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3 Heat Transfer Fundamentals

This section reviews basic heat transfer fundamentals as they relate to glazing technology, specification, and performance.

Heat transfer is the movement of energy that results from a temperature differential. The three basic mechanisms, or modes, of heat transfer are conduction, convection, and radiation.

In general, conduction is the flow of energy across a solid, gas, or liquid due to thermal diffusion between molecules. An everyday example is a pot on a stove becoming hot after contact with the burner. Molecules vibrate according to their energy level (temperature), and this energy is transferred from molecule to molecule through the solid from higher to lower temperatures. The amount of energy transferred by conduction is directly proportional to the temperature difference (referred to as _T or "delta-T") and a material property called the thermal conductivity (k). Conductive heat transfer is also inversely proportional to the thickness of the material (L). These relationships to heat transfer (Qcond) can be stated mathematically as

For a given amount of heat transfer, a material that is very conductive (has a high k-value) or thin (small L) will be more effective at transferring thermal energy and will result in a lower temperature difference. Alternately, a material that is a good insulator (low k-value) or very thick (large L) will suppress heat transfer and will result in a larger temperature difference across the solid.

Glass is a good conductor of thermal energy because of its relatively high k and low thickness (L)*. Air is a relatively poor conductor, which is why double-pane glazing (containing a blanket of air) provides additional insulation. The air acts as a thermal break to reduce thermal bridging between good conductors (the glazing panes). Some types of gas fills (argon) can further reduce the conductive properties of glass and often replace air in insulated glazing units.

Convective heat transfer is the term used to describe the heat transfer that occurs between a solid and a fluid, or a solid and a gas, at different temperatures. Convection consists of both conductive heat transfer and heat transfer resulting from the bulk motion of a fluid or gas. Convective heat transfer is directly proportional to the convection coefficient (h), which can be viewed as a measure of the ability of the fluid or gas to impart its thermal energy to or from the surface. As the h-value of a surface/fluid interface increases, the temperature of the surface will approach that of the fluid. The mathematical relationship for convective heat transfer (Qconv) is given below.

Convection is dependent on many factors, the most important of which is the velocity of the fluid or gas over the solid surface. This is demonstrated by blowing on a hot object to cool it quickly before touching it. Convection can be further described as either natural or forced. Natural convection occurs when the motion of the gas or liquid is driven by differences in density (caused by temperature differentials within the entity). The force of gravity pulls the heavy fluid/gases down, which pushes the lighter fluid/gases up (that is, hot air rises, cool air falls). Forced convection is when the motion of the fluid or gas is externally induced (e.g., by a fan or the wind).

Heat transfer is usually higher for forced convection than for natural convection, because the velocity of the fluid/gas is often greater. Therefore, we blow on a hot object to cool it faster than the naturally rising hot air could. In typical glazing systems, convective heat transfer occurs between all gas/solid interfaces.

Radiative heat transfer is the exchange of electromagnetic energy between surfaces of different temperatures. Radiative energy is emitted by any piece of matter that has a finite temperature. (A finite temperature is any temperature above absolute zero. Even very cold surfaces emit radiant energy, although very little.)

Physically, radiant energy leaves a surface via electromagnetic waves and travels until it is incident on another surface. If a surface "receives" more radiative energy than it "emits," its temperature will increase (omitting other forms of heat transfer), and vice-versa. One can experience a net positive radiative heat exchange when sitting near a wood-burning stove or radiant heater. The "heat" does not need air to travel through, and can in fact travel through empty space (e.g., sunlight). The equation that describes emitted radiation from a surface (Qemitted) is

For a given temperature, materials with high _ values radiate more effectively than those with small values.

All surfaces emit radiant energy levels according to their mean temperature. That is, a high-temperature surface emits high levels of radiant energy; a low-temperature surface emits low levels of radiant energy. From this fact it can be concluded that other nearby objects are also emitting their radiant energy back toward the surface in question. This incident radiant energy on a surface can be absorbed by the surface, reflected off the surface, or transmitted through the surface.

For glass, most of the incident radiant energy is transmitted through the surface, although reflection and absorption are also factors (their values being dependent upon the spectral properties of the glass type). These modes of radiation are illustrated in Figure 1 for a typical wood window section, along with other heat transfer modes.

The radiative energy exchange for the illustration is the net energy transferred from the warmer room surfaces to the cooler exterior surface of the glazing. Actually, both surfaces emit energy toward each other. However, since the room surfaces will be warmer than the glazing surfaces, the resultant net radiant heat transfer is from the room to the glazing. This does not consider the effects of incident sunlight from the outdoors, which may tip the balance.

In a separate process, convection also causes energy to be transferred from the warm interior air temperature to the glazing. Heat transfer then occurs across the glazing itself via conduction, and at the outdoor surface, convection and radiant emission again take over as the dominant modes of heat transfer, transferring thermal energy to the outdoors.

Infiltration can also be a factor in the heat transfer process of the above assembly. Infiltration is the exchange of air through cracks in the window assembly.

Figure 1. Modes of radiation for a typical wood window section.

Along with the described modes of heat transfer, three glazing-related factors must be considered when evaluating the overall energy performance of a building:

These values will vary depending on some physical forces

The processes outlined above not only illustrate how energy is gained or lost through glazing, but are also important to understanding the performance of advanced glazing technologies. These technologies, which are discussed in more detail in Chapter 4, often involve material properties that enhance or suppress heat transfer, depending upon the design intent of the glazing system. To complete the discussion of the physics involved in glazing design, the properties of thermal radiation and the ways in which it contributes to solar gain are discussed in the following sections.

Solar radiation can be characterized by its wavelength, intensity, and direction. The visible and invisible portions of solar radiation can be identified within certain wavelength regions or spectrums. The energy in solar radiation varies with wavelength, so that the amount of energy delivered within each spectrum differs. The majority of solar radiation energy exists in the wavelength spectrum between about 0.3 and 3.0 _m, although some of it is attenuated in the earth's atmosphere.

Figure 2 illustrates the different wavelengths that exist in the solar spectrum near the surface of the earth. The solar spectrum can be broken into three main groups: ultraviolet (UV), infrared, and visible light.

Ultraviolet energy is mostly invisible and embodies only about 7 percent of the energy in sunlight. Infrared energy is also invisible and contains about 46 percent of the energy in the solar spectrum. The visible spectrum contains about 47 percent of the energy in the solar spectrum. Figure 3 illustrates the relationship between energy intensity and wavelength in the three spectrums near the surface of the earth. Peak intensity is reached at about 0.45 _m in the green portion of the visible spectrum.

Solar heat gain is the measure of total heat gain (visible, infrared and UV) from sunlight that passes through a glazed surface and is eventually dissipated to the indoors. The amount of sunlight that a glazed surface receives is largely dependent on its size, solar orientation and the time of day the measurement is taken. However, different glazing types possess unique solar heat gain characteristics.

Advances in glazing and coating technologies have resulted in products that can selectively transmit or reflect certain wavelengths of light. A spectrally selective glazing unit possesses optical properties that behave differently in one part of the spectrum than in others. Therefore, glazings can be chosen to either transmit or reject solar heat.

Figure 2. The solar spectrum.

Figure 3. Energy intesity and wavelength.

Almost all architectural glass blocks long-wave radiation (far infrared) emitted by surfaces at temperatures below about 250 °F. This characteristic is instrumental in producing the greenhouse effect. The greenhouse effect is caused by exterior visible and near infrared light that is transmitted through a glazed surface and is absorbed by interior surfaces. This energy heats up the interior objects and is re-emitted at a much longer wavelength. The longer wavelength energy cannot escape the interior by transmission through the glass, because, as mentioned, glass blocks long-wave radiation. This long-wave radiation is then absorbed by the glass and re-emitted to both sides of the glass surface, reheating the objects within the space and effectively "trapping" large portions of the energy inside.

As noted previously, the three main radiative properties of glass are transmittance, reflectance, and absorptance. Together they describe what can happen to radiative energy when it is incident to, or falls upon, a pane of glass. The radiative energy is transmitted through the glass, reflected by the glass, or absorbed by the glass. Values that are typically assigned to the three properties range between 0.0 and 1.0 and reflect the percentage of incident radiant energy that is transmitted, absorbed, and reflected. For example, if we consider a sheet of clear glass and combine all of the possible wavelengths and directions of incoming sunlight, the solar properties are roughly as follows: transmittance (0.86), reflectance (0.08), and absorptance = (0.06). Note that these three properties must add up to 1.0 to account for all the radiant energy.

If 86 percent of the available solar energy is transmitted, the transmittance is said to be equal to 0.86 (Figure 4). If 6 percent is absorbed, the absorptance is 0.06. Likewise, if 8 percent is reflected, the reflectance is equal to 0.08. At any time, the sum of these radiative properties must equal 1.

The properties can vary considerably depending on glass thickness, number of panes of glass, amount of impurities, texture, and any coatings or tints that have been added. The properties will also depend on the wavelength and direction of the incoming light. It is important to be aware of the spectral (wavelength) aspects of radiative properties, because many coatings and tints alter these properties to enhance or suppress the transmission of radiant energy through the glazing.

Figure 4. Effects of light on glass.

R-value, shading coefficient, coolness index, and solar heat gain coefficient are performance indicators that must be considered to effectively evaluate heat transfer behavior. In cold weather conditions it is desirable to suppress conductive, convective, and radiative heat transfer from the high-energy indoors to the low-energy outdoors. However, it is also desirable to enhance the solar radiative heat transfer from the outdoors (sun) to the indoors. Therefore, when considering a glazing performance indicator, it is important to know what modes of heat transfer are being measured by that indicator. Because glazing systems can differ greatly and their surrounding thermal environments are constantly changing, performance indicators do not remain constant and might vary slightly in an actual application.

If we disregard solar radiation, air leakage, and moisture condensation, the rate of heat transfer through a glazing system is proportional to the difference in air temperature between the outdoors and the indoors as expressed by the equation

where

The U-value is a measure of that system's ability to transfer energy under the above assumptions. It is the rate of energy (Btu) flowing through a 1 ft2 piece of material or assembly with a 1 °F difference in temperature between sides for 1 hr. U-value can be thought of as a "nonsolar" performance indicator that combines the effects of conduction, convection, and thermal radiation caused by the indoor-outdoor temperature difference.

It should be noted that U-values do not take into account the ability to transmit solar radiation. For comparison purposes and for code compliance, U-values are measured under standardized thermal conditions, because the actual U-value for a glazing system will change as conditions around it change. A designer may sometimes encounter a "summer" U-value (when heat flow is primarily from outside toward the inside) and a "winter" U-value (when heat flow is primarily from inside toward the outside).

Also, different regions of a glazing system will have different U-values. Reported U-values are sometimes a combination of the U-values measured at the center-of-glass, edge-of-glass, and the frame. Sometimes only the center-of-glass U-value is offered. Care must be taken when comparing U-values to ensure that they were calculated in a consistent manner. The most accurate information is the measure of the total window system. Good sources of U-values for windows are the American Society of Heating, Refrigerating, and Air-Conditioning Engineers' (ASHRAE 1993) "Handbook of Fundamentals" (Chapter 27, Table 5) and the National Fenestration Rating Council's "Certified Products Directory."

Another thermal performance indicator is the R-value. The R-value is the inverse of the U-value and is thus a measure of the system's ability to resist heat transfer*

Table 1 describes the physical and optical properties for 14 glazing configurations. Glazing configuration No. 2 (a single pane of 1/8-in. clear glass) is used as the baseline (1.0) for calculating shading coefficients. All values shown are for center-of-glass measurements. Other factors, such as dividers and window frame type, material, and size, can affect a system's performance. Therefore, the values shown in Table 1 are for the glazing only.

The shading coefficient (SCc) is an indicator of how well a glazing transmits solar energy. It can be thought of as the "solar" performance indicator. The SC is the ratio of solar energy transmission through a specific glazing relative to that of a clear, double-strength, 1/8-in.-thick single-pane glass. The SCc is a number between 0 and 1, with high SCc values indicative of a glazing type that transmits almost as much as clear glass, ideal for winter or for high solar heat gains. Lower SCc values indicate that the glazing will block a portion of the incident solar energy, ideal for the summer or for reduced cooling loads. SCc values alone do not determine the amount of solar energy that will pass through a surface; glazing size, orientation, and shading devices are also factors.

The solar heat gain coefficient (SHGFc) is a measure of the rate of solar heat flowing through a window or skylight. Solar heat gain coefficients allow consumers to compare the solar heat gain properties of different windows and skylights. The solar heat gain coefficient accounts for the transmissive glazing element, as well as the opaque frame and sash.

Tsol is the solar transmittance of the glazing system, with a value of 1.0 indicating full transmission and zero indicating an opaque surface. This is a measure of the solar transmittance across the entire solar spectrum, including UV, visible, and infrared energy.

Table 1. Physical and optical properties of sample configurations

Visible transmittance (Tvis) is the ability of the glazing to transmit daylight, or radiation in wavelengths visible to the human eye. The visible transmittance is an important factor in determining daylight penetration. The visible transmittance can be very different from solar transmittance in two panes that appear identical.

The coolness index or (Ke) is the ratio of visible transmittance to shading coefficient. It is represented in the formula Ke = (Tvis/SCc).

Excluding far-infrared, clear glass is evenly transmissive throughout the solar spectrum. The Ke of clear glass is given a value of 1.0. Tints that lower the visible transmittance but maintain the transmittance of infrared (or solar heat gain) have a Ke less than 1.0. Low emissivity (low-e), selective tints, and other products that have a lower shading coefficient and more visible light have a Ke greater than 1.0. A superior, spectrally selective glass will have a Ke > 1.0, while inferior glass will have a Ke < 1.0.

Additional glazing layers provide more barriers to solar radiation, thus reducing the solar heat gain coefficient of a window. Tinted glazings, such as bronze and green, provide lower solar heat gain coefficients than clear glass. Low-e coatings can be engineered to reduce window solar heat gain coefficients by rejecting more of the incident solar radiation. Spectrally selective glazings block out much of the sun's heat while maintaining a higher visible transmittance and more neutral colors than more heavily tinted bronze and gray glazings. High-transmittance, low-e coatings, used in conjunction with a tinted outer glass layer, also reduce solar heat gain by preventing the absorbed heat from reaching the interior space. Mirror-like reflective glazings are commonly used in office buildings, but are rarely chosen for residences. While reflective glazings may have very low solar heat gain coefficients, they block so much of the light and view that they are not normally desirable in homes.

Additional reference sources on energy efficient design of windows and glazing are listed in Appendix B.

Table 2 shows representative solar heat gain coefficients and visible transmittances for glazings with typical wood or vinyl frames and aluminum spacers. Aluminum-frame windows of comparable size and glazing type generally have slightly higher solar heat gain coefficients because of their thinner frames and greater glazing areas. It should also be noted that the total window visible transmittance can be considerably less than the glazing visible transmittance due to frame and divider shading effects. Table 2 also illustrates that it is possible to have windows with high visible transmittance while having a relatively low solar heat gain coefficient.

Table 2. Representative window solar heat gain coefficients and visible transmittances*

Figure 5 describes the surface numbers (nomenclature) that relate to the description of glazing assemblies that follows. Table 3 shows the temperature profiles for the outside surface (1), center-of-glass (a) and inside surface (2) temperatures for various glazing configurations. Glazing systems 1 through 4 are clear, single-pane glass of varying thickness. Glazing types 5 through 10 are double-pane configurations. For example, No. 5 is two panes of 3/32-in. clear glass with a ½-in. air space between. Number 9 has an outer pane of 1/8-in. glass that has a low-e coating on the inside surface of the outer pane. Number 10 is the same configuration as No. 9 except that the air between the panes has been replaced with argon gas. Numbers 11 through 14 are triple-pane configurations. All temperatures are for center of glass.

Figure 5. Glass pane nomenclature.

Table 3. Temperature profiles (°F) and relative humidity (%)

The column labeled RH (relative humidity) is the indoor relative humidity at which condensation would occur on the inside surface of the glass. It is interesting to note the vast difference between the high and low values. Also note the significant difference that occurs simply by replacing air with argon (No. 9 versus. No. 10).

The comfort implications of the various glazing configurations are clearly illustrated by observing the innermost surface temperature. A human body will radiate far more energy toward a surface that is in the high teens (17-19 °F) than it will toward a surface that is in the range of 45 to 58 °F. The single-pane glazing will appear as a very cold surface compared with the other configurations. Colder surfaces can also contribute significantly to the creation of drafts and uncomfortably cold air currents.

Configuration types 13 and 14 (Table 3) replace the center pane of glass in a triple-pane configuration with a special heat-rejecting film. Different types of low-emissivity, wavelength-selective films are available. The difference between the films is their ability to reflect infrared energy. It is interesting to note how effective these films are in reflecting heat back to the interior, and conversely, blocking infrared energy during the summer.

Standard conditions (outside air = 0 °F; inside air = 70 °F) were used for all the analyses. All air spaces were ½ in. wide.

When determining the energy performance of glazed surfaces, it is important to note the entire assembly of the window unit. Prior to 1989, the ASHRAE method for determining overall window R-value was based on estimating the losses associated with the particular glazing type (typically calculated at the center of the glass component). A correctional factor was then applied for the frame R-value. Frames were assumed to slightly improve the overall R-value of the window assembly.

Recent technological improvements in glazing thermal performance have created the opposite condition. Glazing is now typically the most thermally efficient component of the window system, with edges and frames reducing the overall R-value. The new calculation method has, in some cases, reduced reported R-values from 1989 levels.

Ultraviolet radiation is the main component of sunlight that can fade and damage drapes, carpets, furniture, and paintings when transmitted through windows and skylights. Efforts to produce window glazings that transmit less ultraviolet energy have met with some success. In general, windows and skylights with plastic glazing layers or low-e coatings reduce UV transmission. However, even without any UV radiation, sunlight can still cause fading of fabrics and other furnishings.

Clear glass transmits approximately 70 percent of the UV radiation. It is possible to remove most, but not all, of the UV light. Plastics inherently block more UV than glass, reducing the transmission to a total of 0.05 percent for units that use suspended films (see Chapter 4, Low-e and Reflective Coatings). It should be noted that some UV is visible and cannot be blocked without reducing the visible light. Glass with high visible transmittance (Tvis) will transmit more UV, than glass with a lower Tvis.

Air can hold varying amounts of water vapor or moisture. The warmer the air is, the more moisture it can hold. The amount of moisture in the air, expressed as a percentage of the maximum amount the air could hold at a given temperature, is called its relative humidity. For health and comfort, indoor air should contain some moisture. The relative humidity should generally be between 30 percent and 40 percent at normal room temperature.

The relative humidity of air can be increased by adding more moisture or by reducing the temperature. When the relative humidity reaches 100 percent, the air can hold no more moisture and water begins to condense from it. The temperature at which this condensation occurs is called the dew point temperature of the air. When moist air comes in contact with a cold surface in a home, it may be cooled to its dew point temperature, resulting in condensation on the surface.

Windows do not cause condensation. Typically, however, windows are the first and most obvious place that condensation in a building occurs. This is because windows generally have a lower thermal resistance than insulated walls, ceilings, and floors. As a result, their inside temperatures are usually lower than those of other surfaces in a home during cold weather. If the air in a home is humid enough, water will condense from it when it is cooled at a window surface. Condensation is most often thought of as a cold-climate, winter problem. However, in hot humid weather, moisture can condense on the outside surface of a poorly insulated window in an air-conditioned building.

Left unchecked, condensation can damage window frames, sills, and interior shades. Water can deteriorate the surrounding paint, wallpaper, plasterboard, and furnishings. In severe cases, it can seep into adjoining walls, causing damage to the insulation and framing.

The indoor air coming into contact with energy-efficient windows is less likely to be cooled to its dew point temperature because the inside surface temperatures remain higher during cold weather than do those of windows with single glazing, traditional metal spacers, and metal frames.

Figure 6 illustrates conditions under which condensation will form on the center of the glass of three glazing types with widely varied U-factors. The graph shows clearly that the risk of condensation at the center of the glass is reduced as the insulating value of the glass increases. Even at an outdoor air temperature of -30 °F, the indoor air relative humidity must be nearly 50 percent before condensation will form on the triple glazing with two low-e coatings. On the other hand, at an outdoor temperature of 10 °F, condensation will form on the single glazing at an indoor relative humidity of only 18 percent.

Figure 6 shows outdoor air temperature and indoor air RH combinations at which condensation will occur on the center of the glass for single glazing, double glazing, and triple glazing with two low-e (e = 0.15) coatings. On or above each curve, the conditions are right for condensation. Below each curve, condensation will not occur on that glazing type as long as the glazing is exposed to room air circulation. Results are based on winter conditions: 70 °F indoor air temperature, 15 mph outdoor air velocity, and no incident solar radiation.

Condensation is even more likely to occur at window spacers and frames, which are usually less insulative than the corresponding glazings. With so many insulating glazing types available, efforts to prevent condensation have shifted toward the development of better insulating spacers and frames.

Figure 6. Conditions for window condensation.

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