Psychrometrics & Heating/Cooling Loads.

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

2. We will have our first Quizon 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 – airdensity (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? 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

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 l k A 90 °F 70 °F 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 At 300 K Table 2-3Tao 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. Surface Air Film 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 Ri Ro R1 R2 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. 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 • Air transport Sensible energy Previously defined • Q = m× cp × ΔT [BTU/hr, W] • ΔT= T indoor – T outdoor • or Q = 1.1BTU/(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 = 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

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