Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T13:07:09.589Z Has data issue: false hasContentIssue false

Conduction of heat in a solid with periodic boundary conditions, with an application to the surface temperature of the moon

Published online by Cambridge University Press:  24 October 2008

J. C. Jaeger
Affiliation:
The Australian National UniversityCanberra

Extract

The object of this note is to indicate a numerical method for finding periodic solutions of a number of important problems in conduction of heat in which the boundary conditions are periodic in the time and may be linear or non-linear. One example is that of a circular cylinder which is heated by friction along the generators through a rotating arc of its circumference, the remainder of the surface being kept at constant temperature; here the boundary conditions are linear but mixed. Another example, which will be discussed in detail below, is that of the variation of the surface temperature of the moon during a lunation; in this case the boundary condition is non-linear. In all cases the thermal properties of the solid will be assumed to be independent of temperature. Only the semi-infinite solid will be considered here, though the method applies equally well to other cases.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1953

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Carslaw, H. S. and Jaeger, J. C.Operational methods in applied mathematics, 2nd ed. (Oxford, 1948), § 129.Google Scholar
(2)Pettit, E. and Nicholson, S. B.Astrophys. J. 71 (1930), 102.CrossRefGoogle Scholar
(3)Piddington, J. H. and Minnett, H. C.Aust. J. sci. Res. A, 2 (1949), 63.Google Scholar
(4)Waidelich, D. L.Proc. Inst. Radio Engrs, N.Y., 34 (1946), 78P.Google Scholar
(5)Wesselink, A. J.Bull. astr. Insts Netherlds, 10 (1948), 351.Google Scholar