Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T11:58:43.001Z Has data issue: false hasContentIssue false
  • English
  • Français

Insulating circular rugs

Published online by Cambridge University Press:  17 February 2009

G. J. Weir
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A thin, partially insulating circular rug is placed on a uniform half space up through which a steady heat flow passes. The corresponding dual integral equations are solved using Tranter's method, finite Legendre transforms and Mellin-Bames contour integrals. An untabulated Bessel (or Stieltjes) transform similar to the discontinuous WeberSchafheitlin integral is evaluated, and a simple expression derived for the rug's surface temperature.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 4 , April 1983 , pp. 359 - 365
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Gradshteyn, I. S. and Ryzhik, I. M., Tables of integrals, series and products (Academic, New York, 1980).Google Scholar
[2]Oberhettinger, F., Tables of Bessel transforms (Springer, Berlin, 1972).CrossRefGoogle Scholar
[3]Tranter, C. J., Integral transforms in mathematical physics (Methuen, London; John Wiley, New York, 1962).Google Scholar
[4]Watson, G. N., A treatise on the theory of Bessel functions (Cambridge University Press, Cambridge, 1944).Google Scholar
[5]Wooding, R. A., “Steady infiltration from a shallow circular pond,” Water Resources Res. 4 (1968), 1259–1273.Google Scholar