Open AccessHeat‐Flow Refraction across Dissimilar Media
Author(s) -
Lee TienChang,
Henyey Thomas L.
Publication year - 1974
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1974.tb05457.x
Subject(s) - mechanics , cylinder , refraction , ellipsoid , heat flow , perturbation (astronomy) , finite element method , anisotropy , position (finance) , thermal conductivity , flow (mathematics) , mathematical analysis , geometry , mathematics , physics , optics , thermodynamics , finance , quantum mechanics , astronomy , thermal , economics
Summary Refraction of heat flow across near surface boundaries between dissimilar media results in local variations in heat flow. The magnitude of the perturbation from the regional value is a function of position, conductivity ratio, and the configuration of media. New analytical solutions are given for a semi‐ellipsoid and a pair of parallel semi‐cylinders immersed in an otherwise homogeneous semi‐infinite medium. An analytical solution is also derived for the case of a buried cylinder. For two‐dimensional but arbitrary geometric configurations, a numerical scheme based on the finite element method is formulated to include the effects of conductivity contrast as well as relief, non‐uniform surface temperature, and internal heat generation. The applicability of this scheme is demonstrated by comparing the numerical results with analytical solutions and results obtained from a finite difference method.