For convenience of the designer, tables have been constructed that give overall coef- ficients for many common building sections, including walls and floors, doors, win- dows, and skylights. The tables used in the ASHRAE Handbook(1) have a great deal of flexibility and are summarized in the following pages.
Walls and Roofs
Walls and roofs vary considerably in the materials from which they are constructed.
Therefore, the thermal resistance or the overall heat transfer coefficient is usually computed for each unique component using Eqs. 5-14 and 5-19. This procedure is
q˙ =UA t∆ U = R A R
′ =
1 1
Btu/(hr-ft -F) or W/(m -C)2 2
demonstrated for a wall and a roof in Tables 5-4aand 5-4b. Note that in each case an element has been changed. The tabular presentation makes it simple to recalculate the thermal resistance due to the element change. In each case the unit thermal resistance and the overall heat-transfer coefficient have been computed for one set of conditions.
EXAMPLE 5-1
A frame wall is modified to have in. of mineral fiber insulation between the studs.
Compute the overall heat-transfer coefficient Uif the unit thermal resistance without the insulation is 4.44 (hr-ft2-F)/Btu. Assume a mean temperature of 0 F and a tem- perature difference of 20 F.
SOLUTION
Total unit resistance given 4.44
Deduct the air space unit resistance, Table 5-3 –1.14 Add insulation unit resistance given in Table 5-1a
R =1/C=1/0.067 =14.93 14.93
Total Rin (hr-ft2-F)/Btu 18.23
312
5-2 Tabulated Overall Heat-Transfer Coefficients 139
Table 5-4a Coefficients of Transmission Uof Masonry Cavity Walls, Btu/(hr-ft2-F)a
Between At Between At
Item Furring Furring Furring Furring
1. Outside surface 0.17 0.17 0.17 0.17
(15 mph wind)
2. Face brick, 4 in. 0.44 0.44 0.44 0.44
3. Cement mortar, 0.5 in. 0.10 0.10 0.10 0.10
4. Concrete blockb 1.72 1.72 2.99 2.99
5. Reflective air space, 2.77 — 2.77 —
0.75 in. (50 F mean;
30 F temperature difference)
6. Nominal 1 × 3 in. — 0.94 — 0.94
vertical furring
7. Gypsum wallboard, 0.45 0.45 0.45 0.45
0.5 in., foil backed
8. Inside surface (still air) 0.68 0.68 0.68 0.68 Total thermal resistance R Ri=6.33 Rs=4.50 Ri=7.60 Rs=5.77 Construction 1:Ui=1/6.33 =0.158; Us=1/4.50 =0.222. With 20% framing (typical of 1 ×3 in.
vertical furring on masonry @ 16 in. o.c.),Uav=0.8(0.158) +0.2(0.222) =0.171 Construction 2:Ui=1/7.60 =0.132Us=1/5.77 =0.173.
With framing unchanged,Uav=0.8(0.132) +0.2(0.173) =0.140
aUfactor may be converted to W/(m2-C) by multiplying by 5.68.
b8 in. cinder aggregate in construction 1; 6 in. lightweight aggregate with cores filled in construction 2.
Source: Adapted by permission from ASHRAE Handbook, Fundamentals Volume,1997.
Construction 1 Construction 2 Resistance R (hr-ft2-F)/Btu
1 2 3 4 5 6 7 8
Then, based on one square foot, we see that
Equation 5-18 may be used to correct Ror Ufor framing (2 ×4 studs on 16 in. centers):
where:
At =total area, using Ucorrected,Uc
Ab=area between studs, using Ub=Ufor wall section described Af=area occupied by the studs, using Utconsidering studs
The unit thermal resistance of a section through the 2 ×4 stud is equal to the total resistance less the resistance of the air gap plus the resistance of the stud from Table 5-1a. A 2 ×4 stud is only in. deep and in. wide. Thus,
Rf = U1f = − + = 4 4. 1 14. 3 5 0 9. / . 7 15.
312 312
1 1 1
′ =
′ +
′ = +
R R R or U A U A U A
c f
c t b b f f
, U = R1 = 1 =
18 23 0 055
. . Btu/(hr-ft -F)2 Table 5-4b Coefficients of Transmission Uof Flat Built-up Roofsa
Item Construction 1 Construction 2
1. Outside surface 0.17 0.17
(15 mph wind)
2. Built-up roofing, 0.375 in. 0.33 0.33
3. Rigid roof deck insulationb — 4.17
4. Concrete slab, lightweight 2.22 2.22 aggregate, 2 in.
5. Corrugated metal deck 0 0
6. Metal ceiling suspension 0c 0c
system with metal hanger rods
7. Nonreflective air space, 0.93d 0.93d greater than 3.5 in. (50 F mean;
10 F temperature difference)
8. Metal lath and lightweight 0.47 0.47 aggregate plaster, 0.75 in.
9. Inside surface (still air) 0.61 0.61
Total thermal resistance R 4.73 8.90
Construction 1:Uavg=1/4.73 =0.211 Btu/(hr-ft2-F)e Construction 2:Uavg=1/8.90 =0.112 Btu/(hr-ft2-F)e
aHeat flowup. Use largest air space (3.5 in.) value shown in Table 5-3a.
bIn construction 2 only.
cArea of hanger rods is negligible in relation to ceiling area.
dUse largest air space (3.5 in.) shown in Table 5-3a.
eU-factor may be converted to W/(m2-C) by multiplying by 5.68.
Resistance R
9 8 7 6 5 4 3 2 1
so that
Then using Eq. 5-18 we get
EXAMPLE 5-2
Compute the overall average coefficient for the roof–ceiling combination shown in Table 5-4b with 3.5 in. of mineral fiber batt insulation (R-15) in the ceiling space rather than the rigid roof deck insulation.
SOLUTION
The total unit resistance of the ceiling–floor combination in Table 5-4b,construction 1, with no insulation is 4.73 (hr-ft2-F)/Btu. Assume an air space greater than 3.5 in.
Total resistance without insulation 4.73
Add mineral fiber insulation, 3.5 in. 15.00
Total R[(hr-ft2-F)/Btu] 19.73
Total U[Btu/(ft2-hr-F)] 0.05
The data given in Tables 5-4aand 5-4band Examples 5-1 and 5-2 are based on 1. Steady-state heat transfer
2. Ideal construction methods
3. Surrounding surfaces at ambient air temperature
4. Variation of thermal conductivity with temperature negligible
Some caution should be exercised in applying calculated overall heat transfer coeffi- cients such as those of Tables 5-4aand 5-4b, because the effects of poor workman- ship and materials are not included. Although a safety factor is not usually applied, a moderate increase in Umay be justified in some cases.
The overall heat-transfer coefficients obtained for walls and roofs should always be adjusted for thermal bridging, as shown in Tables 5-4aand 5-4b, using Eq. 5-18.
This adjustment will normally be 5 to 15 percent of the unadjusted coefficient.
The coefficients of Tables 5-4aand 5-4bhave all been computed for a 15 mph wind velocity on outside surfaces and should be adjusted for other velocities. The data of Table 5-2a may be used for this purpose.
The following example illustrates the calculation of an overall heat-transfer coef- ficient for an unvented roof–ceiling system.
EXAMPLE 5-3
Compute the overall heat-transfer coefficient for the roof–ceiling combination shown in Fig. 5-6. The wall assembly is similar to Table 5-4awith an overall heat-transfer
Uc = ( . )( . )+( . )( . ) = 0 055 14 5 0 140 1 5 .
16 0 063 Btu/(hr-ft -F)2 Uf =0 140. Btu/(hr-ft -F)2
5-2 Tabulated Overall Heat-Transfer Coefficients 141
coefficient of 0.16 Btu/(hr-ft2-F). The roof assembly is similar to Table 5-4bwithout the ceiling and has a conductance of 0.13 Btu/(hr-ft2-F) between the air space and the outdoor air. The ceiling has a conductance of 0.2 Btu/(hr-ft2-F) between the condi- tioned space and the ceiling air space. The air space is 2.0 ft in the vertical direction.
The ceiling has an area of 15,000 ft2and a perimeter of 500 ft.
SOLUTION
It is customary to base the overall heat-transfer coefficient on the ceiling area. Note that heat can enter or leave the air space through the roof or around the perimeter through the wall enclosing the space. The thermal resistances of the roof and the wall are in parallel and together are in series with the resistance of the ceiling. Then for roof and wall, since R′ =1/CAand conductances in parallel are summed,
The thermal resistance for the roof–wall assembly is
Further, the thermal resistance for the roof–wall–ceiling is
and
Substitution yields
′ = + +
′ = =
R
R U A
o
o
o c
1
0 16 2 500 0 13 15 000
1 0 2 15 000 0 000807 1
( . )( )( ) ( . )( , ) ( . )( , ) .
′ = + +
Ro C Aw w C Ar r C Ac c
1 1
′ = ′ + ′ Ro Rrw Rc
′ = =
R +
C A C A C A
rw
rw rw w w r r
1 1
C Arw rw =C Aw w +C Ar r Figure 5-6 Section of a roof–ceiling combination.
Roof assembly
Ceiling Air space
Wall
assembly Conditioned space
Then
Ceiling spaces should be vented to remove potentially damaging moisture, but only moderate ventilation rates are required. The effect of ventilation on the transfer of heat through the air space above the ceiling is not significant provided the ceiling is insu- lated with a unit thermal resistance of about 19 or more. This is true for both winter and summer conditions. It once was thought that increased ventilation during the sum- mer would dramatically reduce the heat gain to the inside space; however, this is apparently incorrect (2). It is generally not economically feasible to use power venti- lation. The main reason for the ineffectiveness of ventilation is the fact that most of the heat transfer through the attic is by thermal radiation between the roof and the ceil- ing insulation. The use of reflective surfaces is therefore much more useful in reduc- ing heat transfer. It is recommended that calculation of the overall transmission coefficient for ceiling spaces be computed using the approach of Example 5-3 with appropriate unit resistances and assuming no ventilation.
Windows
Tables 5-5a and 5-5b contain overall heat-transfer coefficients for a range of fenes- tration products for vertical installation. The values given are for winter design con- ditions; however, when corrected for wind velocity using Table 5-7, the data are appropriate for estimating design loads for summer conditions. The U-factors are based on the rough opening area and account for the effect of the frame. Transmission coefficients are given for the center and edge of the glass. Tables 5-5aand 5-5bapply only for air-to-air heat transfer and do not account for solar radiation, which will be discussed in Chapter 6.
Table 5-6 gives U-factors for only the frames of fenestrations that are useful in some cooling load procedures (see Chapter 8).
Doors
Table 5-8 gives overall heat-transfer coefficients for common doors. The values are for winter design conditions; however, they are also appropriate for estimating design loads for summer conditions. Solar radiation has not been included.
Concrete Floors and Walls Below Grade
The heat transfer through basement walls and floors depends on the temperature differ- ence between the inside air and the ground, the wall or floor material (usually concrete), and the conductivity of the ground. All of these factors involve considerable uncertainty.
Mitalas (3) and Krarti and colleagues (4) have studied the below-grade heat-transfer problem and developed methods that predict seasonal heat losses for basement walls and floors below grade. However, these methods are not readily adapted to simple heat load calculations. Tables 5-9 and 5-10 give reasonable results for load calculations but should not be used for annual or seasonal load estimates. Judgment must be used in selecting data for basement floors less than 5 ft (1.5 m) below grade since published data is not available. The situation gradually changes from that of a basement floor to a slab near
Uo = 1 =
0 000807 15 000 0 083
( . )( , ) . Btu/(hr-ft -F)2
5-2 Tabulated Overall Heat-Transfer Coefficients 143
Fixed Frame:
Glass Only
Operable (Including Sliding and Swinging Glass Doors) Table 5-5a U-Factors for Various Fenestration Products, Btu/(hr-ft2-F) (Vertical Installation)a
Aluminum Aluminum Reinforced
Center Edge without with Vinyl/ Insulated Insulated of of Thermal Thermal Aluminum- Wood/ Fiberglass/ Fiberglass/
Glass Glass Break Break Clad Wood Vinyl Vinyl Vinyl Single Glazing
in. glass 1.04 1.04 1.27 1.08 0.90 0.89 0.81 0.94
in. acrylic/ 0.88 0.88 1.14 0.96 0.79 0.78 0.71 0.81
polycarb
in. acrylic/ 0.96 0.96 1.21 1.02 0.85 0.83 0.76 0.87
polycarb Double Glazing
in. air space 0.55 0.64 0.87 0.65 0.57 0.55 0.49 0.53
in. air space 0.48 0.59 0.81 0.60 0.53 0.51 0.44 0.48
in. argon space 0.51 0.61 0.84 0.62 0.55 0.53 0.46 0.50
Double Glazing,=0.60 on surface 2 or 3
in. air space 0.52 0.62 0.84 0.63 0.55 0.53 0.47 0.51
in. air space 0.44 0.56 0.78 0.57 0.50 0.48 0.42 0.45
in. argon space 0.47 0.58 0.81 0.59 0.52 0.50 0.44 0.47
Double Glazing,=0.10 on surface 2 or 3
in. air space 0.42 0.55 0.77 0.56 0.49 0.47 0.41 0.43
in. air space 0.32 0.48 0.69 0.49 0.42 0.40 0.35 0.35
in. argon space 0.35 0.50 0.71 0.51 0.44 0.42 0.36 0.37
in. argon space 0.27 0.44 0.65 0.45 0.39 0.37 0.31 0.31
Triple Glazing
in. air space 0.38 0.52 0.72 0.51 0.44 0.43 0.38 0.40
in. air space 0.31 0.47 0.67 0.46 0.40 0.39 0.34 0.34
in. argon space 0.34 0.49 0.69 0.48 0.42 0.41 0.35 0.36
Triple Glazing,=0.20 on surfaces 2 or 3 and 4 or 5
in. air space 0.29 0.45 0.65 0.44 0.38 0.37 0.32 0.32
in. air space 0.20 0.39 0.58 0.38 0.32 0.31 0.27 0.25
in. argon space 0.23 0.41 0.61 0.40 0.34 0.33 0.29 0.28
Triple Glazing,=0.10 on surfaces 2 or 3 and 4 or 5
in. air space 0.27 0.44 0.64 0.43 0.37 0.36 0.31 0.31
in. air space 0.18 0.37 0.57 0.36 0.31 0.30 0.25 0.23
in. air space 0.21 0.39 0.59 0.39 0.33 0.32 0.27 0.26
Quadruple Glazing,=0.10 on surfaces 2 or 3 and 4 or 5
in. air space 0.22 0.40 0.60 0.39 0.34 0.33 0.28 0.27
aHeat transmission coefficients are based on winter conditions of 0 F outdoors and 70 F indoors with 15 mph wind and zero solar flux. Small changes in the indoor and outdoor temperatures will not significantly affect the overall U-factors. Glazing layers are numbered from outdoor to indoor.
Source: Reprinted by permission from ASHRAE Handbook, Fundamentals Volume, 1997.
1 4 1 4 1 2 1 4 1 4 1 2 1 4 1 4 1 2 1 4 1 2 1 4 1 2 1 4 1 4 1 2 1 4 1 4 1 2 1 4 1 8 1 4 1 8
5-2 Tabulated Overall Heat-Transfer Coefficients 145
Table 5-5b U-Factors for Various Fenestration Products, W/(m2-K) (Vertical Installation)a
Aluminum Aluminum Reinforced
Center Edge without with Vinyl/ Insulated Insulated of of Thermal Thermal Aluminum- Wood/ Fiberglass/ Fiberglass/
Glass Glass Break Break Clad Wood Vinyl Vinyl Vinyl Single Glazing
3.2 mm glass 5.91 5.91 7.24 6.12 5.14 5.05 4.61 5.35
6.4 mm acrylic/ 5.00 5.00 6.49 5.43 4.51 4.42 4.01 4.58
polycarb
3.2 mm acrylic/ 5.45 5.45 6.87 5.77 4.82 4.73 4.31 4.97
polycarb Double Glazing
6.4 mm air space 3.12 3.63 4.93 3.70 3.25 3.13 2.77 3.04
12.7 mm air space 2.73 3.36 4.62 3.42 3.00 2.87 2.53 2.72
6.4 mm argon 2.90 3.48 4.75 3.54 3.11 2.98 2.63 2.85
space
Double Glazing,=0.60 on surface 2 or 3
6.4 mm air space 2.95 3.52 4.80 3.58 3.14 3.02 2.67 2.90
12.7 mm air space 2.50 3.20 4.45 3.26 2.85 2.73 2.39 2.54
6.4 mm argon 2.67 3.32 4.58 3.38 2.96 2.84 2.49 2.67
space
Double Glazing,=0.10 on surface 2 or 3
6.4 mm air space 2.39 3.12 4.36 3.17 2.78 2.65 2.32 2.45
12.7 mm air space 1.82 2.71 3.92 2.77 2.41 2.28 1.96 1.99
6.4 mm argon 1.99 2.83 4.05 2.89 2.52 2.39 2.07 2.13
space
12.7 mm argon 1.59 2.49 3.70 2.56 2.22 2.10 1.79 1.76
space Triple Glazing
6.4 mm air space 2.16 2.96 4.11 2.89 2.51 2.45 2.16 2.25
12.7 mm air space 1.76 2.67 3.80 2.60 2.25 2.19 1.91 1.93
6.4 mm argon 1.93 2.79 3.94 2.73 2.36 2.30 2.01 2.07
space
Triple Glazing,=0.20 on surfaces 2 or 3 and 4 or 5
6.4 mm air space 1.65 2.58 3.71 2.52 2.17 2.12 1.84 1.84
12.7 mm air space 1.14 2.19 3.31 2.15 1.84 1.78 1.52 1.43
6.4 mm argon 1.31 2.32 3.45 2.27 1.95 1.90 1.62 1.56
space
Triple Glazing,=0.10 on surfaces 2 or 3 and 4 or 5
6.4 mm air space 1.53 2.49 3.63 2.44 2.10 2.05 1.77 1.75
12.7 mm air space 1.02 2.10 3.22 2.07 1.76 1.71 1.45 1.33
6.4 mm argon 1.19 2.23 3.36 2.19 1.87 1.82 1.55 1.47
space
Quadruple Glazing,=0.10 on surfaces 2 or 3 and 4 or 5
6.4 mm air spaces 1.25 2.28 3.40 2.23 1.91 1.86 1.59 1.52
aHeat transmission coefficients are based on winter conditions of –18 C outdoors and 21 C indoors with 24 km/h wind and zero solar flux. Small changes in the indoor and outdoor temperatures will not significantly affect the overall U-factors. Glazing layers are numbered from outdoor to indoor.
Source: Reprinted with permission from ASHRAE Handbook, Fundamentals Volume, 1997.
Fixed Frame:
Glass Only
Operable (Including Sliding and Swinging Glass Doors)
Table 5-6 Representative Fenestration Frame U-Factors, Btu/(hr-ft2-F) or W/(m2-K) (Vertical Installation)
Type of
Framed Material Spacer Singleb Doublec Tripled Singleb Doublec Tripled
Aluminum without All 2.38 2.27 2.20 1.92 1.80 1.74
thermal break (13.51) (12.89) (12.49) (10.90) (10.22) (9.88)
Aluminum with Metal 1.20 0.92 0.83 1.32 1.13 1.11
thermal breaka (6.81) (5.22) (4.71) (7.49) (6.42) (6.30)
Insulated n/a 0.88 0.77 n/a 1.04 1.02
(n/a) (5.00) (4.37) (n/a) (5.91) (5.79)
Aluminum-clad wood/ Metal 0.60 0.58 0.51 0.55 0.51 0.48
reinforced vinyl (3.41) (3.29) (2.90) (3.12) (2.90) (2.73)
Insulated n/a 0.55 0.48 n/a 0.48 0.44
(n/a) (3.12) (2.73) (n/a) (2.73) (2.50)
Wood vinyl Metal 0.55 0.51 0.48 0.55 0.48 0.42
(3.12) (2.90) (2.73) (3.12) (2.73) (2.38)
Insulated n/a 0.49 0.40 n/a 0.42 0.35
(n/a) (2.78) (2.27) (n/a) (2.38) (1.99)
Insulated fiberglass/ Metal 0.37 0.33 0.32 0.37 0.33 0.32
vinyl (2.10) (1.87) (1.82) (2.10) (1.87) (1.82)
Insulated n/a 0.32 0.26 n/a 0.32 0.26
(n/a) (1.82) (1.48) (n/a) (1.82) (1.48) Note: This table should only be used as an estimating tool for the early phases of design.
aDepends strongly on width of thermal break. Value given is for in. (9.5 mm) (nominal).
bSingle glazing corresponds to individual glazing unit thickness of in. (3 mm) (nominal).
cDouble glazing corresponds to individual glazing unit thickness of in. (19 mm) (nominal).
dTriple glazing corresponds to individual glazing unit thickness of in. (34.9 mm) (nominal).
Source: ASHRAE Handbook,Fundamentals Volume. © American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 2001.
138
3 4 1 8 3 8
Operable
Product Type/Number of Glazing Layers Fixed
Table 5-7 Glazing U-Factor for Various Wind Speeds U-Factor, Btu/(hr-ft2-F) [W/(m2-C)]
Wind Speed 15 (24) 7.5 (12) 0 mph (km/h) 0.10 (0.5) 0.10 (0.46) 0.10 (0.42) 0.20 (1.0) 0.20 (0.92) 0.19 (0.85) 0.30 (1.5) 0.29 (1.33) 0.28 (1.27) 0.40 (2.0) 0.38 (1.74) 0.37 (1.69) 0.50 (2.5) 0.47 (2.15) 0.45 (2.12) 0.60 (3.0) 0.56 (2.56) 0.53 (2.54) 0.70 (3.5) 0.65 (2.98) 0.61 (2.96) 0.80 (4.0) 0.74 (3.39) 0.69 (3.38) 0.90 (4.5) 0.83 (3.80) 0.78 (3.81) 1.0 (5.0) 0.92 (4.21) 0.86 (4.23) 1.1 (5.5) 1.01 (4.62) 0.94 (4.65) 1.2 (6.0) 1.10 (5.03) 1.02 (5.08) 1.3 (6.5) 1.19 (5.95) 1.10 (5.50) Source:Reprinted with permission from ASHRAE
Handbook, Fundamentals Volume, 1997.
5-2 Tabulated Overall Heat-Transfer Coefficients 147
Table 5-8 Transmission Coefficients Ufor Wood and Steel Doors
No Metal
Nominal Door Storm Storm
Thickness in. (mm) Description Door Door1a
Wood Doorsb,c Btu/(hr-ft2-F) [W/(m2-c)]
(35) Panel door with in. panelsd 0.57 (3.24) 0.37 (2.10)
(35) Hollow core flush door 0.47 (2.67) 0.32 (1.82)
(35) Solid core flush door 0.39 (2.21) 0.28 (1.59)
(45) Panel door with in. panelsd 0.54 (3.07) 0.36 (2.04)
(45) Hollow core flush door 0.46 (2.61) 0.32 (1.82)
(45) Panel door with in. panelsd 0.39 (2.21) 0.28 (1.59)
(45) Solid core flush door 0.40 (2.27) 0.26 (1.48)
(57) Solid core flush door 0.27 (1.53) 0.21 (1.19)
Steel Doorsc
(45) Fiberglass or mineral wool core with steel 0.60 (3.41) — stiffeners, no thermal breake
(45) Paper honeycomb core without thermal breake 0.56 (3.18) — (45) Solid urethane foam core without thermal breakb 0.40 (2.27) — (45) Solid fire-rated mineral fiberboard core without 0.38 (2.16) —
thermal breake
(45) Polystyrene core without thermal break 0.35 (1.99) —
(18-gage commercial steel)e
(45) Polyurethane core without thermal break 0.29 (1.65) —
(18-gage commercial steel)e
(45) Polyurethane core without thermal break 0.29 (1.65) —
(24-gage commercial steel)e
(45) Polyurethane core with thermal break and wood 0.20 (1.14) — perimeter (24-gage residential steel)e
(45) Solid urethane foam core with thermal breakb 0.20 (1.14) 0.16 (0.91) Note: All U-factors are for exterior door with no glazing, except for the storm doors that are in addition to the main exterior door. Any glazing area in exterior doors should be included with the appropriate glass type and analyzed. Interpolation and moderate extrapolation are permitted for door thicknesses other than those specified.
aValues for metal storm door are for any percent glass area.
bValues are based on a nominal 32 ×80 in. door size with no glazing.
cOutside air conditions: 15 mph wind speed, 0 F air temperature; inside air conditions: natural convection, 70 F air temperature.
d55 percent panel area.
eASTM C 236 hotbox data on a nominal 3 ×7 ft door with no glazing.
Source: ASHRAE Handbook,Fundamentals Volume. © American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 2001.
134 134 134 134 134 134 134 134 134 214 134
118 134
134
7
138 16
138 138
7
138 16
Table 5-9 Heat Loss Through Below-Grade Basement Wallsa
R-4.17 R-0.73 R-8.34 R-1.47 R-12.5 R-2.20
(hr-ft2-F)/ (m2-C)/ (hr-ft2-F)/ (m2-C)/ (hr-ft2-F)/ (m2-C)/
ft m Uninsulated Btu W Btu W Btu W
1 0.3 0.410 2.33 0.152 0.86 0.093 0.53 0.067 0.38
2 0.6 0.316 1.79 0.134 0.76 0.086 0.49 0.063 0.36
3 0.9 0.262 1.49 0.121 0.69 0.080 0.45 0.060 0.34
4 1.2 0.227 1.29 0.110 0.63 0.075 0.43 0.057 0.32
5 1.5 0.200 1.14 1.102 0.58 0.071 0.40 0.054 0.31
6 1.8 0.180 1.02 0.095 0.54 0.067 0.38 0.052 0.29
7 2.1 0.164 0.93 0.089 0.51 0.064 0.36 0.050 0.28
aLatta and Boileau,Canadian Building(5).
bSoil conductivity, 9.6 Btu-in./(hr-ft2-F) or 1.38 W/(m-C).
cAverage U-factor to the given depth.
d∆t=(ti− ta− A).
Source: Reprinted with permission from ASHRAE Handbook, Fundamentals Volume,1997.
Average Heat Loss Coefficient, Btu/(hr-ft2-F)/Btu or W/(m2-C)b,c,d Basement
Depth
Table 5-10 Heat Loss Through Basement Floorsa,b
ft m ft m ft m ft m
ft m 20.009 6.00 24.009 7.30 28.000 8.50 32.000 9.70
5 1.5 0.032 0.18 0.029 0.16 0.026 0.15 0.023 0.13
6 1.8 0.030 0.17 0.027 0.15 0.025 0.14 0.022 0.12
7 2.1 0.029 0.16 0.026 0.15 0.023 0.13 0.021 0.12
aLatta and Boileau,Canadian Building(6).
b∆t=(ti− ta− A).
Source: Reprinted with permission from ASHRAE Handbook, Fundamentals Volume,1997.
Heat Loss Coefficient, Btu/(hr-ft2-F) or W/(m2-C)b Shortest Width of Basement
Depth of Basement Wall below Grade
Figure 5-7 Lines of constant amplitude of ground surface temperature variation. (Reprinted by permission from ASHRAE Handbook, Fundamentals Volume, 1989.)
27 F (15 C)
18 F (10 C)
18 F (10 C)
9 F (5 C) 5 F (3 C) 60
40
20
10 20 30 40 50 60
14 F (8 C) 22 F (12 C)
or on grade. It is reasonable to use slab on grade data, discussed below, down to about 3 ft (90 cm) and use the data of Table 5-10 for 5 ft (1.5 m) below 3 ft (90 cm).
Studies have shown that the heat losses from below-grade walls and floors are far more dependent on the ground temperature near the surface than on the deep ground temperature. Ground surface temperature is known to vary about a mean value by an amplitude (Amp) that varies with geographic location (Fig. 5-7). The mean ground sur- face temperature is assumed to be the average annual air temperature (1) (Table 5-11).
However, research by Kusuda (7) suggests that the mean ground temperatures are about 10 F (6 C) higher.
The heat loss is given by
(5-20) where:
U=overall heat-transfer coefficient from Tables 5-9 or 5-10, Btu/(hr-ft2-F) or W/(m2-C)
A=wall or floor surface area below 3 ft (0.9 m), ft2or m2 ti=inside air temperature, F or C
and
(5-21) where:
tg=design ground surface temperature, F or C
tavg=average annual air temperature, F or C (Table 5-11)
Amp=amplitude of ground temperature variation about tavg, F or C (Fig. 5-7) The minimum ground surface temperature in the northern hemisphere is assumed to occur around February 1st, about the same time as the peak heating load occurs.
When basement spaces are conditioned as living space, the walls should be furred and finished with a vapor barrier, insulating board, and some type of finish layer such
tg = tavg −Amp
˙ ( )
q =UA ti −tg
5-2 Tabulated Overall Heat-Transfer Coefficients 149
Table 5-11 Average Annual Air Temperatures for Selected Cities in the United Statesa
State and City F C
Arkansas, Little Rock 50.5 10.6
Colorado, Denver 37.6 3.44
District of Columbia, Washington 45.7 7.94
Illinois, Chicago 35.8 2.44
Kentucky, Louisville 44.0 6.70
Maine, Portland 33.0 0.6
Michigan, Alpena 29.7 −1.3
Minnesota, Duluth 23.4 −4.8
Montana, Glasgow 26.4 −3.1
New York, Syracuse 35.2 1.8
North Dakota, Minot 22.4 −5.3
Oklahoma, Oklahoma City 48.3 9.39
aData from Monthly Normals of Temperature, Precipitation and Heating Degree Days, 1962, for the period 1931–1960.
Average Winter Temperature
as paneling. This will add thermal resistance to the wall. The basement floor should also be finished by installing an insulating barrier and floor tile or carpet. The overall coefficients for the finished wall or floor may be computed as
(5-22)
Floor Slabs at Grade Level
Analysis has shown that most of the heat loss is from the edge of a concrete floor slab.
When compared with the total heat losses of the structure, this loss may not be sig- nificant; however, from the viewpoint of comfort the heat loss that lowers the floor temperature is important. Proper insulation around the perimenter of the slab is essen- tial in severe climates to ensure a reasonably warm floor.
Figure 5-8 shows typical placement of edge insulation and heat loss factors for a floor slab. Location of the insulation in either the vertical or horizontal position has
′ = ′ + ′ = + ′ =
R R R
UA R
a f f U A
a
1 1
Figure 5-8 Heat loss factors for slab floors on grade. (Reprinted by permission from ASHRAE Handbook, Systems and Equipment Volume,2000.)
2.6 2.4 2.0
1.6
Insulation Conductance, W/(m2− C)
Edge heat loss coefficient, Btu/(hr−ft−Ft) Edge heat loss coefficient, W/(m − C)
0.8 1.2 2.25
2.2 2.0 1.8 1.6 1.4
1.2 0.6
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
0.4 0.3
Insulation conductance, Btu/(h−ft2−F) 0.2
0.1
Insulation at slab edge only (d = 0) Heat loss = 1.8 Btu/(hr-ft-F) [3.1 W/(m − C)] with no insulation
d = 1 ft (0.3 m) d = 2 ft (0.61 m)
d = 3 ft (0.91 m) Either way Foundation
Grade
Slab
d Earth
about the same effect. Insulation may also be placed on the outside of the foundation wall, extending down to the footing with about the same result. Sometimes heating ducts are installed below the floor slab with air outlets near the perimeter. This will increase the heat loss by 30 to 50 percent even with insulation as shown in Fig. 5-8.
Note that the heat-loss factors given in Fig. 5-8 are expressed as heat-transfer rate per unit length of perimeter per degree temperature difference between the inside and out- door design temperatures. For summer conditions the heat transfer to the floor slab is negligible.
The heat loss from the slab is expressed as
(5-23) where:
U′ =heat loss coefficient, Btu/(hr-ft-F) or W/(m-C) P =Perimeter of slab, ft or m
ti =inside air temperature, F or C to=outdoor design temperature, F or C
Crawl Spaces
The usual approach to determining the heat loss through a crawl space is to first esti- mate its temperature. A heat balance on the crawl space taking into account the vari- ous gains and losses will yield the temperature. Heat is transferred to the crawl space through the floor and lost through the foundation wall and the ground, much as it is through a slab on grade. Outdoor air may also infiltrate the crawl space and contribute to the heat loss. The inside or outside of the foundation wall may be insulated, and insulation may extend inward from the base of the foundation wall. The following example illustrates the crawl space problem.
EXAMPLE 5-4
Estimate the temperature and heat loss through the crawl space of Fig. 5-9. The con- ductance for the floor is 0.20 Btu/(hr-ft2-F) including the air film on each side. The conductance for the foundation wall including the insulation and inside and outside air film resistances is 0.12 Btu/(hr-ft2-F). Assume an indoor temperature of 70 F and an outdoor temperature of −6 F in Chicago, IL. The building dimensions are 50 ×75 ft.
Neglect any infiltration of outdoor air.
SOLUTION
The first step is to make an energy balance on the crawl space as suggested above. We have
or
C A t t C A t t U P t t
t t CA t U P t CA
CA CA U P
fl fl i c fo fo c o o g
c
o fo o i fl
fl fo g
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
− = − + ′ −
= + ′ +
+ + ′
˙ ˙ ˙
qfl = qfo +qground
˙ ( )
q = ′U P ti −to
5-2 Tabulated Overall Heat-Transfer Coefficients 151