The problem of determining the effective thermal conductivity of a two-phase system, given the conductivities and volume fractions of the components, is examined. Equations are described which have been proposed as solutions to this problem, including those of Maxwell, de Vries, and Kunii and Smith, the weighted geometric mean equation, and an equation based on a three-element resistor model found applicable to the analogous electrical conductivity problem. Experimental results are presented for five unconsolidated samples: three quartz sand packs, a glass bead pack, and a lead shot pack. The method of conductivity measurement using the transient line heat source (thermal conductivity probe) is described. Data are reported showing the variation of effective thermal conductivity with porosity, solid particle conductivity, saturating fluid conductivity, and the pressure of the saturating gas. From considerations based on the kinetic theory of gases, it is shown that the characteristic dimension of the pore space, with respect to heat conduction in the gas occupying this space, is smaller than the mean particle diameter by a factor of roughly 100. The thermal conductivity equations which best represent the observed data are those of de Vries, and Kunii and Smith, and a slightly modified version of the resistor model equation.

Measurements have been made of the effective thermal conductivity of porous sandstones. The method is based on the transient heating effect resulting from use of a line heat source. Data are presented for six sandstones ranging in porosity from 3 to 59% and show the variation of thermal conductivity with porosity, the conductivity of the saturating fluid, the pressure of the gas filling the pore space, and overburden pressure. The results are compared with those previously obtained for unconsolidated sands. All samples, except one, exhibited a lower thermal conductivity when saturated with a gas at atmospheric pressure than when saturated with a liquid of the same conductivity as the gas. An explanation for this effect, in terms of the kinetic theory of gases, is advanced and substantiated by other data. Finally, the validity of certain equations for the thermal conductivity of two-phase systems is examined; the weighted geometric mean of the two constituent conductivities is found to agree well with the measured effective conductivities.

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/npsi/ctrl?lang=en http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?lang=fr Access and use of this website and the material on it are subject to the Terms and Conditions set forth at http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=en NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. Physics, 36, 7, pp. 815-823, 1958 Calculation of the thermal conductivity of porous media Woodside, W. Canadian Journal of ANALYZED CALCULATION OF THE THERMAL CONDUCTIVITY OF POROUS MEDIALABSTRACT The problem of dctcr~nining the etTecLive thernial co~~ductivities of porous and other composite materials from the conductivities and volume fractions of theilconstituents is examined. -411 approximate equation is derived for the case of a cubic lattice of identical spherical particles in a medium having properties different from those of the particles. This equation is applied to the calculatio~~ of the thermal conductivity of snow at different densities in the range 0.10 to 0.48 gm/cc. The effect of water vapor diffusion in snow ~lnder a temperature gradient is taken into account by adding a latent heat term to the conductivity value for dry air. Conductivity values for snow, calculatcd in this manner, are found to agree satisfactorily with experimental data. An equation due to Russell is also shown to give conductivity \~alues for several cellular thermal insulating materials which are in good agreement with experilrlel~tal values.

Obesity in the Zucker rat is accompanied by hyperlipemia, hyperinsulinism, insulin resistance, pancreatic hyperplasia, and islet hypertrophy. This study correlates the morphologic heterogeneity of isolated pancreatic islets with secretion of insulin and glucagon in the perifusion system. Islet size was arbitrarily defined as large (greater than 0.45 mm) or small (smaller than 0.12 mm). Protein content and volume (V = 4/3pir3) were calculated for groups and individual islets, respectively. Islets from obese rats secreted more insulin in response to glucose and aminophylline than islets from lean rats (peak 7.8 +/- 2.4 vs. 1.5 +/- 0.37 microU/islet/min, P less than 0.005). Insulin release was related directly to islet size and protein content. Small islets from lean and obese animals produced less insulin per islet than large islets (P less than 0.005). In terms of islet volume, however, large islets were inefficient insulin releasers as compared to small islets (P less than 0.005). Stimulation with Br-cAMP released glucagon from islets of lean but not from large islets of obese animals (peak 11 +/- 3.3 vs. 4.1 +/- 0.3 pg/microgram protein per minute, P less than 0.05). Arginine produced the same effect on glucagon release (P less than 0.05) as stimulation with Br-cAMP. The observed increased insulin release rates and the blunted glucagon response are related to islet size in the pancreas of the Zucker rat.