Practical correlation for thermal resistance of horizontal enclosed airspaces with downward heat flow for building applications

Abstract

The 2009 ASHRAE Handbook of Fundamentals (Chapter 26) provides a table that contains the thermal resistances (R-values) of enclosed airspaces for different values of airspace thickness, effective emittance, mean airspace temperature, and temperature differences across the airspace. This table is extensively used by modellers, architects and building designers in the design for thermal resistance of building enclosures. 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, the previous studies by the author that focused on determining the R-value for vertical enclosed airspaces and horizontal enclosed airspace under upward heat flow condition are extended to investigate the effect of the aspect ratio on the R-value of horizontal enclosed airspaces under a downward heat flow condition for different airspace thicknesses and having a wide range of values for effective emittance, mean temperature, and temperature differences across the 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 correlation was developed for determining the R-values of horizontal enclosed airspaces for future use by modellers, architects and building designers. T he simplicity of this correlation derived for horizontal airspaces under downward heat flow condition together with those that were previously developed for vertical airspaces and horizontal airspaces under upward heat flow condition suggests that these correlations could be included in the ASHRAE Handbook of Fundamentals.

Effective R-value of enclosed reflective space for different building applications

“…Unlike the R-values provided in ASHRAE table (2017), the results of those studies showed that the aspect ratios of the enclosed airspaces can have significant effects on their R-values (Saber, 2013a(Saber, , 2013b(Saber, , 2013c(Saber, , 2014a(Saber, , 2014b. In some of the studies (Saber, 2013a(Saber, , 2013b(Saber, , 2013c(Saber, , 2014a(Saber, , 2014b, considerations were given to investigate the potential increase in the R-value of the enclosed airspace when a thin sheet having different values of emissivity on both sides was placed in the middle of the airspace as shown in Figure 4(b). As will be shown later, the results showed that, depending on the value of the effective emittance, thickness of the airspace, orientation of the airspace, and direction of heat flow, the R-value could be easily doubled and in some cases could be tripled by incorporating this thin sheet along the middle of the enclosed airspace.…”

“…In previous studies (Saber, 2013a(Saber, , 2013b(Saber, , 2013c(Saber, , 2014a(Saber, , 2014b, the results showed that the R-value could be doubled due to installing a thin sheet in the middle of (a) low-sloped enclosed airspaces (u = 30°) with downward heat flow (Saber, 2014b), (b) high-sloped enclosed airspaces (u = 45°) with downward heat flow (Saber, 2013b), (c) vertical enclosed airspace (u = 90°; Saber, 2013a), and (d) horizontal enclosed airspace (u = 0°) with downward heat flow (Saber, 2014a). However, the R-value could be tripled if a thin sheet is installed horizontally in the middle of the horizontal enclosed airspace (u = 0°) with upward heat flow condition (Saber, 2013c).…”

“…It is important to accurately determine the effective R-values of the enclosed spaces of different dimensions, effective emittances, inclination angles, directions of heat flow, mean airspace temperatures, and temperature differences across the airspaces (Tariku and Iffa, 2017). Many studies were conducted to determine the R-values of RI products and low-e coatings in IGUs, and wall and roofing systems incorporating RI products (Craven and Garber-Slaght, 2011;Desjarlais and Tye, 1990;Desjarlais and Yarbrough, 1991;D'Orazio et al, 2012;Escudero et al, 2013;European Commission, 2010;Fairey, 1985;Fricker and Yarbrough, 2011;Glicksman, 1991;Gross and Miller, 1989;Han et al, 1986;IEA, 1987;Kahsay et al, 2019;Laouadi et al, 2013;Medina, 2000;Saber, 2012Saber, , 2013aSaber, , 2013bSaber, , 2013cSaber, , 2013dSaber, , 2014aSaber, , 2014bSaber et al, 2011aSaber et al, , 2011bSaber et al, , 2012aSaber et al, , 2012bSaber et al, , 2013Saber and Laouadi, 2011;Saber and Maref, 2012;Saber and Swinton, 2010;Tariku and Iffa, 2017;Tenpierik and Hasselaar, 2013;Vrachopoulos et al, 2012;Yarbrough, 1983). Also, there are many claims indicating that RI products can have high thermal resistance.…”

“…A number of previous studies (Saber, 2013a(Saber, , 2013b(Saber, , 2013c(Saber, , 2014a(Saber, , 2014b were focused on predicting the thermal performance and the effective R-values of vertical enclosed airspaces (Tenpierik and Hasselaar, 2013), horizontal enclosed airspaces with upward heat flow (Saber, 2013c), horizontal enclosed airspaces with downward heat flow (Saber, 2014a), high-sloped (45°) enclosed airspaces with downward heat flow (Saber, 2013b), and low-sloped (30°) enclosed airspaces with downward heat flow (Saber, 2014b), for a wide range of thickness, aspect ratio, mean temperature, temperature differential, effective emittance, and direction of heat flow. Unlike the R-values provided in ASHRAE table (2017), the results of those studies showed that the aspect ratios of the enclosed airspaces can have significant effects on their R-values (Saber, 2013a(Saber, , 2013b(Saber, , 2013c(Saber, , 2014a(Saber, , 2014b. In some of the studies (Saber, 2013a(Saber, , 2013b(Saber, , 2013c(Saber, , 2014a(Saber, , 2014b, considerations were given to investigate the potential increase in the R-value of the enclosed airspace when a thin sheet having different values of emissivity on both sides was placed in the middle of the airspace as shown in Figure 4(b).…”

“…Effect of the type of filling gas in sample stack heated from top (shown in Figure 5) and the foil/coating emissivity on the effective R-value for the case of u = 0°(horizontal): (a) total R-value, and (b) contribution of the enclosed space to the R-value. (Saber, 2013c) and downward heat flow (Saber, 2014a); high-sloped airspaces (u = 45°) with downward heat flow (Saber, 2013b); and low-sloped airspaces (u = 30°) with downward heat flow (Saber, 2014b). These studies covered a wide range of enclosed space: (a) thickness (d = 13 mm (0.5 in.…”