Coupled heat and mass transport material model - HeMoKunzel

The presented formulation is based on the work of Kuenzel [15]. The model is suitable for problems with dominating water diffusion and negligible water convection. The governing equations for temperature and humidity reads


$\displaystyle =$ (249)
$\displaystyle =$ (250)


Table 59: Parameters from Kunzel's model.
$ T$ (K) Temperature
$ H$ (-) Relative humidity 0-1
J/K/m$ ^3$ Heat storage capacity per volume
kg/m$ ^3$ Moisture storage capacity - sorption isotherm
J/m$ ^3$ Total amount of heat in unit volume
W/m$ ^2$ Heat flux
$ \lambda$ W/m/K Thermal conductivity
J/kg Evaporation enthalpy of water
kg/m/s/Pa Water vapour permeability
Pa Water vapour saturation pressure
$ w$ kg/m$ ^3$ Moisture content
kg/m/s Liquid conduction coefficient
m$ ^2$/s Water diffusivity


Numerical solution leads to the system of equations

    (251)

where
                    (252)


                    (253)


$\displaystyle \mbox{\boldmath$C$}$         $\displaystyle \mbox{\boldmath$C$}$           (254)


$\displaystyle \mbox{\boldmath$C$}$         $\displaystyle \mbox{\boldmath$C$}$           (255)


              (256)

where


$\displaystyle =$ (257)
$\displaystyle =$ (258)
$\displaystyle =$ (259)
$\displaystyle =$ (260)
$\displaystyle =$ (261)
$\displaystyle =$ (262)
$\displaystyle =$ (263)
$\displaystyle =$ (264)

Note, that conductivity matrix $ K$ is unsymmetric hence unsymmetric matrix storage needs to be used (smtype).

The model parameters are summarized in Tab. 60.

Table 60: Coupled heat and mass transfer material model Kunzel - summary.
Description Coupled heat and mass transfer material model
Record Format HeMoKunzel num(in) # d(rn) # iso_type(in) # iso_wh(rn) # mu(rn) # permeability_type(in) # A(rn) # lambda0(rn) # b(rn) # cs(rn) # [ pl(rn) #] [ rhoH2O(rn) #] [ cw(rn) #] [ hv(rn) #]
Parameters -num material model number
  -d bulk density of dry building material [kg/m$ ^3$]
  -iso_type=0 is isotherm from Hansen needing iso_n, iso_a, =1 is Kunzel which needs iso_b
  -iso_wh maximum adsorbed water content [kg/m$ ^3$]
  -mu water vapor diffusion resistance [-]
  -permeability_type =0 is Multilin_h needing perm_h, perm_Dw(h), =1 is Multilin_wV needs perm_wV, perm_DwwV, =2 is Kunzelperm needs A as water absorption coefficient [kg/m/s]
  -lambda0rn thermal conductivity [W/m/K]
  -b thermal conductivity supplement [-]
  -cs specific heat capacity of the building material [J/kg/K]
  -[pl] ambient air pressure [Pa], default = 101325
  -[rhoH2O] water density [kg/m3], default = 1000
  -[cw] specific heat capacity of liquid water, default = 4183
  -[hv] latent heat of water phase change [J/kg], default = 2.5e+6
Supported modes _2dHeMo, _3dHeMo


Borek Patzak
2018-01-02