Pressure‐dependent gas heat transport in a spherical pore

Abstract

AbstractA mean free path gas kinetic theory is used to model the conductive heat transport of a gas within a void volume enclosed in a Fourier solid. A variational upper bound principle is derived for a void of arbitrary shape and applied to obtain a rigorous upper bound equation for the void gas conductivity in a spherical void. The variational void gas conductivity equation is exact in both the large and small Knudsen number (Kn) limits and provides a means to determine the accuracy of the reciprocal additivity interpolation formula as applied to thermal conductivity rather than diffusive mass transfer (maximum error 6% at Kn = 0.5 and α = 1). Temperature jump will occur even at atmospheric pressures and higher for sufficiently small thermal accommodation coefficients (α < 0.1). Experimental void gas heat conductivities vs. pressure data for H2, He, Ne, N2, CO2, and F12 in a polyurethane foam are compared with theoretical mean free path void gas conductivity vs. inverse Knudsen number curves drawn for various α. Estimates of the thermal accommodation coefficients for the gas‐ polyurethane surface exhibit a maximum with increasing molecular mass of the gas molecules, which qualitatively agrees with the predictions of Baule's classical theory. Results also point to a rather sharp shift of the S curve to higher pressures with decreasing thermal accommodation.