Practical correlation for thermal resistance of 45° sloped-enclosed airspaces with upward heat flow for building applications

Assessing the energy performance of building components with enclosed airspaces requires accurate determination of the thermal resistance (R-value) of the airspaces. The R-value of enclosed airspace depends on its size and orientation, direction of heat transfer through the airspace, and temperatures and emissivities of all surfaces that define the airspace. In previous studies, practical correlations were developed to determine the R-values for vertical enclosed airspaces, horizontal enclosed airspaces with upward heat flow and downward heat flow, and 30° and 45° sloped-enclosed airspaces with downward heat flow. However, to the authors’ best knowledge, there is no such practical correlations available to determine the R-values for wide ranges of dimensions and operating conditions for 30° and 45° sloped-enclosed airspaces with upward heat flow. This paper focused on the thermal performance of 45° sloped-enclosed airspaces with upward heat flow, and the predicted R-values were compared with the R-values provided in ASHRAE Handbook of Fundamentals at different conditions. The dependence of the R-value on the aspect ratio of the enclosed airspaces was also investigated. As well, considerations were given to quantify the potential increase in the R-value of enclosed airspace when a thin sheet having different values of emissivity on both sides was placed in the middle of the airspace. The results showed that depending on the value of the effective emittance and the thickness of the airspace, the R-value could be tripled by incorporating thin a sheet in the middle of the enclosed airspace. Finally, practical correlation were developed to determine the effective R-values of 45° sloped-enclosed airspaces with upward heat flow for wide ranges of aspect ratio, temperature difference across the airspace, mean temperature, and effective emittance. The results showed that the calculated R-values using this correlation were in good agreement with the predicted R-values.