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Thermal conductivity of an individual grain and bulk thermal conductivity of a cometary nucleus

  It has been assumed that a grain in a cometary nucleus is of silicate core - ice mantle structure, and the ice is initially amorphous. In the course of the thermal evolution of comets the amorphous ice may partially crystallize in general. Thus thermal conductivity tex2html_wrap_inline1456 of a core-mantle individual grain is a function of thermal conductivities of amorphous ice, crystalline ice, and silicate, respectively denoted by tex2html_wrap_inline1404 , tex2html_wrap_inline1460 , and tex2html_wrap_inline1462 , the crystalline fraction tex2html_wrap_inline1464 , and mass fraction of silicate x:

displaymath1468

For small degree of crystallization where tex2html_wrap_inline1470 , tex2html_wrap_inline1456 may be approximated (Haruyama et al., 1993) by

  equation252

with the use of eq. (7), where g is a geometrical factor determined by the ratio of the core radius to the whole radius of a core-mantle grain, and is on the order of unity. Note that when tex2html_wrap_inline1470 , tex2html_wrap_inline1456 is independent of tex2html_wrap_inline1404 , and is determined by tex2html_wrap_inline1460 and tex2html_wrap_inline1464 alone.

Thermal conductivity tex2html_wrap_inline1486 of a cometary nucleus as a whole is smaller than the thermal conductivity of an individual grain tex2html_wrap_inline1456 because of the porous structure of the nucleus. Introducng a parameter tex2html_wrap_inline1490 which we call a reduction factor, we express the thermal conductivity of the nucleus tex2html_wrap_inline1486 by

  equation263

where the right-hand-side is an approximation which holds when tex2html_wrap_inline1470 .

It is difficult to evaluate tex2html_wrap_inline1490 quantitatively, since tex2html_wrap_inline1486 depends on the porosity of the nucleus as well as spatial configuration of grains in the nucleus. It is plausible that tex2html_wrap_inline1500 because of highly porous structure of a cometary nucleus. Greenberg et al. (1989) estimate tex2html_wrap_inline1502 on the basis of the assumption that each particle interface is about tex2html_wrap_inline1504 of its total area and each particle is in contact with an average of five particles, as deduced from a model of porosity of 0.8 (Greenberg, 1988). We take tex2html_wrap_inline1506 to 0.5 in the model calculations shown later (Haruyama et al., 1993).


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Next: Heating by decay of Up: Key Physical Quantities in Previous: Thermal conductivity of amorphous

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Mon Sep 16 16:23:29 JST 1996