Heat and Mass Transfer in Hygroscopic Porous Media: Consequences of Invoking Tóth’s Sorption Isotherm

Abstract

The thermal performance of ventilated beds of hygroscopic porous media depends strongly on the sorption properties of the solid phase. Furthermore, the published literature shows that the predicted performance of ventilated beds of hygroscopic porous media is extremely sensitive to the form and accuracy of the sorption isotherm. This is particularly apparent under idealized conditions when thermodynamic equilibrium is deemed to exist between the solid and fluid phases. When Tóth’s isotherm is invoked in an equilibrium model used to analyse the performance of a bed of initially warm and dry silica gel ventilated with cool, humid air, it is predicted that a shock wave develops downstream of air entering the bed. In contrast, it is shown that non-equilibrium solutions result in a transfer wave, the width of which decreases as the velocity of the interstitial air decreases. The Tóth isotherm gives rise to erroneous values of the integral heat of wetting of silica gel. Previously published studies of simultaneous heat and mass transfer in beds of hygroscopic materials refer to conceptual difficulties in interpreting the results, and some published mathematical analyses are somewhat terse. A secondary aim of this work is to assuage these difficulties by detailing the analyses in Supplementary Information.