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140 2 Mass transfer losses, equal to the driving force, allows calculation of the airflow then as a function of the pressure differential. 2.2.4 Airflow in open-porous materials 2.2.4.1 The conservation law adapted With neither a source nor a sink present, the equation for conservation of mass simplifies to: div ga ˆ @wa @t (2.20) The air content wa depends on the total open porosity Ψ0, the air saturation degree Sa, the air pressure Pa and temperature T, or: wa ˆ Ψ0Saρa ˆ Ψ0SaPa=…RaT† Whereas the gas constant Ra is more or less invariable and the open porosity Ψ0 remains constant at least as long as no liquid fills the pores, the variables are the air saturation degree, the air pressure and the temperature. The differential of air content to time can thus be expressed as: @wa @t ˆ Ψ0 RaT Sa @Pa @t ‡ Pa @Sa @t SaPa T @T @t With the saturation degree constant, this equation simplifies to: @wa @t ˆ Ψ0Sa RaT @Pa @t Pa T @T @t In isothermal conditions, which excludes thermal stack, the derivative of temperature versus time becomes zero, or: div ga ˆ Ψ0Sa RaT @Pa @t (2.21) The ratio Ψ0Sa=…RaT† is called the isothermal volumetric specific air content, symbol ca, units kg/(m3.Pa). As the open porosity and saturation degree for air can never pass 1, replacing Ra by its value 287 J/(kg.K) gives: ca ˆ Ψ0Sa=…RaT† < 0:00348=T meaning that the specific air content is a negligible quantity. Insertion of the air flux equation into the isothermal mass balance gives: div ka grad Pa … †ˆ ca @Pa @t


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