Other
Scientific paper
Mar 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986em%26p...34..283l&link_type=abstract
Earth, Moon, and Planets (ISSN 0167-9295), vol. 34, March 1986, p. 283-304.
Other
2
Elastic Deformation, Geotemperature, Lithosphere, Thermoelasticity, Conductive Heat Transfer, Earth Mantle, Mathematical Models, Navier-Stokes Equation, Radial Distribution, Temperature Distribution
Scientific paper
The problem of the thermoelastic deformation of a spherical earth with constant elastic parameters heated from within by the spontaneous decay of radiogenic elements is examined. The problem consists of the simultaneous solution of the Navier-Stokes equation and the heat conduction equation. An integrodifferential equation is obtained which is then solved by means of the Laplace transform and the Green's function approach. Analytic solutions for the temperature distribution and radial deformation are obtained as infinite series of functions of the radial distance and time, depending also on a sequence of eigenvalues. Particular solutions are provided for the case when the two specific heats Cp and Cv are approximately equal. It is believed that these analytical results are applicable to the study of the oceanic lithosphere deformations, and that the approach could be successfully applied to ascertain the deformation according to other regimes of internal heating.
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