1. Technology in Architecture
Lecture 5
Heat Flow in Opaque Materials
Thermal Mass

2. Conductive Heat Flow Conductive Heat Flow through opaque materials:
Q= U x A x ΔT
Q: heat flow (Btuh)
U: transmission coefficient (Btu/h-ºF-ft2)
A: area (ft2)
ΔT: temperature difference (Ti-To)

3. Transmission Coefficient
Transmission Coefficient (U):
U= 1/ΣR
U: transmission coefficient (Btu/h-ºF-ft2)
ΣR: sum of resistance values (R-values) for layers of a construction assembly

4. Summing R-values Sum of R-values (ΣR):
ΣR= 1/hO+R1+R2+R3+…+1/hI
hO,hI: film surface conductance coefficients
R1,R2,R3,…: Resistance values (R-values) for each layer of a construction assembly

5. Film surface conductance coefficient Outdoor air film: R= 1/hO
Air Films
Film surface conductance coefficient
Outdoor air film: R= 1/hO
Indoor air film: R=1/hI

6. Finding hO and hI – Emittance
Emittance(ε): absorption of radiant heat
S: p.1612, T.E.3B

7. Finding hO and hI Direction of Heat Flow
Film surface conductance coefficient (S: p. 158, T4.3)
Emittance
Position of Surface
Air Motion
S: p. 1612, T.E.3A

8. Finding hO and hI – Emittance
Emittance(ε): absorption of radiant heat
Effective Emittance (εeff):
1/εeff=1/ε1+1/ε2-1
S: p.1612, T.E.3B

9. R-values for Enclosed Air Cavities
Air Space Width
Air Space Temperature
Direction of Heat Flow
Film surface conductance coefficient (S: p. 161, T4.4)
Emittance
Position of Air Space
S: p. 1614, T.E.4

10. R-values For Solid Materials
Conductance
Resistance
Conductivity
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
Density
S: p. 1593, T. E.1

11. Conductivity and Conductance
Conductivity (k) heat flow through a material per unit thickness
Conductance (C): heat flow through a material of stated thickness
C=k/x
where x= unit thickness (in.)

12. Conductivity and Conductance
Example 1 x”
1ºF
Say x=4”
Conductivity vs. Conductance 1’ 1”
1ºF
Conductance C=k/x=0.25/4”= Btuh
Conductivity k=0.25 Btuh
S: p. 186, F.7.8

13. Converting to Resistance
Resistance (R): measure of resistance to the passage of heat (h-ft2-ºF/Btu)
R=1/C or R=x/k

14. Converting to Resistance
Example 1 (cont.) x”
1ºF
Say x=4”
Conductivity vs. Conductance 1’ 1”
1ºF
Conductance C=k/x=0.25/4”= Btuh
Resistance R=x/k=4/0.25=16
Conductivity k=0.25 Btuh
Resistance R=1/k=1/0.25= 4
S: p. 186, F.7.8

15. Thermal Properties Table
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
S: p. 1603, T.E.1

16. U-Value Calculation Wall 1 indoor air film ½” gypsum board
2”x4” nominal stud (pine) w/3.5” Ins.
½” fiberboard
wood shingles (16” long, 12” exposure)
outdoor air film
Section View

17. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

18. Finding Indoor Air Film Coefficient –hI
Vertical surface
Horizontal heat flow
Non-reflective surface
hI=1.46
R=0.68
Film surface conductance coefficient (S: p. 158, T4.3)
S: p. 1612, T.E. 3A

19. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

20. Finding Gypsum Board R-value
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
S: p. 1593, T.E.1

21. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

22. Finding Framing R-value
Nominal 2x4 Pine stud depth is 3.5”
Ravg=( )/2=1.23/inch
R=3.5x1.23
=4.35
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
S: p , T.E.1

23. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

24. Thermal Properties Table
3.5” Insulation
Mineral Fiber
R=13.00
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
S: p , T.E.1

25. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

26. Finding Fiberboard R-value
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
S: p. 1593, T.E.1

27. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

28. Finding Wood Shingle R-value
Wood shingles (16”, 12” exposure)
R=1.19
Table 4.2 Thermal Properties of Typical Building and Insulating Materials
S: p. 1600, T.E.1

29. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

30. Finding Outdoor Air Film Coefficient--hO
Winter Wind
Horizontal heat flow
Non-reflective surface
hO=6.0
R=0.17
Film surface conductance coefficient (S: p. 158, T4.3)
S: p. 1612, T.E.3A

31. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123

32. U-Value Calculation At At Insulation Frame Component (RI) (RF) Ref.
indoor air film T.E.3A
½” gypsum board T.E.1
2x4 stud (3.5” pine) n.a T.E.1
3.5” Insulation n.a. T.E.1
½” fiberboard T.E.1
wood shingles T.E.1
outdoor air film T.E.3A
Totals ΣRI ΣRF 8.16
UI UF 0.123
U= 1/ΣR

33. U-Value — Overall Average
At At Insulation Frame Component (RI) (RF)
Totals ΣRI ΣRF 8.16
UI UF 0.123
15% framing:
UAVG=0.85(0.059)+0.15(0.123)=0.069

34. Thermal Gradient Calculation
Temperature Conditions
Indoor Air Temperature (TI)
68ºF/50% RH
Outdoor Air Temperature (TO)
13ºF
Temperature Difference (TI-TO)
68-13=55ºF
Dewpoint Temperature (DPT)
58ºF

35. Thermal Gradient Calculation
“With Insulation” ΔT from
Component (RI) ΣR Interior Outer Edge
indoor air film º 65.8º
½” gypsum board º 61.3º
3-½” insulation º 21.8º
½” fiberboard º 17.4º
wood shingles º 13.5º
outdoor air film º 13.0º + =
ΔT from Interior =ΣR x (TI-TO)/ΣRI
=0.68x55/16.81=2.2º
Edge= TI- ΔT from Interior
=68-2.2=65.8º

36. Vapor Barrier Placement
Show Thermal Gradient on Wall Section
Select location for vapor barrier
T>DPT=58ºF
Section View
68ºF
13ºF
13.5ºF
17.4ºF
20.7ºF
65.8ºF
61.3ºF

37. Thermal Gradients Observations:
Interior surface temperature with insulation
(ΣRI=16.81) 65.8ºF
Interior surface temperature without insulation
(ΣRC=4.82) 60.2ºF

38. Thermal Mass Component #/cf #/sf
Density Weight
Component #/cf #/sf
indoor air film
½” gypsum board
3-½” insulation
½” fiberboard
wood shingles
outdoor air film #/sf
Weight (#/sf)=Density (#/cf) x Thickness (ft.)
½” Gyp. Bd. =50#/cf x ’= 2.08 #/sf

39. Insert Microclimate critiques here
Insert Exam results here