1
3.1 Solar Radiation
Thermal Radiation
Solar radiation is made up of several broad classes of electromagnetic radiation, all of which have some common characteristics, but which differ in the effect they produce, primarily because of their wavelength. These broad classes of the solar spectrum include ultraviolet, visible light, and infrared. Overlapping the wavelengths of most of the infrared, all of the visible light, and part of the ultraviolet spectrum is a range referred to as thermal radiation, since it is this part of the electromagnetic spectrum that primarily creates a heating effect. In turn, when a substance has its thermal energy level (temperature) increased, the electromagnetic radiation produced by this temperature increase is primarily in the thermal radiation band. Thermal radiation is that portion of the electromagnetic spectrum with wavelengths from 0.1 x 10-6 m up to approximately 100 x 10-6 m. In both the IP and the SI systems the common unit for wavelength is the micron ( 1 m = 10-6 m); therefore, the approximate range of thermal radiation is from 0.1 to 100 microns. A portion of the shorter wavelengths in this range is visible to the human eye. Radiant energy or radiation should be understood to mean thermal radiation.
The total thermal radiation that impinges on a surface from all directions and from all sources is called the total or global irradiation (G). Its units are Btu/(hr-ft2) or W/m2.
The thermal radiation energy that falls on a surface is subject to absorption and reflection as well as transmission through transparent bodies. Absorption is the transformation of the radiant energy into thermal energy stored by the molecules. Reflection is the return of radiation by a surface without change of frequency. In effect the radiation is "bounced" off of the surface. Transmission is the passage of radiation through a medium without change of frequency. Energy falling on a surface must be subject to one of these three actions; therefore,
where:
= the absorptance, the fraction of the total incident thermal radiation absorbed
= the reflectance, the fraction of the total incident thermal radiation reflected
= the transmittance, the fraction of the total incident radiation transmitted through the body
When the material is optically smooth and of sufficient thickness to show no change of reflectance or absorptance with increasing thickness, the terms reflectivity and absorptivity are used to describe the reflectance and absorptance, respectively.
Radiant energy originates at a surface or from the interior of a medium because of the temperature of the material. The rate of emission of energy is stated in terms of the total emissive power (E). Its value depends only on the temperature of the system and the characteristics of the material of the system. Some surfaces emit more energy than others at the same temperature. The units of E may be expressed in Btu/(hr-ft2) or W/m2. E is the total energy emitted by the surface into the space and is a multidirectional, total quantity.
It follows that radiant energy leaving an opaque surface ( = 0) comes from two sources: (1) the emitted energy and (2) the reflected irradiation.
A surface that reflects no radiation ( = 0) is said to be a blackbody, since in the absence of emitted or transmitted radiation it puts forth no radiation visible to the eye and thus appears black. A blackbody is a perfect absorber of radiation and is a useful concept and standard for study of the subject of radiation heat transfer. It can be shown that the perfect absorber of radiant energy is also a perfect emitter; thus the perfect radiant emitter is also given the name blackbody. For a given temperature T in degrees R, a black emitter exhibits a maximum monochromatic emissive power at wavelength max, given by
This equation is known as Wien's displacement law. The maximum amount of radiation is emitted in the wavelengths around the value of max. According to Wien's displacement law, as the temperature of a black emitter increases, the major part of the radiation that is being emitted shifts to shorter wavelengths. It implies that higher-temperature surfaces are primarily emitters of short-wavelength radiation and lower-temperature surfaces are primarily emitters of long-wavelength radiation. The sun, which has a surface temperature of approximately 10,000 F (6000 K), emits radiation with a maximum in the visible range. Building surfaces, which are at a much lower temperature, emit radiation primarily at much longer wavelengths.
Most surfaces are not blackbodies, but reflect some incoming radiation and emit less radiation than a blackbody at the same temperature. For such real surfaces we define one additional term, the emittance . The emittance is the fraction of the blackbody energy that a surface would emit at the same temperature, so that
The emittance can vary with the temperature of the surface and with its conditions, such as roughness, degree of contaminations, and the like.
The Earth's motion about the sun
The sun's position in the sky is a major factor in the effect of solar energy on a building. Equations for predicting the sun's position are best understood by considering the earth's motion about the sun. The earth moves in a slightly elliptical orbit about the sun (Figure 1).
The plane in which the earth rotates around the sun (approximately once every 365 ¼ days) is called the ecliptic plane or orbital plane. The mean distance from the center of the earth to the center of the sun is approximately 92.9 x 106 miles (1.5 x 108 km). The perihelion distance, when the earth is closest to the sun, is 98.3 percent of the mean distance and occurs on January 4. The aphelion distance, when the earth is farthest from the sun, is 101.7 percent of the mean distance and occurs on July 5. Because of this the earth receives about 7 percent more total radiation in January than in July.
As the earth moves it also spins about its own axis at the rate of one revolution each 24 hours. There is an additional motion because of a slow wobble or gyroscopic precession of the earth. The earth's axis of rotation is tilted 23.5 deg with respect to the orbital plane. As a result of this dual motion and tilt, the position of the sun in the sky, as seen by an observer on earth, varies with the observer's location on the earth's surface and with the time of day and the time of year. For practical purposes the sun is so small as seen by an observer on earth that it may be treated as a point source of radiation.
At the time of the vernal equinox (March 21) and of the autumnal equinox (September 22 or 23), the sun appears to be directly overhead at the equator and the earth's poles are equidistant from the sun. Equinox means "equal nights," and during the time of the two equinoxes all points on the earth (except the poles) have exactly 12 hours of darkness and 12 hours of daylight.
During the summer solstice (June 21 or 22) the north pole is inclined 23.5 deg toward the sun. All points on the earth's surface north of 66.5 deg N latitude (the Arctic Circle) are in continuous daylight, whereas all points south of 66.5 deg S latitude (the Antarctic Circle) are in continuous darkness. Relatively warm weather occurs in the northern hemisphere and relatively cold weather occurs in the southern hemisphere. The word solstice means sun standing still.
During the summer solstice the sun appears to be directly overhead at noon along the Tropic of Cancer, whereas during the winter solstice it is overhead at noon along the Tropic of Capricorn. The torrid zone is the region between, where the sun is at the zenith (directly overhead) at least once during the year. In the temperate zones (between 23.5 and 66.5 deg latitude in each hemisphere) the sun is never directly overhead but always appears above the horizon each day. The frigid zones are those zones with latitude greater than 66.5 deg, where the sun is below the horizon for at least one full day (24 hours) each year. In these two zones the sun is also above the horizon for at least one full day each year.
Time
Because of the earth's rotation about its own axis, a fixed location on the earth's surface goes through a 24-hour cycle in relation to the sun. The earth is divided into 360 deg of circular arc by longitudinal lines passing through the poles. Thus, 15 deg of longitude corresponds to 1/24 of a day or 1 hour of time. A point on the earth's surface exactly 15 deg west of another point will see the sun in exactly the same position as the first point after one hour of time has passed. Universal Time or Greenwich civil time (GCT) is the time along the zero longitude line passing through Greenwich, England. Local civil time (LCT) is determined by the longitude of the observer, the difference being four minutes of time for each degree of longitude, the more advanced time being on meridians further east. Thus when it is 12:00 noon GCT, it is 7:00 A.M. LCT along the seventy-fifth deg W longitude meridian.
Clocks are usually set for the same reading throughout a zone covering approximately 15 deg of longitude, although the borders of the time zone may be irregular to accommodate local geographical features. The local civil time for a selected meridian near the center of the zone is called the standard time. The four standard times zones in the lower 48 states and their standard meridians are
Eastern standard time, EST 75 deg
Central standard time, CST 90 deg
Mountain standard time, MST 105 deg
Pacific standard time, PST 120 deg
In much of the United States clocks are advanced one h our during the late spring, summer, and early fall season, leading to daylight saving time.
Whereas civil time is based on days that are precisely 24 hours in length, solar time has slightly variable days because of nonsymmetry of the earth's orbit, irregularities of the earth's rotational speed, and other factors. Time measured by the position of the sun is called solar time.
The local solar time (LST) can be calculated from the local civil time (LCT) with the help of a quantity called the equation of time: LST = LCT + (equation of time). The following relationship, developed from work by Spencer, may be used to determine the equation of time EOT:
where N = (n-1)(360/365), and n is the day of the year, 1 n 365. In this formulation, N is given in degrees. Values of the equation of time are given in Table 1 for the twenty-first day of each month.
Example 1
Determine the local solar time (LST) corresponding to 11:00 A.M. CDST on February 21 in the United States at 95 deg W longitude.
Given:
CDST = 11:00 A.M., February 21, 95 deg W longitude
Required:
LST
Solution:
It is first necessary to convert Central Daylight Saving Time to Central Standard Time:
CST = CDST – 1 hour = 11:00 – 1 = 10:00 A.M.
Then CST is local civil time at 90 deg W longitude. Now local civil time at 95 deg W is 5 x 4 = 20 minutes less advanced than LCT at 90 deg W. Then
LCT = CST – 20 min = 9:40 A.M.
From Table 1 the equation of time is -13.9 min. Then
LST = LCT + equation of time
LST = 9:40 – 0.14 = 9:26 A.M.
Solar Angles
The direction of the sun's rays can be described if three fundamental quantities are known:
Location on the earth's surface
Time of day
Day of the year
It is convenient to describe these three quantities by giving the latitude, the hour angle, and the sun's declination, respectively. Figure 2 shows a point P located on the surface of the earth in the northern hemisphere. The latitude l is the angle between the line OP and the projection of OP on the equatorial plane. This is the same latitude that is commonly used on globes and maps to describe the location of a point with respect to the equation.
The hour angle h is the angle between the projection of P on the equatorial plane and the projection on that plane of a line from the center of the sun to the center of the earth. Fifteen degrees of hour angle corresponds to one hour of time. The hour angle varies from zero at local solar noon to a maximum at sunrise or sunset. Solar noon occurs when the sun is at the highest point in the sky, and hour angles are symmetrical with respect to solar noon. Thus, the hour angles of sunrise and sunset on a given day are identical.
The sun's declination d is the angle between a line connecting the center of the sun and earth and the projection of that line on the equatorial plane. Figure 3 shows how the sun's declination varies throughout a typical year.
On a given day in the year, the declination varies slightly from year to year but for typical HVAC calculations the values from any year are sufficiently accurate. The following equation, developed from work by Spencer, may be used to determine declination in degrees:
where N = (n-1)(360/365), and n is the day of the year, 1 n 365. In this formulation, N is given in degrees.
It is convenient in HVAC computations to define the sun's position in the sky in terms of the solar altitude and the solar azimuth , which depend on the fundamental quantities l, h, and d.
The solar altitude (sun's altitude angle) is the angle between the sun's ray and the projection of that ray on a horizontal surface (Fig. 4). It is the angle of the sun above the horizon. It can be shown by the analytic geometry that the following relationship is true:
The sun's zenith angle is the angle between the sun's rays and a perpendicular to the horizontal plane at point P (Fig. 4). Obviously
The daily maximum altitude (solar noon) of the sun at a given location can be shown to be
where "l – d" is the absolute value of l – d.
The solar azimuth angle is the angle in the horizontal plane measured between south and the projection of the sun's rays on that plane (Fig. 4). Again by analytic geometry it can be shown that
For a vertical surface the angle measured in the horizontal plane between the projection of the sun's rays on that plane and a normal to the vertical surface is called the wall solar azimuth . Figure 5 illustrates this quantity.
If is the wall azimuth measured east or west from south, then obviously
The angle of incidence is the angle between the sun's rays and the normal to the surface, as shown in Figure 5. The angle of tilt is the angle between the normal to the surface and the normal to the horizontal surface. It may be shown that
Then for a vertical surface
And for a horizontal surface
Example No. 2
Find the solar altitude and azimuth at 10:00 A.M. central daylight saving time on July 21 at 40 deg N latitude and 85 deg W longitude.
Solution:
The local civil time
LCT = 10:00 – 1:00 + 4(90 – 85) = 9:20 A.M.
The equation of time is -6.2 min (Table 1, July 21); therefore the local solar time to the nearest minute is
LST = 9:20 – 0.06 = 9:14 A.M.
Then , (solar altitude)
h = 12:00 – 9:14 = 2 hr 46 min = 2.767 hr x 15 deg/hr = 41.5 deg
Table 1, July 21
d = 20.6 deg
l = 40 deg (given)
For (azimuth),
Solar Irradiation
The mean solar constant Gsc is the rate of irradiation on the surface normal to the sun's rays beyond the earth's atmosphere and at the mean earth-sun distance. The mean solar constant is approximately
The irradiation from the sun varies about ± 3.5 percent because of the variation in distance between the sun and earth. Because of the large amount of atmospheric absorption of this radiation, and because this absorption is so variable and difficult to predict, a precise value of the solar constant is not used in most HVAC calculations.
A part of the solar radiation entering the earth's atmosphere is scattered by gas and water vapor molecules and by cloud and dust particles. The blue color of the sky is a result of the scattering of some of the shorter wavelengths from the visible portion of the spectrum. The familiar red at sunset results from the scattering of longer wavelengths by dust or cloud particles near the earth. Some radiation (particularly ultraviolet) may be absorbed by ozone in the upper atmosphere, and other radiation is absorbed by water vapor near the earth's surface. That part of the radiation that is not scattered or absorbed and reaches the earth's surface is called direct radiation. It is accompanied by radiation that has been scattered or reemitted, called diffuse radiation. Radiation may also be reflected onto a surface from nearby surfaces. The total irradiation Gt on a surface normal to the sun's rays is thus made up of normal direct irradiation GND, diffuse irradiation Gd, and reflected irradiation GR:
ASHRAE Clear Sky Model
The value of the solar constant is for a surface outside the earth's atmosphere and does not take into account the absorption and scattering of the earth's atmosphere, which can be significant even for clear days. The value of the solar irradiation at the surface of the earth on a clear day is given by the ASHRAE Clear Sky Model:
where:
GND = normal direct irradiation, Btu/(hr-ft2) or W/m2
A = apparent solar irradiation, Btu/(hr-ft2) or W/m2
B = atmospheric extinction coefficient
= solar altitude
Values of A and B are given in Table 1 for the twenty-first day of each month and for an atmospheric clearness number CN of unity. The data in Table1, when used in the above equation do not give the maximum value of GND that can occur in any given month, but are representative of conditions on average cloudless days. The value of CN expressed as a percentage are given in Figure 6 for non-industrial locations in the United States. The use of these values will be shown below.
The diffuse radiation on a horizontal surface is given by the use of the factor C from Table 1:
where C is obviously the ratio of diffuse irradiation on a horizontal surface to direct normal irradiation. The parameter C is assumed to be a constant for an average clear day for a particular month.
A critical review of the ASHRAE Solar Radiation Model is given by Galanis and Chatigny in which they show the contradiction of using the concept of a clearness number as a multiplying factor for both the normal direct irradiation and the diffuse radiation. They suggest dividing by the square of the clearness number to give the correct behavior for the diffuse component:
Their model would then combine with an equation for the direct radiation GD on a surface of arbitrary orientation, corrected for clearness:
where is the angle of incidence between the sun's rays and the normal to the surface . The result is, for a horizontal surface where cos = sin .
To estimate the rate at which diffuse radiation Gd strikes a non-horizontal surface on a clear day, the following equation is used:
in which Fws is the configuration factor or angle factor between the wall and the sky. The configuration factor is the fraction of the diffuse radiation leaving one surface that would fall directly on another surface. For diffuse radiation this factor is a function only of the geometry of the surface or surfaces to which it is related.
The symbol for configuration factor always has two subscripts designation the surface or surfaces that it describes. For example, the configuration factor F12 applies to the two surfaces numbered 1 and 2. Then F12 is the fraction of the diffuse radiation leaving surface 1 that falls directly on surface 2. F11 is the fraction of the diffuse radiation leaving surface 1 that falls on itself and obviously is zero except for non-plane surfaces.
A very important and useful characteristic of configuration factors is the reciprocity relationship:
Its usefulness is in determining configuration factors when the reciprocal factor is known or when the reciprocal factor is more easily obtained than the desired factor.
For example, the fraction of the diffuse radiation in the sky that strikes a given surface would be difficult to determine directly. The fraction of the energy that leaves the surface and "strikes" the sky directly, Fws, however, can be easily determined from the geometry:
is the tilt angle of the surface from horizontal = in degrees.
The rate at which diffuse radiation from the sky strikes a given surface of area a is, per unit area of surface,
By reciprocity
Therefore
Thus, although the computation involves the irradiation of the sky on the surface or wall, the configuration factor most convenient to use is Fws, the one describing the fraction of the surface radiation that strikes the sky.
Example No. 3
Calculate the clear day direct, diffuse, and total solar radiation rate on a horizontal surface at 36 deg N latitude and 84 deg W longitude on June 21 at 12:00 noon CST.
Given:
l = 36 deg
84 deg W longitude
June 21 at 12:00 noon CST.
Required:
Clear day direct, diffuse, and total solar radiation rate (GD, Gd and Gt)
Solution:
From Table 1. June 21.
Equation of time = - 1.4 min, d = 23.45 deg, A = 346.3 Btu/(hr-ft2), B = 0.185, C = 0.137
Local solar time:
Hour angle, h
Solar altitude ,
For a horizontal surface cosq = sinb, so
Direct radiation
Diffuse radiation
Total radiation
A particular useful curve (Figure 8) gives the ratio of diffuse sky radiation on a vertical surface to that incident on a horizontal surface on a clear day.
The curve may be approximated by
When > -0.2; otherwise, GdV/GdH = 0.45.
In determining the total rate at which radiation strikes an arbitrarily oriented surface at any time, one must also consider the energy reflected onto the surface.
The most common case is reflection of solar energy from the ground to a tilted surface or vertical wall. For such a case the rate at which energy is reflected to the wall is
Where:
GR = rate at which energy is reflected onto the wall, Btu/(hr-ft2) or W/m2
GtH = rate at which the total radiation (direct plus diffuse) strikes the horizontal surface or ground in front of the wall, Btu/(hr-ft2) or W/m2
g = reflectance of ground or horizontal surface
Fwg = configuration or angle factor from wall to ground, defined as the fraction of the radiation leaving the wall of interest that strikes the horizontal surface or ground directly.
For a surface or wall at a tilt angle to the horizontal ( = ).
Example No. 4
Calculate the total incidence of solar radiation on a window facing south located 6 ft above the ground. In front of the window is a concrete parking area that extends 50 ft south and 50 ft to each side of the window. The window has no setback. The following parameter have been previously computed: = 69 degrees 13 min, = 17 degrees 18 min, GND = 278 Btu/(hr-ft2), GtH = 293 Btu/(hr-ft2), GdH = 33 Btu/(hr-ft2), 1 = 0.33, Fwg = 0.433.
Given:
= 69 degrees 13 min, = 17 degrees 18 min, GND = 278 Btu/(hr-ft2), GtH = 293 Btu/(hr-ft2), GdH = 33 Btu/(hr-ft2), 1 = 0.33, Fwg = 0.433.
Required:
Total incidence of solar radiation on a window
Solution:
For wall azimuth facing south, = 0
For wall solar azimuth, = + = = 17 degrees 18 min
For angle of incidence
Direct radiation:
Diffuse radiation: (From Figure 7)
Reflected component
Total radiation:
Heat Gain Through Fenestrations
The term fenestration refers to any glazed aperture in a building envelope. The components of fenestrations include:
Glazing material, either glass or plastic
Framing, mullions, muntins, and dividers
External shading devices
Internal shading devices
Integral (between-glass) shading systems
Fenestrations are important for energy use in a building, since they affect rates of heat transfer into and out of the building, are sources of air leakage, and provide daylighting, which may reduce the need for artificial lighting. The solar radiation passing inward through the fenestration glazing permits heat gains into a building that are quite different from the gains of the nontransmitting parts of the building envelope. This behavior is best seen by referring to Figure 8.
The solar gain is the sum of the transmitted radiation and the portion of the absorbed radiation that flows inward. Because heat is also conducted through the glass whenever there is an outdoor-indoor temperature difference, the total rate of heat admission is
Total heat admission through glass = Radiation transmitted through glass + Inward flow of absorbed solar radiation + Conduction heat gain.
The first two quantities on the right are related to the amount of solar radiation falling on the glass, and the third quantity occurs whether or not the sun is shining. In winter the conduction heat flow may well be outward rather than inward. The total heat gain becomes
Total heat gain = Solar heat gain + Conduction heat gain
The conduction heat gain per unit area is the product of the overall coefficient of heat transfer U for the existing fenestration and the outdoor-indoor temperature difference (to – ti).
Solar Heat Gain Coefficients
The heat gain through even the simplest window is complicated by the fact that the window is finite in size, it is framed, and the sunlight striking it does so at varying angles through the day. To fully take all of the complexities into account requires the use of not only spectral methods but also the angular radiation characteristics involved. The equation requires become quite complex, the required properties are sometimes difficult to determine, and lengthy computer calculations are involved.
The spectral method involves the development of one solar heat gain coefficient, the fraction of the incident irradiance (incident solar energy) that enters the glazing and becomes heat gain:
The SHGC includes both the directly transmitted portion and the absorbed and readmitted portion. It does not include the portion of the fenestration heat gain due to a difference in temperature between the inside and outside air. In multiple pane glazing, where the special method is required for accurate predictions, the determination of the SHGC requires a term to allow for inward flow of absorbed radiation for each of the layers.
Simplified Solar Heat Gain Calculations – SHGF
The hourly solar heat gains that occur in a unit area of double-strength sheet glass (DSA) for a given orientation and time are called the solar heat gain factors (SHGF). The term makes into account for the combined effects of both transmitted solar heat gain and absorbed solar heat gain conducted into the space. Because of refinements made in the method for calculating cooling loads, the transmitted and the absorbed solar heat gain components are now treated separately. The transmitted solar heat gain that occurs in a unit area of DSA glass for a given orientation and time is referred to as the transmitted solar heat gain factor (TSHGF). The absorbed solar heat gain that occurs in a unit area of DSA glass for a given orientation and time is referred to as the absorbed solar heat gain factor (ASHGF).
Both solar heat gain factors are calculated assuming that the direct solar irradiation GD and the diffuse solar irradiation Gd have already been determined.
The transmittance D of DSA glass to direct (beam) radiation incident at an angle is
where tj is the transmission coefficients for glass (Table 2). The transmittance D of DSA glass to diffuse radiation is given by
Note that both calculations use the transmission coefficients for glass found in Table 2. These coefficients give a normal transmittance for DSA glass of 0.80, which is slightly higher than values sometimes used. The transmitted solar heat gain factor is
Table 2. Coefficients for DSA Glass for Calculation of Transmittance and Absorptance
j
ai
tj
0
0.01154
-0.00885
1
0.77674
2.71235
2
-3.94657
-0.62062
3
8.57811
-7.07329
4
-8.38135
9.75995
5
3.01188
-3.89922
Source: ASHRAE Handbook, Fundamentals Volume, 1989 (From Reference)
The units of TSHGF will be consistent with the units of GD and Gd.
The fraction of direct (beam) solar radiation incident at an angle that is absorbed by DSA glass is
where aj is the absorption coefficients for glass (Table 2). The fraction of diffuse solar radiation absorbed by DSA glass is given by
The absorbed solar heat gain factor is then given by
Shading Coefficients (SC)
Procedures for estimating solar heat gain assume that a constant ratio exists between the solar heat gain through any given type of fenestration system and the solar heat gain (under exactly the same solar conditions) through DSA glass. This ratio, is called the shading coefficient and abbreviated SC, is unique for each type of fenestration or each combination of glazing and internal shading device:
Since the solar heat gain coefficient SHGC for standard DSA glass is 0.87 at normal incidence and for a standard solar spectrum, and since the shading coefficient SC for such a glass is 1.0, the relationship between SC and SHGC for standard glass is
This equation applies only to the glazing portion of a fenestration and does not include frame effects. The ratio remains constant as the solar spectral shape varies, and as the angle of incidence varies for clear single- and double-pane glazings and for many tinted single-pane glazings. With spectrally and angularly selective multiple pane and coated glazings, the ratio is not constant.
The shading coefficients are determined experimentally from the total solar heat gain, lumping the transmitted and absorbed components together. Thus the transmitted solar heat gain TSHG is given by
and the absorbed solar heat gain ASHG is given by
where Ni is the inward-flowing fraction of absorbed solar heat gain.
The inward-flowing fraction of the absorbed solar heat gain is dependent on the relative magnitude of the indoor and outdoor heat-transfer coefficients and is given approximately by
The values of SC are based on natural convection conditions at the inner surface of the fenestration, and a 7.5 mph (3.35 m/s) wind at the outer surface. For these conditions hi is 1.46 Btu/(hr-ft2) (0.257 W/(m2-C)) and ho is 4.0 Btu/(hr-ft2) (0.704 W/(m2-C)), which yields a value of Ni equal to 0.267. For significantly different conditions Ni may be recalculated. Finally, the instantaneous solar heat gain is SHG = TSHG + ASHG.
Example No. 5
Calculate SHGF for 2:30 P.M. local solar time, for a SW facing wall at 36 deg N latitude, 97 deg W longitude. The direct solar irradiation GD = 131 Btu/(hr-ft2), and the diffuse solar irradiation Gd = 64.1 Btu/(hr-ft2).
Given:
LST = 2:30 P.M.
SW facing wall
36 deg N latitude
97 deg W longitude
Direct solar irradiation GD = 131 Btu/(hr-ft2)
Diffuse solar irradiation Gd = 64.1 Btu/(hr-ft2).
Required:
SHGF
Solution:
Transmitted solar heat gain factor, using Table 2.
where cos = cos(61.7) = 0.4741.
Absorbed solar heat gain factor, using Table 2
Then, total solar heat gain is the sum of transmitted and the inward-flowing part of the absorbed energy
External Shading
A fenestration may be shaded by roof overhangs, side fins or other parts of the building, trees, or another building. External shading of fenestrations is effective in reducing solar heat gain to a space and may be produce reductions of up to 80 percent. The shading coefficient SC is not appropriate to use in determining the effect of external shade, since its purpose is to allow only for the effect of the fenestration and its internal shading devices. The SC will be used in heat gain calculations whether the fenestration is externally shaded or not. What is needed in considering heat gains affected by external shade is the areas of the fenestrations that are externally shaded. These areas on which external shade falls can be calculated from the geometry of the external objects creating the shade and from knowledge of the sun angles for that particular time and location.
Figure 9 illustrates a window that is set back into the structure, where shading may occur on the sides and top, depending on the time of day and the direction the window faces. It can be shown that the dimensions x and y in Figure 9 are given by
where
and
= sun's altitude angle
= wall solar azimuth angle ( ± )
= solar azimuth
= wall azimuth measured east or west from the south
The following rules aid in the computation of the wall solar azimuth angle : For morning hours, with walls facing east of south and afternoon hours with walls facing west of south
For afternoon hours with the walls facing east of south and morning hours with walls facing west of south.
If is greater than 90 deg, the surface is in the shade.
Example 6
A 4 x 5 ft, ¼ in. regular plate glass windows faces southwest. The top of the window has a 2 ft overhang that extends a great distance on each side of the window. Compute the shaded area of the window on July 21 at 3:00 P.M. solar time at 40- deg N latitude.
Given:
Window area = 4 ft x 5 ft
Facing southwest
2 ft overhung
July 21 at 3:00 P.M. solar time
40 deg N latitude
Required:
Shaded area of the window
Solution:
To find the area, the dimension y must be computed.
From equations given before, = 47.0 deg and = 76.6 deg, respectively.
The wall azimuth for a window facing southwest is 45 deg.
For a wall facing west of south and for afternoon hours on July 21 at 3:00 P.M. solar time at 40 deg N latitude,
Then
The shaded area is then
and the sunlit portion has an area of
The shaded portion of a window receives only indirect (diffuse) radiation.
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