Theory for Heat Transfer in Building Materials
The Heat Transfer in Building Materials Interface solves for the following equations derived from Ref. 16:
(4-50)
(4-51)
which is derived from Equation 4-15, considering the building material as a porous medium in local thermal equilibrium in which the following mixing rules apply:
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(ρCp)eff (SI unit: J/(m3·K)) is the effective volumetric heat capacity at constant pressure, defined to account for both solid matrix and moisture properties:
where ρs (SI unit: kg/m3) is the dry solid density, Cp,s (SI unit: J/(kg·K)) is the dry solid specific heat capacity, w(ϕw) (SI unit: kg/m3) is the water content given by a moisture storage function, and Cp,w (SI unit: J/(kg·K)) is the water heat capacity at constant pressure.
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keff (SI unit: W/(m·K)) is the effective thermal conductivity, defined as a function of the solid matrix and moisture properties:
where ks (SI unit: W/(m·K)) is the dry solid thermal conductivity and b (dimensionless) is the thermal conductivity supplement.
This definition neglects the contribution due to the volume fraction change of the moist air.
The heat source due to moisture content variation is expressed as the vapor diffusion flow multiplied by latent heat of evaporation:
where Lv (SI unit: J/kg) is the latent heat of evaporation, δp (SI unit: s) is the vapor permeability, ϕw (dimensionless) is the relative humidity, and psat (SI unit: Pa) is the vapor saturation pressure. See Saturation State for the definition of saturation pressure psat as a function of temperature.