Quiz First 10 minutes of the class

Lecture Objectives Define Heating and Cooling Loads Learn how to Calculate Heating Loads Cooling Loads

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

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 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

Material k Values Material k [W/(m K)] Steel 64 - 41 Soil 0.52 Wood 0.16 - 0.12 Fiberglass 0.046 - 0.035 Polystyrene 0.029 At 300 K Table 2-3 Tao and Janis (k=λ) values in [Btu in/(h ft2 F)]

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

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

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

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

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 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

Heat transfer in the building Not only conduction and convection !

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]

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

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

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

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 floor Multiply 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

Cooling loads

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/pubsearch/psMain.asp

More about Windows Spectral coatings (low-e) Tints Polyester films 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 Tao and Janis - People only - Table 2.17 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

Summary: Heating and cooling loads Heating - Everything gets converted to a UA, UF, mcp Sum and multiply it by the design temperature difference Cooling loads have additional components Internal gains Solar gain Increased gain through opaque surfaces Also need to calculate latent cooling load

Heating and Cooling Load Procedures Handout Calculate heating load Calculate cooling load Need to also calculate latent cooling load

Conclusions Conduction and convection principles can be used to calculate heat loss for individual components Air transport principles used to account for infiltration and ventilation Radiation for solar gain and increased conduction Include sensible and internal gains

Reading Assignment Readings: Tao and Janis Chapter 2

Example problem Calculate the cooling load for the building in Pittsburgh PA with the geometry shown on figure. On east north and west sides are buildings which create shade on the whole wall. Windows: Horizontal slider, Manufacturer:  American Window Alliance, Inc, CDP number AMW-K-3-00028 ttp://cpd.nfrc.org/pubsearch/psMain.asp Walls: 4” face brick + 2” insulation + 4” concrete block, Uvalue = 0.1, Dark color Roof: 2” internal insulation + 4” concrete , Uvalue = 0.120 , Dark color Below the building is basement wit temperature of 75 F. Internal design parameters: air temperature 75 F Relative humidity 50% Find the amount of fresh air that needs to be supplied by ventilation system.

Example problem Internal loads: Infiltration: 10 occupants, who are there from 8:00 A.M. to 5:00 P.M.doing moderately active office work 1 W/ft2 heat gain from computers and other office equipment from 8:00 A.M. to 5:00 P.M. 0.2 W/ft2 heat gain from computers and other office equipment from 5:00 P.M. to 8:00 A.M. 1.5 W/ft2 heat gain from suspended fluorescent lights from 8:00 A.M. to 5:00 P.M. 0.3 W/ft2 heat gain from suspended fluorescent lights from 5:00 P.M. to 8:00 A.M. Infiltration: 0.5 ACH per hour

Example solution SOLUTION steps (see handouts): 1. Calculate cooling load from conduction through opaque surfaces using TETD. 2. Calculate conduction and solar transmission through windows. 3. Add sensible internal gains and infiltration. 4. The result is your raw sensible cooling load. 5. Calculate latent internal gains. 6. Calculate latent gains due to infiltration. 7. The sum of 5 and 6 is your raw latent cooling load.

Example solution SOLUTION: For which hour to do the calculation ? With computer calculation for all and select the largest.

Example solution For which hour to do the calculation when you do manual calculation? Identify the major single contributor to the cooling load and do the calculation for the hour when the maximum cooling load for this contributor appear. For example problem major heat gains are through the roof or solar through windows! Roof: maximum TETD=61F at 6 pm (Table 2.12) South windows: max. SHGF=109 Btu/hft2 at 12 am (July 21st Table 2.15 A) If you are not sure, do the calculation for both hours: at 6 pm Roof gains = A x U x TETD = 900 ft2 x 0.12 Btu/hFft2 x 61 F = 6.6 kBtu/h Window solar gains = A x SC x SHGF =80 ft2 x 0.71 x 10 Btu/hft2 = 0.6 kBtu/h total = 7.2 kBtu/h at 12 am Roof gains = A x U x TETD = 900 ft2 x 0.12 Btu/hFft2 x 30 F = 3.2 kBtu/h Window solar gains = A x SC x SHGF =80 ft2 x 0.71 x 109 Btu/hft2 = 6.2 kBtu/h total= 9.4 kBtu/h For the example critical hour is July 12 AM.

Solution On the board

Example 2 How to calculate Cooling Load for HVAC design If the room with no outdoor influence has 4 lighting fixtures with 100 W each and 10 students, what is the needed relative humidity and temperature of supply air if only required amount of fresh air is supplied and room temperature is 75 F and RH 50%?