vol. 9, no. 3, pp. 189–197. doi.org/10.1016/0017-9310(66)90017-2.
Review
Views: 978
Email this article 