Objectives

• Lean about energy transport by air

• Calculate Cooling and Heating loads • Solve 1-D conduction• Design whether condition• Use knowledge of heat transfer to calculate

• Solar gains

• Internal gains

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

Ground Contact• 3-D conduction problem

• Ground temperature is often much closer to indoor air temperature

• Use F- value for slab floorMultiply by slab edge length

and Add to ΣUA

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

Where do you get information about amount of ventilation required?

• ASHRAE Standard 62• Table 2

• Tao and Janis Table 2.9A

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

• For cooling use the 1% DB and

coincident WB for load calculations

• 1% of hours during the summer will be warmer than this Design Temperature

• Use the 1% design WB for specification of equipment

Weather Data

Solar Gain• Affects conductive heat gains because outside surfaces

get hot• Use Q = U·A·ΔT

Replace ΔT with TETD – total equivalent temperature differential

Q = U·A· TETD

• Tables 2-12 – 2-14 in Tao and Janis

Replace ΔT with CLTD (Tables 1 and 2 Chapter 29 of ASHRAE Fundamentals)

Solar Gain

TETD depends on:

- orientation,

- time of day,

- wall properties - surface color- thermal capacity

Glazing

• Q = U·A·ΔT+A×SC×SHGF• Calculate conduction normally Q = U·A·ΔT

• Use U-values from NFRC National Fenestration Rating Council

• ALREADY INCLUDES AIRFILMS• http://cpd.nfrc.org/pubsearch/psMain.asp

• Use the U-value for the actual window that you are going to use

• Only use default values if absolutely necessary• Tao and Janis - no data • Tables 4 and 15, Chapter 31 ASHRAE Fundamentals

Shading Coefficient - SC

• Ratio of how much sunlight passes through relative to a clean 1/8” thick piece of glass

• Depends on• Window coatings• Actually a spectral property• Frame shading, dirt, etc.• Use the SHGC value from NFRC for a particular window

SC=SHGC/0.87• Lower it further for blinds, awnings, shading, dirt

•http://cpd.nfrc.org/search/cpd/cpd_search_default.aspx?type=W

More about Windows

• Spectral coatings (low-e)• Allows visible energy to pass, but limits infrared

radiation• Particularly short wave

• Tints

• Polyester films

• Gas fills

• All improve (lower) the U-value

Low- coatings

Internal gains

• What contributes to internal gains?

• How much?

• What about latent internal gains?

Internal gains

• ASHRAE Fundamentals ch. 29 or handouts• Table 1 – people

• Table 2 – lighting, Table 3 – motors

• Table 5 – cooking appliances

• Table 6 -10 Medical, laboratory, office

• Tao and Janis - People only - Table 2.17

Readings:

• Tao and Janis 2.4-2.8.10