| This paper reports on a transient model of coupled heat and moisture transfer through fibrous insulation, which for the first time takes into account of evaporation and mobile condensates. The model successfully explained the experimental observations of Farnworth [Tex. Res. J. 56 (1986) 653], and the numerical results of the model were found to be in good agreement with the experimental results of a drying test. Based on this model, numerical simulation was carried out to better understand the effect of various material and environmental parameters on the heat and moisture transfer. It was found that the initial water content and thickness of the fibrous insulation together with the environmental temperature are the three most important factors influencing the heat flux.
Author Keywords: Heat and moisture transfer; Water evaporation; Numerical simulation
Ca
water vapor concentration in the inter-fiber void space (kg m-3)
Ca*
saturated water vapor concentration in the inter-fiber void space (kg m-3)
Cf
water vapor concentration in a fiber over its radius at a position of the fibrous batting at a certain time (kg m-3)
Cv
effective volumetric heat capacity of the fibrous batting (kJ m-3 K-1)
Cv0
volumetric heat capacity of the dry fibrous batting (kJ m-3 K-1)
Cw
volumetric heat capacity of water (kJ m-3 K-1)
Da
diffusion coefficient of water vapor in the air (m2 s-1)
Df
disperse coefficient of moisture in the fiber (m2 s-1)
Dl
disperse coefficient of free water in the fibrous batting (m2 s-1)
E
the evaporation coefficient, dimensionless
Ei
surface emissivity of the lining fabrics (i=1: inner lining; i=2: outer lining)
F
total thermal radiation incident on a point (W) (i.e. R: travel to the right, L: travel to the left)
Hc
convective mass transfer coefficient (m s-1)
HT
convective thermal transfer coefficient (kJ m-2 K-1)
ke
effective thermal conductivity of the fibrous batting (kJ m-1 K-1)
kf
thermal conductivity of fiber (kJ m-1 K-1)
ka
thermal conductivity of air filling in the fabric batting (kJ m-1 K-1)
kw
thermal conductivity of water in the fabric batting (kJ m-1 K-1)
L
thickness of the fabric batting (m)
M
the molecular weight of the evaporating substance, 18.0152 (g/mol) for water
p
pressure of water vapor in the inter-fiber void (Pa)
psat
saturation vapor pressure of water at absolute temperature Ts (Pa)
p'sat
the saturated vapour pressure at the temperature Tv (Pa)
pv
vapor pressure in vapor region at Ts (Pa)
r
radius of fibers (m)
R
the universal gas constant, 8.314471กม107 (J K-1 mol-1)
Rti
resistance of direct heat transfer (s m-1) (i.e. i=0: inner fabric, i=1: outer fabric)
Rwi
resistance of water vapor transfer (s m-1) (i.e. i=0: inner fabric, i=1 outer fabric)
RHi
relative humidity (%) (i.e. i=0: surface next to human body, i=1: surrounding air)
Tbi
temperature of the boundaries (K) (i.e. i=0: surface next to human body, i=1: surrounding air)
Cai
moisture concentration at the boundaries (K) (i.e. i=0: surface next to human body, i=1: surrounding air)
Ts
temperature at the interface (K)
Tv
temperature in vapor region (K)
t
real time from change in conditions (s)
wi
resistance to water vapor (i.e. i=0: inner fabric, i=1: outer fabric)
Wf
water content of the fibers in the fabric, Wf=Cf/
W
water content of the fibrous batting
Wc
critical level of water content above which the liquid water becomes mobile
Wi
initial water content
x
distance (m)
porosity of the fabric (=cubic volume of inter-fiber space/total cubic volume of fabric space)
latent heat of (de)sorption or condensation of water vapor by the fibers (kJ kg-1)
density of the fibers (kg m-3)
effective tortuosity of the fabric. The degree of bending or twist of the passage of moisture diffussion due to the bending or twist of fibers in the fibrous insulation. It normally changes between 1.0 and 1.2, depending on the fiber arrangements
radiative sorption constant
Boltzmann constant
the rate of (de)sorption, condensation, freezing and/or evaporation (kg s-1 m-3) |