Transient conductive, radiative heat transfer coupled with moisture transport in attic insulations

Abstract

A transient, one-dimensional thermal model that incorporates combined conduction, radiation heat transfer, and moisture transport for residential attic insulations has been developed. The governing equations are the energy equation, the radiative transport equation for volumetric radiation within the insulation batt, and the species equations for bound H 2 O and vapor H 2 O. A simultaneous solution procedure with a Eulerian control volume-based finite difference method was used to solve the energy equation and the species equations. The method of discrete ordinates was used in solving the radiative transport equation. For H 2 O transport, both diffusion of vapor H 2 O and bound H 2 O, and moisture adsorption/desorption within the insulation binder are included in the model. The experimental data measured at an occupied North Mississippi residence for R19STD (standard R19 fiberglass insulation batt without a foil radiant barrier) were used to validate the model which predicted heat fluxes for summer, spring, winter, and fall seasonal conditions. These predictions were compared with the measured heat flux data and the predictions from the dry model (without the moisture transport). Various profiles such as temperature-time histories, relative humidity time histories, spatial H 2 O concentrations, spatial temperatures, and spatial heat fluxes are presented to explain the overall heat transfer behavior. Nomenclature c f = specific heat, J/kg-K e b = blackbody flux, W/m 2 h ad = heat of adsorption/desorption, J/kg / = radiative intensity, W/m 2 -sr i b = specific enthalpy of bound H 2 O, J/kg i v = specific enthalpy of vapor H 2 O, J/kg k = thermal conductivity, W/m-K m b = bound mass concentration, kg bound H 2 O/m 3 m b = rate of absorption of H 2 O, Eq. (6), kg bound H 2 O/m 3 -s m v = vapor mass concentration, kg vapor H 2 O/m 3 m^ = constant in Eq. (6b), Table 1 n = refractive index of medium q = source/sink term, W/m 3 q r -radiative component of total heat flux, W/m 2 q T = total heat flux, W/m 2 RH = relative humidity T = temperature, K T A = attic temperature, K T c = ceiling temperature, K Tj = inside room temperature, K T R = roof temperature, K T r = reference temperature, 300 K T s = bottom of the batt temperature, TO -top of the batt temperature, K t = time, s X = mass of absorbed moisture/mass of dry fiberglass, kg H 2 O/kg fiberglass y = physical thickness, m y 0 = thickness of insulation batt, m ft -extinction coefficient, r = /3y, cm" 1 K y b = diffusion coefficient of bound H 2 O, m 2 /s y v = diffusion coefficient of vapor H 2 O, m 2 /s e w = emissivity of the roof s s = emissivity of the substrate 0 = polar angle, deg /z, = cosine of polar angle p f = density of fiberglass, kg/m 3 p n = reflectivity of the roof p s = reflectivity of the substrate T = optical thickness T O = optical thickness, /3y 0 O = scattering phase function 4> = relative humidity i/r = azimuthal angle 0} = single scatter albedo Subscripts b = bound / = fiberglass v = vapor 0 = top surface

Substrate Barrier Effects on Total Heat Transfer for a R-30 Fibrous Insulation Batt

“…The numerical/analytical model described in this section has been utilized as an analysis tool in previous studies by the authors including References [4,5]. It is outlined again m this paper for the purpose of clarity and continuity.…”

“…It should be noted that n = 1 for this problem. A quasi-analytical technique with the method of discrete ordinates, employing a sixteen point Gaussian quadrature, was used in solving the radiative transport equation [Equation (5)] and the details are documented in References [16,17]. The radiative heat flux needed in Equation (4) is given by definition as…”

“…fer at the substrate was reduced by 13 % when a plastic nonperforated vapor barrier was added to the substrate (bottom of batt) when compared to a no vapor barrier case. This work will focus on similar issues (moisture has been found, in previous work [2][3][4][5], to increase the heat transfer through fiberglass attic insulation and into the living spaces of a home under humid summer conditions) for R-30 insulation. Once again through a thorough literature survey and several personal contacts [6][7][8], it has been deternuned that there is knowledge of the fact that moisture is instrumental in increasing the substrate heat transfer, but there has been no work found to determine (quantify) the impact on heat transfer of adding a plastic vapor barrier to the substrate as compared to a no vapor barrier situation other than the above mentioned R-19 investigation [1].…”

“…The implementation of a foil radiant barrier at the top of the insulation batt has been studied in previous works [4][5]. In this study, as in its companion work [1], a theoretical investigation of adding a nonperforated foil radiant barrier and a perforated foil radiant barrier at the substrate of the insulation batt was performed.…”

Phenolic Binder Content Impact on Total Heat Transfer for Fibrous Insulation Batts

“…The approach taken here has been to use the computational tool developed in [1][2][3]5,6]. However, a different thermal boundary condition is employed at the top of the batt to allow the top temperature of the batt to be calculated as a function of the binder adsorption/desorption.…”