Practical correlations for thermal resistance of horizontal enclosed airspaces with upward heat flow for building applications

The thermal resistance (R-value) of an enclosed airspace depends on the emissivity of all surfaces that bound the airspace, the size and orientation of the airspace, the direction of heat transfer through the airspace, and the respective temperatures of all surfaces that define the airspace. A table is provided in the 2009 ASHRAE Handbook of Fundamentals (Chapter 26) that contains the R-values of enclosed airspaces. The ASHRAE table is extensively used by modellers, architects and building designers in the design for thermal resistance of building enclosures. This table provides R-values for enclosed airspaces for different values of airspace thickness, effective emittance, mean airspace temperature, and temperature differences across the airspace. The effect of the airspace aspect ratio (length/thickness) on the R-value is not accounted for in the ASHRAE table. However, in previous studies, it was shown that the aspect ratio of the airspace can affect its R-value. In this paper, previous studies undertaken by the author that focused on determining the R-value for vertical enclosed airspaces and horizontal enclosed airspaces with downward heat flow are extended to investigate the effect of the aspect ratio on the R-value of horizontal enclosed airspaces under an upward heat flow condition for different airspace thicknesses and having a wide range of values for effective emittance, mean temperature, and temperature differences across the horizontal airspaces. The R-values predicted from numerical simulation are compared with those provided in the ASHRAE table. Considerations were also given to investigate the potential increase in the R-values of enclosed airspaces when a thin sheet is placed horizontally in the middle of the airspace and whose surfaces have different values of emissivity. Thereafter, practical correlations are developed for determining the R-values of horizontal enclosed airspaces for future use by modellers, architects and building designers. The simplicity of these correlations for horizontal airspaces with upward heat flow along with those that were previously developed for vertical airspaces and horizontal airspaces with downward heat flow suggests that these correlations could be included in the ASHRAE Handbook of Fundamentals.