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Homework 1

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

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Homework 1

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  1. Homework 1 • Interest - HVAC • Lighting • Electrical • Sustainability • Acoustics • Concerns

  2. 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

  3. Which situation has highest RH? • Summer day in Austin, TX • Winter day in Aspen, CO • The air downstream of a cooling coil • Summer day in Seattle, WA

  4. Sensible vs. Latent Heat latent sensible

  5. Changing the mass of water in an air sample always • Causes you to move vertically on the psychrometric chart • Changes the absolute humidity of the sample • Changes the relative humidity of the sample • Causes you to move horizontally on the psychrometric chart • A. and B.

  6. 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.

  7. 1993 ASHRAE Comfort Zone

  8. 1997/2001 ASHRAE Comfort Zone

  9. If you know the dew point temperature (td) and the dry bulb temperature (t) for a sample of air • You can’t get the statepoint because the problem is overspecified (you know the RH = 100%, t and td). • You get the state point by the intersection of the t and td lines. • You get the state point by moving horizontally from td until you intersect the t line • You get the state point by moving vertically from td until you intersect the t line

  10. 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.

  11. Psychrometric Chart • Make sure chart is appropriate for your environment • Figure out what two quantities you know • Understand their slopes on the chart • Find the intersection • Watch for saturation

  12. Homework Assignment 2 • Use the psychrometric chart • Pay attention to units in calculations • Values for Δh and Δw per mass unit of dry air • Differences in nomenclature

  13. 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)

  14. 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)

  15. 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

  16. 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 • To size heating and cooling equipment for a building • Because my supervisor request that

  17. 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

  18. 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

  19. Material k Values 1At 300 K Table 2-3Tao and Janis (k=λ) values in [Btu in/(h ft2 F)]

  20. 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

  21. 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

  22. 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

  23. 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

  24. Which of the following statements about a material is true? • A high U-value is a good insulator, and a high R-value is a good conductor. • A high U-value is a good conductor, and a high R-value is a good insulator. • A high U-value is a good insulator, and a high R-value is a good insulator. • A high U-value is a good conductor, and a high R-value is a good conductor.

  25. 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?

  26. 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

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

  28. 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]

  29. 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

  30. 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

  31. What is the difference between ventilation and infiltration? • Ventilation refers to the total amount of air entering a space, and infiltration refers only to air that unintentionally enters. • Ventilation is intended air entry into a space. Infiltration is unintended air entry. • Infiltration is uncontrolled ventilation.

  32. 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

  33. 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

  34. 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

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