## 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

 (249) (250)

Table 59: Parameters from Kunzel's model.
 (K) Temperature (-) Relative humidity 0-1 J/K/m Heat storage capacity per volume kg/m Moisture storage capacity - sorption isotherm J/m Total amount of heat in unit volume W/m Heat flux W/m/K Thermal conductivity J/kg Evaporation enthalpy of water kg/m/s/Pa Water vapour permeability Pa Water vapour saturation pressure kg/m Moisture content kg/m/s Liquid conduction coefficient m/s Water diffusivity

Numerical solution leads to the system of equations

 (251)

where
 (252)

 (253)

 (254)

 (255)

 (256)

where

 (257) (258) (259) (260) (261) (262) (263) (264)

Note, that conductivity matrix 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] -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] -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