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Abstract
Combined heat, air, and moisture transport between building envelopes and indoor air has a significant effect on indoor thermal and humidity conditions, energy performance of buildings, indoor air quality, durability of constructions, etc. The article presents an analytical method to calculate combined hygrothermal transfer in porous building materials under different boundary conditions, which include the convection surface, adiabatic surface, constant heat and moisture potential surface, etc. An improved Luikov's equation was adopted to describe the heat and moisture transfer in porous media. The interactions between heat and moisture transport were modeled by introducing the temperature gradient coefficient. The governing equations were subjected to the Laplace transformation first, then solved by the transfer function method in the Laplace domain. The inversion theorems for the Laplace transformation were applied to all boundary conditions to get the final results in the time domain. The results were compared with the measured values and numerical solutions obtained from previous studies; good agreement was obtained. The analytical solutions can be used to develop a simpler algorithm for the quick evaluation of heat, air, and moisture transfer in building applications when the diurnal temperature variation is less than 10°C and the relative humidity variation is between 10% and 90%
Nomenclature
| A | = | area of the surface (m2) |
| Cm | = | specific moisture, dry material (m3 kg−1) |
| Cp | = | specific heat, dry material (J kg−1 K−1) |
| hlv | = | heat of phase change (J kg−1) |
| m | = | mass of moist sample (kg) |
| p | = | vapor pressure (Pa) |
| P | = | total pressure (Pa) |
| s | = | Laplace transformation parameter (—) |
| Snr | = | number of attached construction blocks (—) |
| t | = | time (s) |
| T | = | temperature (K) |
| Ta | = | ambient air temperature (K) |
| v | = | vapor content (kg m−3) |
| V | = | volume of the sample (m3) |
| vs | = | vapor content at saturation (kg m−3) |
| wm | = | adsorbed water content corresponding to the first layer (kg m−3) |
Greek letters
| α | = | coefficient of convective heat transfer (W m−2 K−1) |
| β | = | coefficient of convective moisture transfer (m s−1) |
| γ | = | heat of sorption or desorption (J kg−1) |
| δ | = | moisture diffusion coefficient (m2 s−1) |
| ϵ | = | Ttmperature gradient coefficient (kg m−3 K−1) |
| η | = | viscosity (kg m−1s−1) |
| λ | = | thermal conductivity (W m−1 K−1) |
| ρ | = | density of the materials, dry condition (kg m−3) |
| σ | = | phase change criterion (—) |
| φ | = | transformation function (—) |