1. Chapter 7: STEADY STATE HEAT FLOWS
Agami Reddy (rev Dec 2017)
Elements of sensible loads
Sol-air temperature
Soil temperature model
Below grade heat transfer
-basement walls, floor, slab-on-grade
5. Internal heat gains
- occupants, lighting, equipment
6. Steady-state heat balance
7. Treatment of unconditioned spaces
8. Zoning in buildings: need and common design practice
HCB 3- Chap 7: Steady State Heat Flows

2. HCB 3- Chap 7: Steady State Heat Flows
Heat flows affecting room air temperature
Climatic factors
Landscaping
Size, shape of building
Materials used
Window size and
orientation
Type of construction
Type of equipment
Occupant behavior
Equipment sizing: like choose cloth
Figure 7.1
The heat flow terms in a load calculation.
HCB 3- Chap 7: Steady State Heat Flows

3. Recall: Overall heat loss coefficient of an element
A thermal network is used
to represent the heat flow
process through an element
such as a stud wall
HCB 3- Chap 7: Steady State Heat Flows

4. HCB 3- Chap 7: Steady State Heat Flows
Sol-Air Temperature
Figure 7.2
Heat flows on a sunlit opaque wall.
HCB 3- Chap 7: Steady State Heat Flows

5. HCB 3- Chap 7: Steady State Heat Flows
Sol-Air Temperature
By including the radiation heat loss to the sky, we define the sol-air temperature as:
HCB 3- Chap 7: Steady State Heat Flows

6. HCB 3- Chap 7: Steady State Heat Flows
Sol-Air Temperature
ASHRAE Clear Sky Conditions - Phoenix, AZ
Figure 7.3 Diurnal variation of sol–air temperatures (in °C) for a dark- and a light-colored horizontal surface for 2 days in Phoenix, AZ, using TMY3 climatic data. (a) For January 21. (b) For July 21. The corresponding horizontal global radiation (in W/m2) and the ambient dry-bulb temperature (in °C) are also plotted.
HCB 3- Chap 7: Steady State Heat Flows

7. HCB 3- Chap 7: Steady State Heat Flows
Basement Heat Losses
2-Dimensional heat transfer problem
Ground coupling- heat transfer between basement floor slab and ground
Several methods- but these disagree somewhat
Troublesome for residences and single-story buildings
Soil properties vary widely due to diff types of soil, moisture,…
Figure 7.6 Radial isotherms for basement heat loss assumed in the ASHRAE method.
HCB 3- Chap 7: Steady State Heat Flows

8. HCB 3- Chap 7: Steady State Heat Flows
Basement (Below grade)
For the part that is above ground (grade) : use equations discussed in Chap 2
For the part that is below ground (grade): use ASHRAE method
Outside Temperature : surface soil temperature (discussed next)
Indoor Temperature:
If the basement is heated – indoor air temperature
If the basement is not heated – then the basement temperature has to be calculated as discussed later on
If the basement has certain heat sources (boiler or hot pipe is in
basement), then these have to be considered as well Tb
HCB 3- Chap 7: Steady State Heat Flows

9. Soil Temperature Model
HCB 3- Chap 7: Steady State Heat Flows

10. HCB 3- Chap 7: Steady State Heat Flows
For example:
Washington DC
has a average annual
temp. = 45.7o F
From figure,
Amplitude= 18o F
Figure 7.4 Map of amplitude of annual soil temperature swings used for ground coupling calculations (°F). For amplitude in SI units, divide by 1.8°F/K.
HCB 3- Chap 7: Steady State Heat Flows

11. HCB 3- Chap 7: Steady State Heat Flows
……..
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12. HCB 3- Chap 7: Steady State Heat Flows
7.7
7.8
HCB 3- Chap 7: Steady State Heat Flows

13. HCB 3- Chap 7: Steady State Heat Flows
=11.1 oC,
The annual variations for three different depths shown in Fig. 7.5
Surface soil temperature varies the greatest with an amplitude of about 10 0C.
At 3 m depth, the amplitude is 3.5 0C with a 3 month phase shift
HCB 3- Chap 7: Steady State Heat Flows

14. HCB 3- Chap 7: Steady State Heat Flows
Fig. 7.5 Soil Temperatures for Tempe, AZ
HCB 3- Chap 7: Steady State Heat Flows

15. HCB 3- Chap 7: Steady State Heat Flows
Heat Losses from Basement Walls
Basement wall
Basement floor
HCB 3- Chap 7: Steady State Heat Flows

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18. HCB 3- Chap 7: Steady State Heat Flows
use Eq.(7.9 for)
Use Eq.(7.10)
HCB 3- Chap 7: Steady State Heat Flows

19. HCB 3- Chap 7: Steady State Heat Flows
Floor on ground (or Slab on grade)
No crawl space, no basement. Heat loss is greatest near perimeter
Heat loss is proportional to perimeter length rather than area
where Fp is edge or perimeter
heat loss coefficient BTU/h-°F-ft
P is the perimeter or total
length of outside edges of floor, ft
Figure 7.7 Schematic diagram of method of insulating slabs and foundations.
HCB 3- Chap 7: Steady State Heat Flows

20. HCB 3- Chap 7: Steady State Heat Flows

21. HCB 3- Chap 7: Steady State Heat Flows
Crawlspace Heat Loss
Crawl space: A shallow space below the living quarters of a house without a basement normally enclosed by the foundation wall. Or, a shallow space below the roof. It is used for visual inspection and access to pipes and ducts- often vented
Need ventilation to prevent moisture condensation and mold!
HCB 3- Chap 7: Steady State Heat Flows

22. Internal Loads- Occupants
HCB 3- Chap 7: Steady State Heat Flows

23. HCB 3- Chap 7: Steady State Heat Flows
Internal Loads- Lighting
Based on installed lighting systems
7.13
PL = total installed lighting power
FUL = lighting use factor (or diversity factor) [0,1]
FSA = special allowance factor
- fraction of power consumed by fixture to that of light
- for incandescent lamps = 1
- for fluorescent fixture = 1.2 (in general)
Based on space area. This is a simpler approach used during design phase.
Simply assume max allowable lighting power densities (LPD) for the space as stipulated
by ASHRAE 90.1 (2010). Some typical values are shown in Table 7.7
For offices LPD about 12 W/m2 (1.1 W/ft2)
HCB 3- Chap 7: Steady State Heat Flows

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25. HCB 3- Chap 7: Steady State Heat Flows
Equipment Loads
Heat gains from appliances, motors, computers, copiers are quite subjective,
intermittent and harder to estimate
7.14
FUM = motor use factor or fraction of time operated
FLM = load factor or fraction of rated motor power delivered under condition analyzed
HCB 3- Chap 7: Steady State Heat Flows

26. HCB 3- Chap 7: Steady State Heat Flows
Discretion and caution should be exercised when using such tables
HCB 3- Chap 7: Steady State Heat Flows

27. HCB 3- Chap 7: Steady State Heat Flows

28. Treatment of One-Zone Spaces
7.18
7.19
7.21
HCB 3- Chap 7: Steady State Heat Flows

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30. HCB 3- Chap 7: Steady State Heat Flows
Almost
50%
Note: - Solar loads neglected
- Inefficiency of lights and equipment adversely impact building electric use in two ways: direct cost of electricity and additional cooling electricity
HCB 3- Chap 7: Steady State Heat Flows

31. Unconditioned Attached Spaces
Figure 7.11 Sketch for Example 7.11 of an unheated attached garage.
HCB 3- Chap 7: Steady State Heat Flows

32. HCB 3- Chap 7: Steady State Heat Flows
7.29
The garage temperature is quite close to the outdoor temperature because
of the poorer insulation.
Heat lost through garage = 0.1 x 200 x ( ) = 759 Btu/h
With no garage, heat lost = 0.1 x 200 x (70-30) = 800 Btu/h, a 5% difference
HCB 3- Chap 7: Steady State Heat Flows

33. HCB 3- Chap 7: Steady State Heat Flows
Zoning of Spaces
Two common design practices:
Interior/exterior
Building orientation
Definition: An air conditioning zone is a room or group of rooms in which comfortable conditions can be maintained by a single controlling device
Best to zone areas with similar thermal disturbance (weather, solar, internal) and close to each other
Zones share one set of Sensor, Controller, AC system
Figure 7.12 Example of recommended zoning. Thick lines represent zones, labeled 1 through 5. Dashed lines represent subzones.
Each zone has one thermostat
Zoning necessary because heat
gains from different directions are
non-uniform
HCB 3- Chap 7: Steady State Heat Flows

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36. HCB 3- Chap 7: Steady State Heat Flows
Outcomes
Knowledge of the various heat flows affecting room temperature
Understanding of sol-air temperature concept and how to calculate it
Familiarity with the soil temperature model and its application
Understanding of the ASHRAE method to calculate below grade heat losses from basements and slab-on-grade construction
Knowledge of how to calculate internal loads from occupants, lighting and equipment
Be able to determine total heat transmission coefficient of a building
Be able to perform steady-state analysis of a space to evaluate relative contributions of various heat gains
Be able to analyze heat flow interactions in unconditioned spaces
Understanding of why interior spaces have to be zoned and common design practice
HCB 3- Chap 7: Steady State Heat Flows