A Generalized Function in Heat Conductivity Problems for Multilayer Structures with Heat Sources
- 12 Downloads
An accurate analytical solution of the stationary problem of heat conductivity for a multilayer structure with heat sources under asymmetric boundary conditions of the third kind is obtained based on the use of the theory of generalized functions. Using the asymmetric unit function (Heaviside function), the problem for a multilayer structure is reduced to a single-layer with discontinuous (piecewise-continuous) medium properties. By introducing a new independent variable, the nonlinear differential equation (nonlinearity of the second kind—the thermal-physical properties depend on the spatial variable) is reduced to a linear one, direct integration of which allows obtaining an accurate analytical solution of the problem considered. Examples of investigations of the temperature fields for some certain multilayer structures are given.
Unable to display preview. Download preview PDF.
- 1.Kudinov, V.A., Averin, B.V., and Stefanyuk, E.V., Teploprovodnost’ i termouprugost' v mnogosloinykh konstruktsiyakh (Heat Conductivity and Thermoelasticity and Multilayered Constructions), Moscow: Vysshaya Shkola, 2008.Google Scholar
- 2.Averin, B.V., Kolotilkin, D.I., and Kudinov, V.A., Sturm-Liouville problem for a differential equation of second order with discontinuous coefficients, J. Eng. Phys. Thermophys., 2000, vol. 73, no. 4, pp. 735–740.Google Scholar
- 5.Ketch, V. and Teodorescu, P., Introduction to the Theory of Generalized Functions with Applications in Engineering, New York: Wiley, 1978.Google Scholar
- 8.Obraztsov, I.F. and Onanov, G.G., Stroitel’naya mekhanika skoshennykh tonkostennykh sistem (Structural Mechanics of Tapered Thin Walled Systems), Moscow: Mashinostroenie, 1973.Google Scholar
- 10.Protsyuk, B.V., On solution of heat conductivity and thermoelasticity problems for multilayer bodies, Dokl. Akad. Nauk USSR, Ser. A, 1977, no. 11, pp. 1019–1021.Google Scholar
- 12.Volkov, A.G., Radio-transparent shelters for powerful transmitting phased antenna arrays, Extended Abstract of Cand. Sci. Dissertation, Moscow: NIRF, 1984.Google Scholar