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 TVT, 2006, Volume 44, Issue 1, Pages 127–135 (Mi tvt1297)

Heat and Mass Transfer and Physical Gasdynamics

Unsteady-state temperature field in a semi-infinite body heated by a disk surface heat source

V. A. Pinsker

All-Russian Research Institute of Drilling Equipment, Moscow

Abstract: The paper deals with a three-dimensional axisymmetric problem on temperature field in a semi-infinite body heated by a time-constant heat flux distributed uniformly within a circular region on a free surface. Exact formulas are obtained for the unsteady-state temperature on the edge of the heating zone and for the average temperature within the region being heated. A non-obvious property of radial inversion of the value of average temperature is revealed. A new expression for unsteady-state temperature field, which is convenient for use in numerical calculations, is derived in an integral form on a circular cylindrical surface which is a continuation of the boundary of the heating zone. A general analytical solution of the problem is found in a closed form for the steady-state mode. The steady-state temperature field is expressed in terms of a combination of elliptic integrals. Particular cases are treated, in which the general expression derived for temperature assumes a simpler form. The decrease in the degree of concentration of heat flux with increasing depth is calculated. Fields of isotherms are constructed for both steady-state and unsteady-state cases, and the pattern of their distribution is analyzed. The asymptotics of the obtained dependences at low and high values of dimensionless time and in the vicinity of and away from the region being heated are studied. The range of validity of the adopted model of linear heat conduction is identified.

Full text: PDF file (1748 kB)

English version:
High Temperature, 2006, 44:1, 129–138

UDC: 536.2

Citation: V. A. Pinsker, “Unsteady-state temperature field in a semi-infinite body heated by a disk surface heat source”, TVT, 44:1 (2006), 127–135; High Temperature, 44:1 (2006), 129–138

Citation in format AMSBIB
\Bibitem{Pin06} \by V.~A.~Pinsker \paper Unsteady-state temperature field in a semi-infinite body heated by a disk surface heat source \jour TVT \yr 2006 \vol 44 \issue 1 \pages 127--135 \mathnet{http://mi.mathnet.ru/tvt1297} \elib{http://elibrary.ru/item.asp?id=9242454} \transl \jour High Temperature \yr 2006 \vol 44 \issue 1 \pages 129--138 \crossref{https://doi.org/10.1007/s10740-006-0015-1} \elib{http://elibrary.ru/item.asp?id=13527383} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33644931899} 

• http://mi.mathnet.ru/eng/tvt1297
• http://mi.mathnet.ru/eng/tvt/v44/i1/p127

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Manako, “Predstavlenie temperaturnogo polya dlya polubeskonechnogo tela, nagrevaemogo nepodvizhnym lazernym luchom, cherez gipergeometricheskie funktsii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(27) (2012), 115–123