1. Lecture Objectives Psychrometrics Define Heating and Cooling Loads
Practice for the Quiz
Define equation for Sensible and latent heat
Define Heating and Cooling Loads

2. We will have our first Quiz on Tuesday
First 10 minutes of the class
An example is provided in the handout section of the course website
At the end of the class we will solve several examples

3. enthalpy

4. Examples:
1) You heat one pounds of air air A (T=50F, W=0.009 lbW/lbDA) to point T=80F and humidify it to RH 70%. What is the sensible, latent and total heat added to the one pound of air.
2) One pound of air D(T=90F, RH=30%) is humidified by adiabatic humidifier to 90% relative humidity. What is the temperature at the end of humidification process and how much water is added to the air.

5. Process in HVAC systems
Heating
Cooling
Humidification
Dehumidification
All these processes ca be quantified in Psychrometric Chart
Also, all the these quantities can be calculated with and without help of the Psychrometric Chart

6. Equations for sensible energy transport by air
Energy per unit of mass Δhsensible = cp × ΔT [Btu/lb]
cp - specific heat for air (for air 0.24 Btu/lb°F)
Heat transfer (rate) Qs = m × cp × ΔT [Btu/h]
m - mass flow rate [lb/min, lb/h], m = V × r
V – volume flow rate [ft3/min or CFM]
r – air density (0.076lb/ft3)
Qs = 1.1 × CFM × ΔT (only for IP unit system)

7. Equations for latent energy transport by air
Energy per unit of mass Δhlatent = Δw × hfg [Btu/lbda]
hfg - specific energy of water phase change (1000 Btu/lbw)
Heat transfer (rate) Ql = m × Δw × hfg [Btu/h]
Ql = 1000 × WaterFloowRate (only for IP units)

8. Total energy transport calculation using enthalpies from chat
Energy per unit of mass Δh=h1-h2 [Btu/lbda]
Heat transfer (rate) Qtotal = m × Δh [Btu/h]
Qtotal = Qsensible + Qlatent

9. Why do we calculate heating and cooling loads?
10/21/2003
Heating and Cooling Loads
Why do we calculate heating and cooling loads?
To estimate amount of energy used for heating and cooling by a building Or
To size heating and cooling equipment for a building
ARE 346N

10. Introduction to Heat Transfer
Conduction
Components
Convection
Air flows (sensible and latent)
Radiation
Solar gains (cooling only)
Increased conduction (cooling only)
Phase change
Water vapor/steam
Internal gains (cooling only)
Sensible and latent

11. 1-D Conduction U = k/l Q = UAΔT l k U U-Value [W/(m2 °C)] A
90 °F
70 °F l k A
U U-Value [W/(m2 °C)]
U = k/l
k conductivity [W/(m °C)]
l length [m]
Q heat transfer rate [W]
ΔT temperature difference [°C]
A surface area [m2]
Q = UAΔT

12. Material k Values Material k [W/(m K)] Steel 64 - 41 Soil 0.52 Wood
Fiberglass
Polystyrene
0.029
At 300 K
Table 2-3 Tao and Janis (k=λ) values in [Btu in/(h ft2 F)]

13. Wall assembly l1 l2 R = l/k Q = (A/Rtotal)ΔT Add resistances in series
Add U-values in parallel k1 k2
90 °F
70 °F R1 R2
Tout
Tmid
Tin

14. Rsurface= 1/h Rtotal= ΣRi Surface Air Film Table 2-5 Tao and Janis
h - convection coefficient
- surface conductance
[W/m2, Btu/(h ft2)]
Direction/orientation
Air speed
Table 2-5 Tao and Janis
Tout
Tin
Rsurface= 1/h Ro R1 R2 Ri
Rtotal= ΣRi
Tout
Tin

15. What if more than one surface?l1 l2
k1, A1
k2, A2
Qtotal = Q1,2 + Q3
Q1,2
A2 = A1
U1,2 = 1/R 1,2=1/(R1+R2)
k3, A3
Q1,2 = A1U1,2ΔT Q3
Q3 = A3U3ΔT l3

16. Tin Tout Qtotal= Σ(UiAi)·ΔT
Relationship between temperature and heat loss
U1A1
U2A2
U3(A3+A5)
U4A4
U5A5 A2 A3 A1 A4
Tin
Tout A5 A6
Qtotal= Σ(UiAi)·ΔT

17. Example Consider a 1 ft × 1 ft × 1 ft box
Two of the sides are 2” thick extruded expanded polystyrene foam
The other four sides are 2” thick plywood
The inside of the box needs to be maintained at 120 °F
The air around the box is still and at 80 °F
How much heating do you need?

18. The Moral of the Story Calculate R-values for each series path
Convert them to U-values
Find the appropriate area for each U-value
Multiply U-valuei by Areai
Sum UAi
Calculate Q = Σ(UAi)ΔT

19. Heat transfer in the building Not only conduction and convection !

20. Infiltration Q = m × cp × ΔT [BTU/hr, W]
Air transport Sensible energy
Previously defined
Q = m × cp × ΔT [BTU/hr, W]
ΔT= T indoor – T outdoor
or Q = 1.1 BTU/(hr CFM °F) × V × ΔT [BTU/hr]

21. Latent Infiltration and Ventilation
Can either track enthalpy and temperature and separate latent and sensible later:
Q total = m × Δh [BTU/hr, W]
Q latent = Q total - Q sensible = m × Δh - m × cp × ΔT
Or, track humidity ratio:
Q latent = m × Δw × hfg

22. Ventilation Example Supply 500 CFM of outside air to our classroom
Outside 90 °F 61% RH
Inside 75 °F 40% RH
What is the latent load from ventilation?
Q latent = m × hfg × Δw
Q = ρ × V × hfg × Δw
Q = lbair/ft3 × 500 ft3/min × 1076 BTU/lb × ( lbH2O/lbair lbH2O/lbair) × 60 min/hr
Q = kBTU/hr

23. Where do you get information about amount of ventilation required?
ASHRAE Standard 62
Table 2
Hotly debated – many addenda and changes
Tao and Janis Table 2.9A

24. Weather Data Table 2-2A (Tao and Janis) or
Chapter 28 of ASHRAE Fundamentals
For heating use the 99% design DB value
99% of hours during the winter it will be warmer than this Design Temperature
Elevation, latitude, longitude

25. Ground Contact Receives less attention:
3-D conduction problem
Ground temperature is often much closer to indoor air temperature
Use F- value for slab floor [BTU/(hr °F ft)]
Note different units from U-value
Multiply by slab edge length
Add to ΣUA
Still need to include basement wall area
Tao and Janis Tables 2.10 and 2.11
More details in ASHRAE handbook -Chapter 29

26. Ground Contact 3-D conduction problem
Ground temperature is often much closer to indoor air temperature
Use F- value for slab floor
Multiply by slab edge length
and Add to ΣUA

27. Summary of Heating Loads
Conduction and convection principles can be used to calculate heat loss for individual components
Convection principles used to account for infiltration and ventilation