Abstract
It is shown that a steady-state problem of heat conduction theory for a wedge releasing heat according to Newton's law is reduced, by means of an integral transformation, to solution of a certain functional equation. For a wedge angle of 2 γ=π/m (m=1, 2, 3, ...) an exact solution of the latter equation is found, and formulas for the temperature distribution are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. N. Lebedev and I. P. Skal'skaya, ZhTF,34, 1556, 1964.
H. Carslaw and J. Jaeger, Conduction of Heat in Solids [Russian translation], Izd. Nauka, 1964.
N. N. Lebedev, I. P. Skal'skaya, and Ya. S. Uflyand, Collected Problems in Mathematical Physics [in Russian], GITTL, 1955.
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series and Products [in Russian], FM, 1962.
Milne-Thomson, The Calculus of Finite Differences, Macmillan, London, 1951.
L. S. Bark, Tables of an Integral Exponential Function in the Complex Domain [in Russian], VTs. AN SSSR, no. 31, 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vasil'ev, B.A. Some steady-state problems in heat conduction theory for wedges with boundary conditions of the third kind. Journal of Engineering Physics 11, 131–135 (1966). https://doi.org/10.1007/BF00831270
Issue Date:
DOI: https://doi.org/10.1007/BF00831270