Mathematics – Logic
Scientific paper
Dec 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agufm.p22a..05w&link_type=abstract
American Geophysical Union, Fall Meeting 2009, abstract #P22A-05
Mathematics
Logic
[5418] Planetary Sciences: Solid Surface Planets / Heat Flow, [5464] Planetary Sciences: Solid Surface Planets / Remote Sensing, [5470] Planetary Sciences: Solid Surface Planets / Surface Materials And Properties, [6225] Planetary Sciences: Solar System Objects / Mars
Scientific paper
We have developed a simple physical model for estimating the effective thermal conductivity (k_eff) of porous planetary regolith as a function of the intrinsic thermal conductivities of the material components (solid and gas), the porosity, mean particle size, air pressure (or vacuum) in the pore space, temperature, and the degree of interparticle contact or cementation. The model is based on the Maxwell-Eucken theoretical expressions for the upper and lower bounds for k_eff of heterogeneous, isotropic material with one continuous phase [1]. These equations provide tighter bounds than the parallel and series approximations typically used to calculate k_eff for porous media. The effect of interparticle cementation is represented by an empirical factor f_cont which represents the fractional continuity of the high conductivity phase, with a value between 0 and 1 determined by comparison with laboratory measurements of k_eff for various geologic materials.
In a dry planetary regolith there are three heat transfer mechanisms: heat conduction through the solid particles and their physical contacts (k_s), heat conduction by the gas in the pore space (k_g), and radiative heat transfer between the solid particles (k_r). For unconsolidated (loose) particulates in the presence of an atmosphere, k_g is the dominant heat transfer mechanism. The thermal conductivity of an ideal gas is independent of pressure, but as the pressure decreases in a porous medium, the mean free path of gas molecules begins to approach the pore size and this reduces the efficiency of gaseous heat transfer. When this ratio (the Knudsen number) becomes >>1, then k_g reaches a minimum and k_eff becomes controlled by k_s and k_r. The rarefied atmosphere of Mars puts it in the transition regime, and laboratory measurements of k_eff for glass beads (as a soil analog) in CO2 gas have quantified the effects of varying pressure and particle size [2,3]. An empirical formula based on a log-linear fit to these measurements [2] has been used extensively for the past 10 years to interpret observations of Mars’ surface thermal properties (e.g. relating thermal inertia to particle size). Our physically-based model is able to fit these data as well as other measurements of particulates in a vacuum [4] and therefore provides a firmer basis for predicting or interpreting thermal properties of surface materials on Mars and other planets and satellites.
References [1] Carson, J.K. et al. (2005), Int. J. Heat Mass Transfer 48, 2150-2158. [2] Presley, M. A. and P. R. Christensen (1997). J. Geophys. Res. 102, 6551-6566. [3] Huetter, E. S. et al. (2008). J. Geophys. Res. 113, E12004. [4] Wechsler, A. E. and P. E. Glaser (1965). Icarus 4, 335-352.
Moody John Atwell
Wood Stephen E.
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