,nl.J. Heur MnssTrrmrfer. Vol. 35. No.5.p~. 1155-1167. 1992 0017-9310;92 $S.OO+O.OO Printed in Great Britain ~8:~ 1992 Pcrgamon Press Ltd The transient thermal response of a glass-fiber insulation slab with hygroscopic effects Y.-X. TAO, R. W. BESANT and K. S. REZKALLAH Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan S7N OWO, Canada zyxwvutsrqponmlkjihgfedcbaZYXWVUT (Received 1 M arch 1991 and irzjnalform 3 May 1991) Abstract-The Brunauer-Emmett-Teller (BET) equation, representing adsorption isotherms, is used in a one-dimensional, transient vapor-diffusion model for heat and moisture transport in a typical, medium- dry density glass-fiber insulation slab to account for the hygroscopic effects (water vapor adsorption, desorption, and capillary condensation). The correction to the latent enthalpy of phase change, used in the energy equation, is derived from empirical desorption isotherms. The results obtained, for two types of boundary conditions (a closed system and an open system), show that the effects of hygroscopicity on the transient temperature distribution are significant for a slab with one boundary open to moist air. The sensitivity of hygroscopicity on the transient heat and mass transfer behavior can be depicted by a transition Fourier number, which is proportional to the adsorption capacity of the glass-fiber slab and increases as the cold side temperature and ambient relative humidity increase. Given the uncertainty in the adsorption properties of fiber-glass and experimental data, the agreement between the mode1 and measured data is reasonable. 1. INTRODUCTION HEAT AND moisture transport through insulation materials has been of considerable interest among researchers, not only because of its practical sig- nificance in energy conservation for building and refrigerated space envelopes, but also because of the physical complexity of problems in various transient circumstances. In practice, the consequences of the failure of vapor retarders in air-tight structures due to installation problems (among other factors) are well known in the design and consulting communities [l]. This failure of vapor retarders may, depending on temperature and air exfiltration rates, result in significant water and/or frost accumulation in build- ing envelopes. In order to understand the physics of the transport processes in those situations, studies have been conducted analytically and numerically [2- 4] along with the experimental efforts [5-81. For applied temperature ranges above the freezing point, the investigation has been conducted to include con- densation effects [9, IO] and air infiltration/exfiltration effects zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA [l zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 11. It has been shown that the additional, steady-state heat loss, due to condensation of water in an insulation slab under a thermal gradient, is neg- ligible if the mass transport process in the slab is dominated by vapor molecular diffusion (i.e. Pe = 0) and the Lewis number (C&~/D&) is small [9]. This conclusion is supported by an early experimental study by Kumaran [7] in which a glass-fiber insulation slab, after being open to a moist air at 97% relative humidity for a long time, showed no significant increase in heat flux as compared to a dry slab. It has also been reported by Wijeysundera et al. [8], for an insulation slab with its impermeable cold side (an ideal vapor ‘barrier’ applied) and the warm side open to a forced convective moist air at a relative humidity of less than 80%, the heat loss is almost the same as if the slab is dry. However, when the cold side of the insulation slab is subject to a temperature below the triple point of water, condensed water may exist as frost which both alters the temperature distribution and increases the effective thermal conductivity of the slab. A numerical study [12] shows that condensation and frosting in a typical glass-fiber slab will result in a l&30% increase in heat flux at the quasi-steady- state when the ambient air relative humidity is above 60%. In all the numerical studies mentioned above, the hygroscopicity of the glass-fiber insulation was not considered in the models. Condensation, or frosting, is assumed to occur when the local vapor density reaches its saturation value, i.e. no water vapor adsorption is considered. Mitalas and Kumaran [13] made an estimate of the hygroscopic effects for a glass- fiber slab which was in a closed system ; their test facility contained a fixed quantity of water and vapor in a sealed cell and was not exposed to ambient moist air. They concluded that the hygroscopic effects on the thermal performance was negligible when this wrapped slab was subject to a temperature difference in their heat flow measurement apparatus. However, previous experimental work [14] shows that, when an initially oven-dried glass-fiber slab has one side open to moist air and is subjected to a large temperature difference across the slab, the measured internal slab temperatures and heat flux from the cold surface are higher than those predicted using a model that excludes the hygroscopicity effects. It was found that only for a slab, that was initially wetted, were the 1155