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2.2 Air 141 If the air permeance (ka) is constant, then: ∇2Pa ˆ ca ka @Pa @t (2.22) The inverse of the ratio ca/ka in Eq. (2.22), ka/ca, stands for the isothermal air diffusivity of an open-porous material, symbol Da (units m2/s). Its value is generally so large that each adjustment to air pressure happens within a few seconds. For pressures that fluctuate over extremely short time spans, such as wind gusts, the pressure response will show some damping and time shift, but usually both are absent. Consider, for example, mineral wool with density 40 kg/m3. The properties are: Thermal Air λ= 0.036 W/(m.K) ka= 8 × 105 s ρc= 33 600 J/(m3.K) ca= 1.17 × 105 kg/(m3.Pa) The thermal diffusivity thus equals 1.1 × 106m2/s and the isothermal air diffusivity 6.8m2/s, 6 355 000 times larger than the thermal diffusivity. Or, when combining air with heat and moisture transfer, the isothermal air balance can remain steady state as ∇2Pa ˆ 0. The combination with the flux equation thus resembles steady-state heat conduction. Although in non-isothermal conditions (i.e. including stack) the isobaric volumetric specific air capacity increases (3525/T2), steady state remains. The equations anyhow become: ∇2 … Pao ρa g z† ˆ 0 ga ˆ ka grad … Pao ρa g z† showing that a solution requires the heat balance. The same holds for nonisothermal flow through air permeable layers, joints, cavities, openings, and so on. 2.2.4.2 One dimension: flat assemblies Assume a flat assembly made of air permeable materials. As the air flux and pressures then resemble steady-state heat conduction, the pressures form a straight line in a single-layer assembly (Figure 2.6), while the flux is: ga ˆ ka ΔPa d ˆ ΔPa d=ka (2.23) The ratio d/ka is called the (specific) air resistance of the assembly: symbol W, units m/s. The inverse gives the air conductance, symbol Ka, units s/m. For a composite assembly, the result is: ga ˆ ΔPa Xn iˆ1 di kai , (2.24) with P di=kai the total air resistance, symbolWT, units m/s. The inverse 1/WT is the total air conductance KaT. The term di/kai, symbol Wi, represents the air resistance,


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