HEAT, AIR, AND MOISTURE CONTROL IN BUILDING ASSEMBLIES FUNDAMENTALS

CHAPTER 25 HEAT, AIR, AND MOISTURE CONTROL IN BUILDING ASSEMBLIES FUNDAMENTALS Terminology and Symbols 25.1 Environmental Hygrothermal Loads and Driving Forces 25.2 HEAT TRANSFER 25.5 Steady-State Thermal Response 25.5 Transient Thermal Response 25.8 AIRFLOW 25.9 MOISTURE TRANSFER 25.10 Moisture Storage in Building Materials 25.10 Moisture Flow Mechanisms 25.12 COMBINED HE A T, AIR, AND MOISTURE TRANSFER...25.14 SIMPLIFIED HYGROTHERMAL DESIGN CALCULATIONS AND ANALYSES 25.15 Surface Humidity and Condensation 25.15 Interstitial Condensation and Drying 25.15 TRANSIENT COMPUTATIONAL ANALYSIS 25.16 Criteria to Evaluate Hygrothermal Simulation Results 25.16 PROPER design of space heating, cooling, and air-conditioning I mean temperature, thickness, age, and moisture content. Thermal systems requires detailed knowledge of the building envelope's s conductivity is normally considered an intrinsic property of a overall heat, air, and moisture performance. This chapter discusses s the fundamentals of combined heat, air, and moisture movement as s it relates to the analysis and design of envelope assemblies. Guidance for designing mechanical systems is found in other chapters of f the ASHRAE Handbook. Because heat, air, and moisture transfer are coupled and closely i interact with each other, they should not be treated separately. In l fact, improving a building envelope's energy performance may f cause moisture-related problems. Evaporation of water and removal 1 of moisture by other means are processes that may require energy. homogenous material. In porous materials, heat flow occurs by a combination of conduction, convection, radiation, and latent heat exchange processes and may depend on orientation, direction, or both. When nonconductive modes of heat transfer occur within the specimen or the test specimen is nonhomogeneous, the measured property of such materials is called apparent thermal conductiv- ity. The specific test conditions (i.e., sample thickness, orientation, environment, environmental pressure, surface temperature, mean temperature, temperature difference, moisture distribution) should be reported with the values of apparent thermal conductivity. The Only a sophisticated moisture control strategy can ensure hygienic : symbol k (or ë á ) is used to denote the lack of pure conduction conditions and adequate durability for modern, energy-efficient t building assemblies. Effective moisture control design must deal 1 with all hygrothermal loads (heat and humidity) acting on the 3 building envelope. or to indicate that all values reported are apparent. Materials with a low apparent thermal conductivity are called insulation materials (see Chapter 26 for more detail). Thermal resistivity r u is the reciprocal of thermal conductivity. Units are (m-k)/w. TERMINOLOGY AND SYMBOLS Thermal resistance R is an extrinsic property of a material or building component determined by the steady-state or time-averaged The following heat, air, and moisture definitions and symbols are temperature difference between two defined surfaces of the material commonly used.. or component that induces a unit heat flux, in (m 2 K)/W. When the A building envelope or building enclosure provides physical two defined surfaces have unequal areas, as with heat flux through separation between the indoor and outdoor environments. A building assembly is any part of the building envelope, such as wall. materials of nonuniform thickness, an appropriate mean area and mean thickness must be given. Thermal resistance formulas involving materials that are not uniform slabs must contain shape factors to assembly, window assembly, or roof assembly, that has boundary conditions at the interior and the exterior of the building. A building ' account for the area variation involved. When heat flux occurs by component is any element or material within a building assembly. conduction alone, the thermal resistance of a layer of constant thickness may be obtained by dividing the material's thickness by its ther Heat mal conductivity. When several modes of heat transfer are involved, Specific heat capacity c is the change in heat (energy) of unit the apparent thermal resistance may be obtained by dividing the mass of material for unit change of temperature in J/(kg-K). material's thickness by its apparent thermal conductivity. When air Volumetric heat capacity pc is the change in heat stored in unit circulates within or passes through insulation, as may happen in lowdensity fibrous materials, the apparent thermal resistance is affected. volume of material for unit change of temperature, in J/(m 3 -K). Heat flux q, a vector, is the time rate of heat transfer through a unit Thermal resistances of common building and insulation materials area, in W/m 2. are listed in Chapter 26. Thermal conductivity k [in Europe, the Greek letter ë (lambda) Thermal conductance C is the reciprocal of thermal resistance. is used] is a material property defined by Fourier's law of heat conduction. Thermal conductivity is the parameter that describes heat Units are W/(m 2 -K). Heat transfer or surface film coefficient h is the proportionality flux through a unit thickness of a material in a direction perpendicular to the isothermal planes, induced by a unit temperature dif factor that describes the total heat flux by both convection and radiation between a surface and the surrounding environment. It is the ference. (ASTM Standard C168 defines homogeneity.) Units are heat transfer per unit time and unit area induced by a unit temperature difference between the surface and reference temperature in the W/(m-K). Materials can be isotropic or anisotropic. For anisotropic materials, the direction of heat flow through the material must surrounding environment. Units are W/(m be noted. Thermal conductivity must be evaluated for a specific -K). For convection to occur, the surrounding space must be filled with air or another fluid. If the space is evacuated, heat flow occurs by radiation only. In the The preparation of this chapter is assigned to TC 4.4, Building Materials s and Building Envelope Performance. 25.1 context of this discussion, indoor or outdoor heat transfer or surface film coefficient A ; or h B denotes an interior or exterior surface

25.2 2013 ASHRAE Handbook Fundamentals (SI) of a building envelope assembly. The heat transfer film coefficient is also commonly known as the surface film conductance. Thermal transmittance U is the quantity equal to the steadystate or time-averaged heat flux from the environment on the one side of a body to the environment on the other side, per unit temperature difference between the two environments, in W/(m 2 K). Thermal transmittance is sometimes called the overall coefficient of heat transfer or U-factor. Thermal transmittance includes thermal bridge effects and the surface heat transfer at both sides of the assembly. Thermal emissivity å is the ratio of radiant flux emitted by a surface to that emitted by a black surface at the same temperature. Emissivity refers to intrinsic properties of a material. Emissivity is defined only for a specimen of the material that is thick enough to be completely opaque and has an optically smooth surface. Effective emittance E refers to the properties of a particular object. It depends on surface layer thickness, oxidation, roughness, etc. Air Air transfer M a is the time rate of mass transfer by airflow induced by an air pressure difference, caused by wind, stack effect, or mechanical systems, in kg/s. Air flux m a, a vector, is the air transfer through a unit area in the direction perpendicular to that unit area, in kg/(s -m 2 ). Air permeability k a is an intrinsic property of porous materials defined by Darcy's Law (the equation for laminar flow through porous materials). Air permeability is the quantity of air flux induced by a unit air pressure difference through a unit thickness of homogeneous porous material in the direction perpendicular to the isobaric planes. Units are in kg/(pa-s-m) or s. Air permeance K a is the extrinsic quantity equivalent to the time rate of steady-state air transfer through a unit surface of a porous membrane or layer, a unit length of joint or crack, or a local leak induced by a unit air pressure difference over that layer, joint and crack, or local leak. Units are kg/(pa s m 2 ) for a layer, kg/(pa s m) for a joint or crack, or kg/(pa-s) for a local leak. Moisture Moisture content w is the amount of moisture per unit volume of porous material, inkg/m 3. Moisture ratio X (in mass) or Ø (in volume) is the amount of moisture per unit mass of dry porous material or the volume of moisture per unit volume of dry material, in percent. Specific moisture content is the ratio between a change in moisture content and the corresponding change in driving potential (i.e., relative humidity or suction). Specific moisture ratio is the ratio between a change in moisture ratio and the corresponding change in driving potential (i.e., relative humidity or suction). Water vapor flux m v, a vector, is the time rate of water vapor transfer through a unit area, in kg/(s-m 2 ). Moisture transfer M m is the moisture flow induced by a difference in suction or in relative humidity, in kg/s. Moisture flux m m, a vector, is the time rate of moisture transfer through a unit area, in kg/(s -m 2 ). Water vapor permeability ì^ is the steady-state water vapor flux through a unit thickness of homogeneous material in a direction perpendicular to the isobaric planes, induced by a unit partial water vapor pressure difference, under specified conditions of temperature and relative humidity. Units are kg/(pa-s-m). When permeability varies with psychrometric conditions, the specific permeability defines the property at a specific condition. Water vapor permeance M is the steady-state water vapor flux by diffusion through a unit area of a flat layer, induced by a unit partial water vapor pressure difference across that layer, inkg/(pa-s-m 2 ). Water vapor resistance Z is the reciprocal of water vapor permeance, in ( m 2 s Pa)/kg. Moisture permeability k m is the steady-state moisture flux through a unit thickness of a homogeneous material in a direction perpendicular to the isosuction planes, induced by a unit difference in suction. Units are kg/(pa-s-m) (suction). Moisture diffusivity D m is the ratio between the moisture permeability and the specific moisture content, in m 2 /s. ENVIRONMENTAL HYGROTHERMAL LOADS AND DRIVING FORCES The main function of abuilding enclosure is separation of indoor spaces from the outdoor climate. This section describes the hygrothermal loads acting on the building envelope. These descriptions are used to predict their influence on the hygrothermal behavior of building assemblies, as a basis for design recommendations and moisture control measures (Künzel and Karagiozis 2004). Cooling and heating load estimations for sizing mechanical systems can be found in Chapters 17 and 18. In Figure 1, the hygrothermal loads relevant for building envelope design are represented schematically for an external wall. Generally, they show diurnal and seasonal variations at the exterior surface and mainly seasonal variations at the interior surface. During daytime, the exterior wall surface heats by solar radiation, leading to evaporation of moisture from the surface layer. Around sunset, when solar radiation decreases, long-wave (infrared) emission may lead to cooling below ambient air temperature (undercooling) of the exterior surface, and surface condensation may occur. The exterior surfaces are also exposed to moisture from precipitation and wind-driven rain. Usually, several load cycles overlap (e.g., summer/winter, day/ night, rain/sun). Therefore, aprecise analysis of the expected hygrothermal loads should be done before starting to design any building envelope component. However, the magnitude of loads is not independent of building geometry and the component's properties. Analysis of the transient hygrothermal loads is generally based on hourly meteorological data. However, determination of local conditions at the envelope's surface is rather complicated and requires specific experience. In some cases, computer simulations are necessary to assess the microclimate acting on differently oriented or inclined building assemblies. Fig. 1 Hygrothermal Loads and Alternating Diurnal or Seasonal Directions Acting on Building Envelope

Heat, Air, and Moisture Control in Building Assemblies Fundamentals 25.3 Ambient Temperature and Humidity Ambient temperature and humidity with respect to partial water vapor pressure are the boundary conditions always affecting both sides of the building envelope. The climate-dependent exterior conditions may show large diurnal and seasonal variations. Therefore, at least hourly data are required for detailed building simulations, though monthly data may suffice in case simple calculation methods are applicable. ASHRAE provides such meteorological data sets, including temperature and relative humidity, for many locations worldwide (see Chapter 14). These data sets usually represent average meteorological years based on long-term observations at specific locations. However, data of more extreme climate conditions may be important to assess the risks of moisture damage. Therefore, Sanders (1996) proposed using data of the coldest or warmest year in 10 years for hygrothermal analysis instead of data from an average year. Another method to obtain a severe annual dataset concerning the moisture-related damage risk from several decades of hourly data has been developed by Salonvaara (2011). This method analyzes the data with respect to their effect on moisture behavior of typical building assemblies. The more severe datasets increase the safety of risk prediction for the service life of building envelope components, but they are less suitable for analyzing the long-term behavior (performance over several years) of constructions because the probability of a sequence of severe years is very low. Also, note that the temperature at the building site may differ from the meteorological reference data when the site's altitude differs from that of the station recording the data. On average, there is a temperature shift of 0.65 K for every ±100 m. The microclimate around the building may result in an additional temperature shift that depends on the season. For example, the proximity of a lake can moderate seasonal temperature variations, with higher temperatures in winter and lower temperatures in summer compared to sites without water nearby. A low-lying site experiences lower temperatures in winter, as city temperatures are higher year round (METEOTEST 2007). Indoor Temperature and Humidity Indoor climate conditions depend on the purpose and occupation of the building. For most commercial constructions, temperature and humidity are controlled by HVAC systems with usually well-defined set points. Indoor humidity conditions in residential buildings, however, are influenced by the outdoor climate and by occupant behavior. Moisture release in an average household is highly variable. According to Sanders (1996), it may range from 3 to 20 kg/day, with an average of approximately 8 kg/day. This moisture must be removed by ventilation or air conditioning. The resulting relative humidity may be determined by hygrothermal whole-building simulation or by simple estimation methods using information on moisture production, air change rates, and climate-dependent HVAC operation (TenWolde and Walker 2001). The presence of spas or swimming pools increases the load substantially. Less obvious but sometimes of equal importance are loads from the ground, from penetrating precipitation, or from construction moisture in the building materials. Moisture loads from occupant behavior show an especially transient pattern: they are characterized by peaks (e.g., cooking, showering). Humidity-buffering envelope materials and furniture (e.g., carpets, curtains, paper) help to dampen indoor humidity peaks, but they also reduce the moisture removal efficiency of intermittent ventilation (e.g., periodically opening windows, operating ventilation fans), which may increase the average humidity level in a room. Information on typical indoor climate conditions of special-purpose constructions such as swimming pools, spas, ice rinks, or agricultural buildings and production plants may be found in the 2011 ASHRAE Handbook HVAC Applications. Fig. 2 Solar Vapor Drive and Interstitial Condensation Solar Radiation Incident solar radiation is the major thermal load at the building envelope's exterior. For direct solar radiation, also called beam solar radiation, the resultant heat source depends on the angle between the sun and the normal on the exposed surface and on its color (short-wave absorptivity). For calculation of incident solar heat flux and spectra, see Chapter 15. Regarding moisture control, solar radiation is usually considered beneficial unless an envelope component is completely shaded. However, in some cases solar radiation combined with water from precipitation or other sources (e.g., construction moisture) can lead to severe moisture problems by solar-driven vapor flow. For example, as shown in Figure 2, if the water-absorbing exterior layer of an assembly (e.g., brick veneer, a typical example of "reservoir" cladding) has been wetted by wind-driven rain, heat from solar radiation drives some of the evaporating water inwards. The resulting high vapor pressure in the cladding causes vapor diffusion toward the outdoor ambient air as well as toward the interior of the building assembly, leading to condensation on and in material layers within the assembly such as sheathing boards, insulation layers, or vapor retarders. Adapting the permeance of vapor retarders and weatherresistive barriers (WRB) to the potential loads may improve the situation. ASHRAE research project RP-1091 (Burnett et al. 2004) showed that cladding ventilation is also an effective remedy within specified exterior air humidity limits. Exterior Condensation Long-Wave Radiant Effects. Long-wave radiation exchange of the envelope surface with the cold layers of the lower atmosphere is a major heat transfer process. At night or with the sun at a low angle, it results in a net heat flux to the sky (i.e., heat energy sink) (see Chapter 15). Depending on the building assembly's thermal properties, this may lead to a drop in the envelope's surface temperature below the ambient air temperature (undercooling). If the surface temperature reaches the air's dew point, condensation occurs on the exterior surface of the building assembly. Massive structures with a high thermal inertia do not usually lose enough heat to the nighttime radiation sink to bring the surface temperature below the dew point for a significant period of time. However, many modern building assemblies, such as lightweight roofs or exterior insulation finish systems (EIFS), have little thermal inertia in their exterior surface layers and are therefore subject to considerable amounts of exterior condensation (Künzel 2007). Interior Temperature Differential. Exterior condensation can also occur on poorly insulated assemblies in cooling climates because of the operation of air-conditioning systems. Repeated

25.4 exterior condensation or long-lasting, high relative humidity often provides the basis for soiling or microbial growth (fungi or algae), which may not be acceptable even though the durability of the assembly is unlikely to be affected. Effect on Other Layers. Under exterior condensation conditions, ventilated assemblies may also experience condensation within the ventilated air layer. This phenomenon was discovered by investigating pitched roofs with cathedral ceiling insulation (Hens 1992; Janssens 1998; Kiinzel and Grosskinski 1989). However, damage because of condensation in the ventilation plane is rare, except in metal roofs and ventilated low-mass, low-sloped roofs with moisture-sensitive underroofs (Hens et al. 2007; Zheng et al. 2004). Occasionally, soiling because of condensate runoff has been reported. Wind-Driven Rain The load from rain, especially wind-driven rain, is the main reason for moisture-related building failure. Because the requirements of sometimes costly rain-protection measures depend on the local climate, some countries have introduced regional drivingrain classifications. Generally, coastal regions and those on the windward side of mountains receive the highest precipitation load. Areas of low rainfall do not have the potential for severe winddriven rain. Regional precipitation and wind loads are significant factors in determining local wind-driven rain load, but local exposure conditions are of equal importance. A building in an open field receives a higher load than one sheltered by a forest or other buildings. A quantification of exposure conditions for walls depending on landscape, neighborhood, and building size and geometry can be found in the British Standard BS 8104 and in the European ISO/DIN Standard 15927-3:2006. The average wind-driven rain \o&àr D in open ground was investigated by Lacy (1965). It may be estimated from normal rain R N and the wind velocity component v parallel to the considered orientation, as shown in the following equation: R D =Ì Í R D = wind-driven rain intensity, kg/(s m 2 ) /= empirical factor = approximately 0.2 s/m v = mean wind velocity, m/s R N = rain intensity on a horizontal surface in openfield,kg/(s-m 2 ) Figure 3 shows a typical plot (a "rain rose") of results from Equation (1) plotted in polar coordinates indicating the amount of wind-driven rain in mass per unit area hitting an unobstructed and isolated vertical surface in the open field. The driving rain load close to a façade is considerably less than in the open field (as shown in Figure 4), and it becomes irregular. (l) 2013 ASHRAE Handbook Fundamentals (SI) Tops and edges of walls generally receive the highest amount. This is caused by the airflow pattern around a building (see Chapter 24 for more information). At the windward side, high pressure gradients coincide with large changes in air velocity. The building acts as an obstacle for the wind, slowing down airflow and subsequently reducing the wind-driven rain load near the façade. Gravity and the rain droplets' momentum prevent them from following the airflow around the building, causing them to strike the façade mainly at the edges of the flow obstacle (Straube and Burnett 2000). However, the irregular driving rain deposition is often evened out by water running off the hard-hit areas, especially when the façade surface has low water absorptivity or the wind-driven rain load is high enough to capillary-saturate the most exposed surface layers. Roof overhangs can reduce the driving rain load on low-rise buildings. Slightly inclined wall sections or protruding façade elements may receive a considerable amount of splash water from façade areas above them, in addition to the direct driving rain deposition. This is often a problem for buildings with walls slightly out of vertical (Kiinzel 2007). Rain penetrating the exterior cladding of exposed walls may cause severe damage if it cannot be drained and dried out fast enough. Experience shows that it is almost impossible to seal joints and connections hermetically against wind-driven rain. Therefore, building envelope assemblies should be designed to tolerate a limited amount of water entry (see ASHRAE Standard 160-2009). Construction Moisture Building damage as a result of migrating construction moisture has become more frequent because tight construction schedules leave little time for building materials to dry. Although often disregarded, construction moisture is either delivered with the building products or absorbed by the materials during storage or construction. Cast-in-place concrete, autoclaved aerated concrete (AAC), calcium silicate brick (CSB), and "green" wood are examples of materials that contain significant moisture when delivered. Stucco, mortar, clay brick, and concrete blocks are examples of materials that are either mixed or brought into contact with water at the construction site. All other porous building materials may take up considerable amounts of precipitation or groundwater when left unprotected during storage or construction before the enclosure of the building. A single-family house made of AAC may initially contain more than 13 Mg of water in its walls. Care must be taken to safely remove that water, either by additional ventilation during the first years of operation or by using construction dryers while heating the building before putting it into service. Even "dry" materials have an initial water content of approximately the equilibrium moisture content at 80% rh (EMC g0 ).When significant construction moisture is encountered, EMC 80 can be exceeded by a factor of two or more. Ground- and Surface Water A high groundwater table or surface water running toward the building and filling the loosefill triangle around the basement represents an important moisture load to the lower parts of the Fig. 3 Typical Wind-Driven Rain Rose for Open Ground Fig. 4 Measured Reduction in Catch Ratio Close to Façade of One-Story Building at Height of 2 m

Heat, Air, and Moisture Control in Building Assemblies Fundamentals 25.5 building envelope. These loads should be met by grading the ground away from the building, perimeter drainage, and waterproofing the basement and foundation. Instead of waterproofing by bituminous membranes or coatings, water-impermeable structural elements may be used (e.g., reinforced concrete, which may, however, be vapor permeable). The resulting vapor flux also presents a load that must be addressed (e.g., by basement ventilation). Moisture loads in the ground may impair performance of exterior basement insulation applied on the outside of the waterproofing layer. Therefore, special care must be taken to protect insulation from moisture accumulation unless the insulation material is itself impermeable to water and vapor [e.g., extruded polystyrene (XPS), foam glass]. Wicking of ground- or surface water into porous walls by capillary action is called rising damp. This phenomenon may be a sign of poor drainage or waterproofing of the building's basement or foundation. However, other phenomena show moisture patterns similar to rising damp. If the wall is contaminated with salts, which may be the case in historic buildings, the wall's moisture content might be elevated because of a hygroscopicity increase caused by water uptake by the salt crystals. Another reason for the appearance of rising damp may actually be surface condensation in unheated buildings during summer. Air Pressure Differentials Wind and stack effects caused by differences between indoor and outdoor temperature result in air pressure differentials over the building envelope. In contrast to wind, stack effect is a permanent load that may not be neglected. Worse, stack pressure may act in the same direction as vapor pressure: from indoors to outdoors during the heating season, and in the opposite direction during the cooling season. Therefore, airflow through cracks, imperfect joints, or airpermeable assembly layers may cause interstitial condensation in a manner similar to vapor diffusion. However, condensation caused by stack-induced airflow is likely to be more intense and concentrated around leaks in the building envelope. This can become a problem at the top of a building, which may be especially vulnerable because of leaks at the parapets. To avoid moisture damage, airflow through and within the building envelope should be prevented by a continuous air barrier. Because it is difficult to guarantee total airtightness of the building envelope, the hygrothermal effect of airflow can be quite important, especially when high pressure differentials are expected (e.g., in multistory or mechanically pressurized buildings). For the practical determination of pressure differentials and airflow, see Chapter 16. Air pressures across the envelope may also drive liquid water inward or outward. HEAT TRANSFER Heat flow through the building envelope is mainly associated with the building's energy performance. However, other aspects are equally important. Interior surface temperature not only serves as an indicator for hygienic conditions in the building (e.g., conditions preventing surface condensation or mold growth), but it can also be a major factor for thermal comfort. Temperature peaks and fluctuations within the building envelope or on its surfaces may further affect the envelope's durability. At low temperature, building materials tend to become less elastic and sometimes brittle, making them vulnerable to strain or mechanical impact. At high temperature, some materials degrade because of chemical reactions or irreversible deformation. Deformation and local mechanical failure can also occur under the influence of steep temperature gradients or transients. Whereas some of these aspects can be assessed by steadystate calculations (e.g., heating energy losses, energy end use), others require transient simulations for accurate evaluation. As explained in Chapter 4, heat transfer by apparent conduction in a solid is governed by Fourier's law: q =-k gjmd(t) = - kjl + kil + kil' x dx?dy z dz (2) q = heat flux, W/m 2 t = temperature, C k x,k y,k z = apparent thermal conductivity in direction of x, y, and z axes, W/(m-K) grad(i) = gradient of temperature (change in temperature per unit length, perpendicular to isothermal surfaces in solid), K/m dt/dx = gradient of temperature along x axis, K/m dt/dy = gradient of temperature along y axis, K/m dt/dz = gradient of temperature along z axis, K/m In Equation (2), the thermal conductivity k of the material is assumed to be directionally dependent. In fact, many building materials (e.g., wood and wood-based materials, mineral fiber insulation, perforated bricks) show considerable anisotropy. Therefore, k x, L, and k z are not equal in these materials; in isotropic materials, they are equal. Substituting Equation (2) into the relationship for conservation of energy yields f t *f x = div[â:grad(i)]+s f \ f d_ d k K- dx by dx frj dt d_ dz ί \ k dt dz h = enthalpy per unit volume, J/m 3 S = heat sources and sinks [e.g., caused by latent heat of evaporation/ condensation in presence of moisture or chemical reactions such as in concrete hydration, or by phase change from solid to liquid or vice versa of special additives consisting of paraffins or salt hydrates, known as phase-change materials (PCM)], W/m 3 with dh dx (3) PA wc. (4) p s = density of solid (dry material), kg/m 3 c s = specific heat capacity of dry solid, J/(kg K) c w = specific heat capacity of liquid water, J/(kg-K) w = moisture content, kg/m 3 STEADY-STATE THERMAL RESPONSE In steady state without sources or sinks, Equation (3) reduces to d_ dx by fr, dz {'dz) = 0 (5) If the steady-state heat flux is only in one direction (e.g., perpendicular to the building envelope) and materials are assumed to be isotropic, Equation (2) can be rewritten for each material layer within the building envelope as q = -k, CAt = -)-Äß R At = temperature difference between two interfaces of one material layer, K Ax = layer thickness, m k m = mean thermal conductivity of material layer with thickness Ax, W/(m-K) C = thermal conductance of layer with thickness Ax, W/(m 2 K) R = thermal resistance of layer with thickness Ax, (m 2 K)/W (6)

25.6 Under steady-state conditions, the one-dimensional heat flux is the same through all material layers, but their individual thermal conductance or resistance is usually different. Surface-to-Surface Thermal Resistance of a Flat Assembly A single layer's thermal resistance to heat flow is given by the ratio of its thickness to its apparent thermal conductivity. Accordingly, the surface-to-surface thermal resistance of a flat building assembly composed of parallel layers (e.g., a ceiling, floor, or wall), or a curved component if the curvature is small, consists of the sum of the resistances (R-values) of all layers in series: R S = R,+R 2 + R 3 +R 4 + -+R n (7) Ä[, R 2,..., R = resistances of individual layers, (m 2 -K)/W R s = resistance of building assembly surface to surface (system resistance), (m 2 -K)/W For building components with nonuniform or irregular sections, such as hollow clay and concrete blocks, use the R-value of the unit as manufactured. Combined Convective and Radiative Surface Heat Transfer The surface film resistances and their reciprocal, the surface film coefficients, specify heat transfer to or from a surface by the effects of convection and radiation. Although heat transfer by convection is affected by surface roughness and temperature difference between air and surface, the largest influence is that of air movement, turbulence, and velocity close to the surface. Because air movement at the envelope's outer surface depends on wind speed and direction, as well as on flow patterns around the building, which are usually unknown, an average surface heat transfer film coefficient at the exterior is normally used. Correlations such as that of Schwarz ( 1971 ) link the convective film coefficient to wind speed recorded at a height of 10 m and to orientation of the surface (windward or leeward side). The same holds for the inside surface, buoyancy plays a prime role. However, because the surface-to-surface thermal resistance of a wall is usually high compared with the surface film resistances, an exact value is of minor importance for most applications. Because air is rather permeable to long-wave radiation, heat transfer by radiation takes place between the surface and objects in the environment, not the surrounding air. Heat transfer by radiation between two surfaces is controlled by the character of the surfaces (emittance and reflectance), the temperature difference between them, and the angle factor through which they see each other. Indoors, the external wall surface exchanges radiation with partition walls, floor, and ceiling, furniture, and other external walls. In winter, most of the other surfaces have a higher temperature than the external wall surface; therefore, there is a net heat flux to the external wall by radiative exchange. Outdoors, the external wall surface sees the ground, neighboring buildings, and the sky. Without the sun, thermal radiation from the sky is normally low compared to the radiation from the wall. This means the wall is losing energy to the sky. Especially during clear nights, the temperature of the exterior surface of the external wall may drop below the ambient air temperature. In this case, convective and radiative heat transfer at the surface are opposed to each other. For simplicity, convective and radiative surface heat transfer are often combined, leading to an apparent surface heat transfer film coefficient h: with q = Kt en -t s ) (8) h = h c + h r (9) 2013 ASHRAE Handbook Fundamentals (SI) q = total surface heat transfer, W/m 2 h = apparent surfacefilmtransfer coefficient, W/(m 2 K) h r = radiant surface film coefficient to account for long-wave radiation exchange, W/(m 2 K) h c = convective surfacefilmcoefficient, W/(m 2 K) t m = environmental reference temperature, C t s = surface temperature, C For indoor surface heat transfer, this approach is acceptable when only heat transport through the building envelope is considered. Environmental temperature t en also includes the air temperature as the mean temperature of all surfaces in the field of view of the considered envelope assembly. When all these surfaces are of partition walls and floors that have the same temperature as the indoor air, t en may be replaced by the indoor air temperature. This approach becomes questionable when heat transfer at the outdoor surface is concerned. Because radiation to the sky can lead to surface temperatures below ambient air temperature, Equation (8) underestimates the real heat flux when environmental temperature is replaced by outdoor air temperature. Therefore, t en must include all short- and long-wave radiation contributions perpendicular to the assembly's exterior surface. However, t en cannot be used for moisture transfer calculations. Therefore, a more convenient way in that case may be to treat heat transfer by convection and radiation exchange separately. In this case, h r is skipped in Equation (9), which now applies to convection only, and t en equals the outdoor air temperature. The heat exchange by radiation is calculated by balancing the solar and environmental radiation onto the assembly's exterior surface with the long-wave emission from it. Steady-state calculation of thermal transport through the building envelope is generally done using surface film resistances based on combined surface heat transfer by radiation and convection, with R being the inverse of the combined surface film coefficient h. Because of greater air movement outdoors, the mean thermal surface film resistance at the exterior surface is lower than at the interior surface. Typical ranges for the combined exterior and interior surface film resistances with surface infrared reflectance so.l (nonmetallic) are R 0 = 0.03 to 0.06 (m 2 -K)/W R t = 0.12 to 0.20 (m 2 -K)/W Heat Flow Across an Air Space Heat flow across an air space is affected by the nature of the boundary surfaces, slope of the air space, distance between boundary surfaces, direction of heat flow, mean temperature of air, and temperature difference between both boundary surfaces. Air space thermal conductance, the reciprocal of the air space thermal resistance, is the sum of a radiation component, a conduction component, and a convection component. For computational purposes, spaces are considered airtight, with neither air leakage nor air washing along the boundary surfaces. The radiation portion depends on the temperature of the two boundary surfaces and their respective surface properties. It is not affected by thickness or slope of the air space, direction of heat flow, or which surface is hot or cold. For surfaces that can be considered ideally gray, the surface properties are emittance, absorptance, and reflectance. Chapter 4 explains all three in depth. For an opaque surface, reflectance is equal to one minus the emittance, which varies with surface type and condition and radiation wavelength. The combined effect of the emittances of the two boundary surfaces is expressed by the effective emittance E of the air space. Table 2 in Chapter 26 lists typical emittance values for reflective surfaces and building materials, and the corresponding effective emittance for air spaces. More exact surface emittance values should be obtained by tests.

Heat, Air, and Moisture Control in Building Assemblies Fundamentals 25.7 U=\IR 7 (11) Fig. 5 Heat Flux by Thermal Radiation and Combined Convection and Conduction Across Vertical or Horizontal Air Layer The convective portion is affected markedly by the slope of the air space, direction of heat flow, temperature difference across the space, and, in some cases, thickness of the space. It is also slightly affected by the mean temperatures of both surfaces. For air spaces in building components, radiation and convection together define total heat flow. An example of their magnitudes in total flow across a vertical or horizontal airspace (up and down) is given in Figure 5. Table 3 in Chapter 26 lists typical thermal resistance values of sealed air spaces of uniform thickness with moderately smooth, plane, parallel surfaces. These data are based on experimental measurements (Robinson et al. 1954). Resistance values for systems with air spaces can be estimated from these results if emittance values are corrected for field conditions. However, for some common composite building insulation systems involving mass-type insulation with a reflective surface in conjunction with an air space, the resistance value may be appreciably lower than the estimated value, particularly if the air space is not sealed or of uniform thickness (Palfey 1980). For critical applications, a particular design's effectiveness should be confirmed by actual test data undertaken by using the ASTM hot-box method (ASTM Standard C1363). This test is especially necessary for constructions combining reflective and nonreflective thermal insulation. Total Thermal Resistance of a Flat Building Assembly Total thermal resistance to heat flow through a flat building assembly component composed of parallel layers between the environments at both sides is given by R T = R i + R,+R n (10) Rj = combined inner-surface film resistance, (m 2 K)/W R 0 = combined outer-surface film resistance, (m 2 K)/W R s = resistance of building assembly surface to surface, including thermal resistances of possible air layers in component (system resistance), (m 2 -K)/W Thermal Transmittance of a Flat Building Assembly The thermal transmittance or U-factor of a flat building assembly composed of parallel layers is the reciprocal ofr T : Calculating thermal transmittance requires knowing the (1) apparent thermal resistance of all homogeneous layers, (2) thermal resistance of the nonhomogeneous layers, (3) surface film resistances at both sides of the construction, and (4) thermal resistances of air spaces in the construction. The lower values of the surface film resistances given previously should be used. The steady-state heat flux Q n across the building envelope assembly is then defined by Qn=A n U n {t i -t 0 ) (12) tj, t 0 = indoor and outdoor reference temperatures, C A n = component area, m 2 U n = U-factor of component, W/(m 2 K) Interface Temperatures in a Flat Building Component The temperature drop through any layer of an assembly is proportional to its thermal resistance. Thus, the temperature drop Äß, through layer y is A tj = *Pi-*o) The temperature in an interface^ then becomes (t 0 < t t ) tj = t 0 R J Ay Ri (13) (14) R ] 0 is the sum of thermal resistances between inside and interfacey in the flat assembly, in (m 2 -K)/W. If the apparent thermal conductivity of materials in a building component is highly temperature dependent, the mean temperature must be known before assigning an appropriate thermal resistance. In such a case, apply successive calculation steps. First, select R-values for the particular layers. Then calculate total resistance Ä r with Equation (9) and the temperature at each interface using Equation (13). The mean temperature in each layer (arithmetic mean of its surface temperatures) can then be used to obtain secondgeneration R-values. The procedure is repeated until the R-values are correctly selected for the resulting mean temperatures. Generally, this demands two or three steps. To calculate interior surface temperatures for risk assessment of surface condensation or mold growth, the higher interior and lower exterior surface film resistance values, given previously, should be used. Series and Parallel Heat Flow Paths In many building assemblies (e.g., wood-frame construction), components are arranged so that heat flows in parallel paths of different conductances. If no heat flows through lateral paths, the thermal transmittance through each path may be calculated. The average transmittance of the enclosure is then U m = au + bu h nu (15) a,b,...,n are the surface-weighted path fractions for a typical basic area composed of several different paths with transmittances U a, U b,..., U. If heat can flow laterally with little resistance in any continuous layer, so that transverse isothermal planes result, the flat construction performs as a series combination of layers, of which one or more provide parallel paths. Total average resistance Rjr av ) in that case is the sum of the resistance of the layers between the isothermal planes, each layer being calculated and the results weighted by the contributing surface area. For further information, see Chapter 27.

25.8 2013 ASHRAE Handbook Fundamentals (SI) The U-factor, assuming parallel heat flow only, is usually lower than that assuming combined series-parallel heat flow. The actual U-factor lies between the two. Without test results, a best choice must be selected. Generally, if the construction contains a layer in which lateral heat conduction is somewhat high compared to heat flux through the wall, a value closer to the series-parallel calculation should be used. If, however, there is no layer of high lateral thermal conductance, use a value closer to the parallel calculation. For assemblies with large differences in material thermal conductivities (e.g., assemblies using metal structural elements), the zone method is recommended (see Chapter 27) or the methods discussed in the following section. Thermal Bridging and Thermal Performance of Multidimensional Construction Passing highly conductive materials through insulation layers (thermal bridging) results in building envelopes with higher overall thermal transmittances and colder surface temperatures compared to an assembly with continuous, unbroken insulation. Not recognizing the effect of thermal bridging on the building envelope's thermal performance can lead to inefficient design of HVAC systems, building operation inefficiencies, inadequate condensation resistance at component intersections, and compromised occupant comfort. Heat flow through building envelopes occurs in two and three dimensions when considering all components and their intersections (e.g., glazing, wall, roof, parapet, balconies, floor slabs). Multidimensional heat flow caused by highly conductive thermal bridges (e.g., steel and concrete sections) cannot be effectively evaluated using simplified hand calculations (see Chapter 27) and must be evaluated using a multidimensional computer model or guarded hot-box test measurement (ASTM Standard C1363). Contributions of heat flow for specific construction details (e.g., slab edges, parapets, glazing transitions) are often lumped into an overall heat flow of the entire opaque area or evaluated separately by defining an effective length or area (or zone of influence). Individual details with transmittances defined by an effective area are combined with other components to calculate an overall thermal transmittance using a weighted average method. However, effective areas often have no real significance or have a large variance that depends on many factors (location of insulation layers in relation to structural framing, insulation levels, orientation of structural framing, predominate heat flow path, etc). Moreover, the effect of individual details is averaged over the adjacent assemblies, regardless of size of the effective area or length. Consequently, the absolute effect or thermal quality of a detail is difficult to assess using an effective area approach (Morrison Hershfield 2011). An alternative to the weighted average method is to determine the extra heat loss caused by an individual detail (i.e., thermal bridge at an intersection of components) above the heat loss of an undisturbed assembly and ascribe that difference to a line or point. This method can simplify calculation of overall heat loss and highlight the impact of the thermal bridge. Linear and Point Transmittances Using linear and point transmittance requires dividing thermal transmittances into three categories: Clear field: heat loss due to thermal bridges uniformly distributed that modify the heat flow of the assembly (area based); not practical to account for on an individual basis (e.g., structuring framing, ties) Linear: additional heat loss along a considerable portion of a building perimeter or height in one dimension (e.g., slab edges, balconies, parapets, corner framing, window interfaces) Point: additional heat loss from thermal bridges at countable points on a building (e.g., three-way corners, beam penetrations) Calculating the overall heat flow is simply adding the contribution of each linear and point thermal transmittance to the clear-field assembly heat flow. The overall heat flow through the opaque elements of the building envelope (wall or roof) is Q = Óä«- + Ó â = Ó (øæ - )+ Ó + Ó â (16) Q = overall heatflowthrough building envelope, W/K Qanomaties = additional heatflowfor linear and point transmittance details, W/K Q 0 = clear-field heat flow without linear and point transmittance details, W/K Ø = linear transmittance, W/(m-K) = point transmittance, W/K L = characteristic length of linear transmittance detail, m The overall heat flow per unit area, U-value, can be derived by dividing the previous equation by the total projected surface area of the opaque area. U = Ó(ØÆ,) + U (17) 1 Total U = overall thermal transmittance, including anomalies, W/(w? K) U 0 = clearfieldthermal transmittance (assembly), W/(m 2 K) Atotal = '"'al opaque projected surface area, m 2 Thermal bridging and multidimensional heat flow also affect surface temperatures, concealed surfaces, and surfaces exposed to the indoor and outdoor environments. The temperature distribution from multidimensional heat flow is important to consider for controlling localized dirt pick-up on cold surfaces, mold growth, and condensation. A practical, convenient means to evaluate surface temperatures for multidimensional construction is to represent the coldest surface temperatures of interest relative to a temperature difference. This nondimensional ratio is sometimes referred to a temperature index, factor, or ratio, with the following basic form but represented by many different symbols (CAN/CSA A440; ISO 13788; Morrison Hershfield 2011): T - T 1 index surface outdoor (18) ndoor outdoor ^index = temperature index ^surface = coldest temperature of surface ^outdoor = outdoor temperature ^indoor = indoor temperature The temperature index for a critical surface can then be compared to a minimum or design temperature index based on numerous performance criteria (e.g., risk of condensation, mold growth, corrosion). More detailed discussion of using temperature ratios and hygrothermal analysis can be found in the section on Simplified Hygrothermal Design Calculations and Analyses. TRANSIENT THERMAL RESPONSE Steady-state calculations are used to define the net heating energy demand in cold and cool climates. However, in climates daily temperature swings oscillate around a comfortable mean temperature, transient analysis to define net energy demand for heating and cooling and judge overheating probability is more appropriate. In order of importance, the thermal response of a building to daily swings in temperature and solar radiation depends on

LIVE GRAPH Next Page Heat, Air, and Moisture Control in Building Assemblies Fundamentals Click here to view 25.9 the thermal transmittance and solar heat gain coefficient (SHGC) of transparent components (fenestration) in the envelope, ventilation strategy, accessible thermal capacity of the internal walls and floors, and thermal transmittance/inertia of opaque components in the envelope. The effects of the mutual dependences of these four factors are complex. In cool climates, a simplified approach that accounts for these interactions combines a steady-state daily mean heat balance for a most probable hot day with a lower-limit value for the daily harmonic temperature damping at room level. Temperature damping at room level increases with higher admittance and higher harmonic thermal resistance of opaque envelope components; higher admittance and higher harmonic thermal resistance of all inside walls, floor, and ceiling; and higher thermal inertia of furniture and furnishings. A lower thermal transmittance of transparent components in the envelope results in decreased daily harmonic temperature damping at room level. In general, however, and in any climate, whole-building simulations complying with ANSI/ASHRAE Standard 140 are recommended when a clear picture of overheating probability and net energy demand for heating and cooling is needed. Phase-Change Materials (PCMs) Adding phase-change materials (PCMs) to building components may help dampen indoor temperature oscillations because of their high effective thermal inertia within the temperature range of phase change. PCMs can store thermal energy in small temperature intervals very efficiently because of their high latent heat. This thermal storage capability can be used in many different forms, including PCM-enhanced boards or membranes, arrays of the PCM containers, or PCMs dispersed in thermal insulation. Other anticipated advantages of PCMs are improved occupant comfort, compatibility with traditional building enclosure technologies, and potential for application in retrofit projects. Materials used as PCMs include paraffins, animal or vegetable fats, and salt hydrates. The heat storage capacity for a specific PCM-enhanced product is a key indicator of its dynamic thermal performance. A theoretical model of the material with temperature-dependent specific heat can be used to calculate phase-change processes in most PCMenhanced building products. For most PCMs, variations of enthalpy with temperature depend to some extent on the direction of the process considered, and are different for melting and solidification. Therefore, a model of the temperature-dependent specific heat, represented by a unique function of temperature, is an approximation of a real material thermal capacitance. Thermal characteristics of PCM and uniform PCM-based blends can be experimentally analyzed using differential scanning calorimeter (DSC) testing. Thermal characteristics of nonuniform PCMbased blends (e.g., PCM-enhanced thermal insulations) cannot be analyzed using DSC testing; instead, transient heat flux measurements should be taken with a heat flow meter apparatus (HFM) built in accordance with ASTM Standard C518 (Kosny et al. 2009). Figure 6 depicts an example of temperature-dependent enthalpy curves for microencapsulated paraffins. In this PCM, melting occurs around 27 C and solidification around 26 C. The temperature difference is called subcooling. Subcooling may delay the release of heat from a PCM. Depending on system design and the PCM used, heat release can be compromised slightly or seriously, affecting overall system effectiveness. Investigations (Feustel 1995; Kissock et al. 1998; Kosny et al. 2006; Salyer and Sircar 1989; Tomlinson 1992) demonstrated that building components with PCM-enhanced layers could have potential for use in residential and commercial buildings because of their ability to reduce energy consumption for space conditioning and reduce peak loads. The optimum location of PCM-containing layers in the building envelope depends on the boundary conditions. The Fig. 6 Example of Enthalpy Curves for Microencapsulated Phase-Change Materials (PCMs) best possible thermal effect is achieved when the PCM layer is in contact with indoor air and the indoor temperature swing goes through a complete phase change. Because the latter is unlikely to happen on a daily basis, a slight shift in position toward the outdoors may render PCMs more effective. PCM-enhanced layers close to the exterior surface make little sense from an energy perspective. However, they may help to solve other problems, such as nighttime condensation on façades responsible for growth of algae and fungi on well-insulated assemblies (Sedlbauer et al. 2011). AIRFLOW Airflow through and within building components is driven by three primary components: stack pressure, wind pressure, and pressure differentials induced by mechanicals. These driving forces are all described in greater detail in Chapters 16 and 24. In calculating air flux in buildings, a distinction must also be made between flow through open porous materials, and that through open orifices such as layers, cavities, cracks, leaks, and intentional vents. Air flux through an open porous material is given by m a = air flux, kg/(s-m 2 ) k a = air permeability of open porous material, kg/(pa-s-m) grad(p a ) = gradient in total air pressure (stack, wind, and mechanical systems), Pa/m The air flux or air transfer equation for flow through the various orifice types is m a o r M a = C(AP a Y (20) the flow coefficient C and flow exponent n are determined experimentally. As shown in Figure 7, there are six simplified single airflow patterns characteristic of flow in buildings: Exfiltration (air outflow): air passes across an envelope component moving from inside the building component to the outdoors Infiltration (air inflow): air passes across an envelope component from the outside of the building component to the inside