Homework 1

• Interest - HVAC

- Lighting- Electrical- Sustainability- Acoustics

• Concerns

Objectives• Review Psychrometrics

• Sensible and latent heat

• Define thermal comfort in Psychrometric chart

• Equations for energy transport by air

• Calculate heat loss and gain due to conduction

• Use knowledge of heat transfer to calculate heating and cooling loads

Which situation has highest RH?

A) Summer day in Austin, TX

B) Winter day in Aspen, CO

C) The air downstream of a cooling coil

D) Summer day in Seattle, WA

sensible

latent

Sensible vs. Latent Heat

Changing the mass of water in an air sample always

A. Causes you to move vertically on the psychrometric chart

B. Changes the absolute humidity of the sample

C. Changes the relative humidity of the sample

D. Causes you to move horizontally on the psychrometric chart

E. A. and B.

Example

Cooling with a oversized air conditioner• How much moisture is removed?

• A central air conditioner fan blows 1500 CFM of 80 °F air @ 50 % RH through a coil.

• The thermostat is satisfied when the air coming off the coil reaches 65 °F.

1993 ASHRAE Comfort Zone

1997/2001 ASHRAE Comfort Zone

If you know the dew point temperature (td) and the dry bulb temperature (t) for

a sample of air

A) You can’t get the statepoint because the problem is overspecified (you know the RH = 100%, t and td).

B) You get the state point by the intersection of the t and td lines.

C) You get the state point by moving horizontally from td until you intersect the t line

D) You get the state point by moving vertically from td until you intersect the t line

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.

Psychrometric Chart

1. Make sure chart is appropriate for your environment

2. Figure out what two quantities you know

3. Understand their slopes on the chart

4. Find the intersection• Watch for saturation

• Use the psychrometric chart

• Pay attention to units in calculations

• Values for Δh and Δw per mass unit of dry air

• Differences in nomenclature

Homework Assignment 2

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 × V – volume flow rate [ft3/min or CFM]

– airdensity (0.076lb/ft3)

Qs = 1.1 × CFM × ΔT (only for IP unit system)

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)

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

Why do we calculate heating and cooling loads?

A) To estimate amount of energy used for heating and cooling by a building

B) To size heating and cooling equipment for a building

C) Because my supervisor request that

Heating and Cooling Loads

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

1-D Conduction

Q heat transfer rate [W]

TR

AQ

RU ,

1

k conductivity [W/(m °C)]l length [m]

90 °F

70 °F

lk

AU = k/l

ΔT temperature difference [°C]A surface area [m2]

U U-Value [W/(m2 °C)]

Q = UAΔT

Material k Values

Material k [W/(m K)]1

Steel 64 - 41

Soil 0.52

Wood 0.16 - 0.12

Fiberglass 0.046 - 0.035

Polystyrene 0.0291At 300 K

Table 2-3 Tao and Janis (k=λ) values in [Btu in/(h ft2 F)]

90 °F

70 °F

l1k1 k2

l2• R = l/k

• Q = (A/Rtotal)ΔT

• Add resistances in series• Add U-values in parallel

2

2

1

1

2121

111

k

l

k

lR

UUURRR

total

totaltotal

R1 R2

Tout TinTmid

Wall assembly

Tout

Tin

R1 R2Ro

Tout

Ri

Tin

•Surface Air Film h - convection coefficient - surface conductance [W/m2, Btu/(h ft2)]

•Direction/orientation•Air speed

• Table 2-5 Tao and Janis

Rtotal= ΣRi

Rsurface= 1/h

l1k1, A1 k2, A2

l2

l3

k3, A3

A2 = A1

What if more than one surface?

Q3

Q1,2

Qtotal = Q1,2 + Q3

U1,2 = 1/R 1,2=1/(R1+R2)

Q3 = A3U3ΔT

Q1,2 = A1U1,2ΔT

U1A1

U2A2

U3(A3+A5)

U4A4

U5A5

Qtotal= Σ(UiAi)·ΔT

Relationship between temperature and heat loss

A1

A5

A4

A3A2

A6

TinTout

Which of the following statements about a material is true?

A) A high U-value is a good insulator, and a high R-value is a good conductor.

B) A high U-value is a good conductor, and a high R-value is a good insulator.

C) A high U-value is a good insulator, and a high R-value is a good insulator.

D) A high U-value is a good conductor, and a high R-value is a good conductor.

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?

The Moral of the Story

1. Calculate R-values for each series path

2. Convert them to U-values

3. Find the appropriate area for each U-value

4. Multiply U-valuei by Areai

5. Sum UAi

6. Calculate Q = Σ(UAi)ΔT

Heat transfer in the building Not only conduction and convection !

Infiltration

• 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]

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

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 = 0.076 lbair/ft3 × 500 ft3/min × 1076 BTU/lb × (0.01867 lbH2O/lbair - .00759 lbH2O/lbair) × 60 min/hr

• Q = 26.3 kBTU/hr

What is the difference between ventilation and infiltration?

A) Ventilation refers to the total amount of air entering a space, and infiltration refers only to air that unintentionally enters.

B) Ventilation is intended air entry into a space. Infiltration is unintended air entry.

C) Infiltration is uncontrolled ventilation.

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

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

Conclusions

• Conduction and convection principles can be used to calculate heat loss for individual components

• Convection principles used to account for infiltration and ventilation

• Readings: Tao and Janis 2.4-2.6.4