PRESSURE-DEPENDENT GAS HEAT-TRANSPORT IN A SPHERICAL PORE

A mean free path gas kinetic theory is used to model the conductive he at transport of a gas within a void volume enclosed in a Fourier solid . A variational upper bound principle is derived for a void of arbitra ry shape and applied to obtain a rigorous upper bound equation for the void gas conductivity in a spherical void. The variational void gas c onductivity equation is exact in both the large and small Knudsen numb er (Kn) limits and provides a means to determine the accuracy of the r eciprocal additivity interpolation formula as applied to thermal condu ctivity rather than diffusive mass transfer (maximum error 6% at Kn = 0.5 and alpha = 1). Temperature jump will occur even at atmospheric pr essures and higher for sufficiently small thermal accommodation coeffi cients (alpha < 0.1). Experimental void gas heat conductivities vs. pr essure data for H-2, He, Ne, N2, CO2, and F12 in a polyurethane foam a re compared with theoretical mean free path void gas conductivity vs. inverse Knudsen number curves drawn for various a. Estimates of the th ermal accommodation coefficients for the gas- polyurethane surface exh ibit a maximum with increasing molecular mass of the gas molecules, wh ich qualitatively agrees with the predictions of Baule's classical the ory. Results also point to a rather sharp shift of the S curve to high er pressures with decreasing thermal accommodation.