Objectives

1. Objectives Finish with Heat transfer Learn about Psychometrics • Psychometric chart

2. ReL = Reynolds number based on length Q = heat transfer rate (W, Btu/hr) ReD = Reynolds number based on tube diameter A = area (m2, ft2) L = tube length (m, ft) t = temperature (°C, °F) k = thermal conductivity (W/m/K, Btu/hr/ft/K) Pr = Prandtl number µ∞ = dynamic viscosity in free stream( kg/m/s, lbm/ft/min) µ∞ = dynamic viscosity at wall temperature ( kg/m/s, lbm/ft/min) hm = mean convection heat transfer coefficient (W/m2/K, Btu/hr/ft2/F) Forced Convection • External turbulent flow over a flat plate • Nu = hmL/k = 0.036 (Pr )0.43 (ReL0.8 – 9200 ) (µ∞ /µw )0.25 • External turbulent flow (40 < ReD <105) around a single cylinder • Nu = hmD/k = (0.4 ReD0.5 + 0.06 ReD(2/3) ) (Pr )0.4 (µ∞ /µw )0.25 • Use with care

3. H = plate height (m, ft) T = temperature (°C, °F) Q = heat transfer rate (W, Btu/hr) g = acceleration due to gravity (m/s2, ft/min2) T = absolute temperature (K, °R) Pr = Prandtl number ν = kinematic viscosity = µ/ρ (m2/s, ft2/min) α = thermal diffusivity (m2/s) Natural Convection • Common regime when buoyancy is dominant • Dimensionless parameter • Rayleigh number • Ratio of diffusive to advective time scales • Book has empirical relations for • Vertical flat plates (eqns. 2.55, 2.56) • Horizontal cylinder (eqns. 2.57, 2.58) • Spheres (eqns. 2.59) • Cavities (eqns. 2.60)

4. Phase Change –Boiling • What temperature does water boil under ideal conditions?

5. Radiation • Transfer of energy by electromagnetic radiation • Does not require matter (only requires that the bodies can “see” each other) • 100 – 10,000 nm (mostly IR)

6. Surface Radiation Issues • 1) Surface properties are spectral, f(λ) • Usually: assume integrated properties for two beams: • Short-wave and Long-wave radiation • 2) Surface properties are directional, f(θ) • Usually assume diffuse

7. Radiation emission The total energy emitted by a body, regardless of the wavelengths, is given by: • Temperature always in K ! - absolute temperatures • – emissivity of surface ε= 1 for blackbody • – Stefan-Boltzmann constant A - area

8. Short-wave & long-wave radiation • Short-wave – solar radiation • <3mm • Glass is transparent • Does not depend on surface temperature • Long-wave – surface or temperature radiation • >3mm • Glass is not transparent • Depends on surface temperature

9. Q1-2 = Qrad = heat transferred by radiation (W, BTU/hr) F1-2 = shape factor hr = radiation heat transfer coefficient (W/m2/K, Btu/hr/ft2/F) A = area (ft2, m2) T,t = absolute temperature (°R , K) , temperature (°F, °C) ε = emissivity (surface property) σ = Stephan-Boltzman constant = 5.67 × 10-8 W/m2/K4= 0.1713 × 10-8 BTU/hr/ft2/°R4 Radiation Equations

10. Combining Convection and Radiation • Both happen simultaneously on a surface • Slightly different temperatures • Often can use h = hc + hr

11. Humidity Ratio, W • W = mw/ma • Degree of saturation, µ = W/Ws • Humidity ratio is hard to measure, but very useful in calculations • What are units? • Is W a function of temperature? What about Ws? Ws = humidity ratio at saturation ma = mass of dry air mw = mass of water vapor

12. Relative Humidity • Φ = xw/xw,s = Pw/Pws • Function of T Easy to measure and useful in some contexts, but often need to know temperature as well x = mole fraction P = pressure μ = degree of saturation W = humidity ratio

13. Dew-point temperature, td • Temperature at which condensation will form • Under appropriate surface conditions • Vapor is saturated • Φ = ? • Ws(P, td) = W

14. Wet-bulb temperature, VBT (t*) • Temperature of wet surface or • Temperature at which water, by evaporating into the air, will bring air to saturation adiabatically • * superscript is designation that variable is evaluated at the wet-bulb temperature • Note, distinct from that measured by a sling psychrometer • Section 9.5

15. Tables for Moist Air (P = 1 atm) • Tables A.4 in your text • Ability to get Ws for calculations • Subscripts: • a = dry air, s = saturated air v = va+µvas h = ha+µhas s = sa+µsas

17. Psychrometric Chart • Need two quantities for a state point • Can get all other quantities from a state point • Can do all calculations without a chart • Often require iteration • Many “digital” psychrometric charts available • Can make your own • Best source is ASHRAE fundamentals (Chapter 6) • Also in your text (back cover fold-out)

18. Ref: Tao and Janis (2001)

19. Ref: Tao and Janis (2001)

20. Ref: Tao and Janis (2001)

21. Ref: Tao and Janis (2001)

22. Examples • What is enthalpy of air in the classroom right now? • Condensation on windows when taking a shower • How cold does it have to be outside for condensation to form on windows? • Assumption is that windows are the same temperature as outside air • 80 °F, RH = 80%

24. Alternate calculation for W • PV = mRT (IGL) • What do we know about R ratio? • P = Pw + Pa R = gas constant P = pressure V = volume T = absolute temperature W = humidity ratio Subscripts: w is water vapor, a is dry air

25. Calculation of psychometric quantities • For an ideal gas, • hda = ∫cpadT, hw = ∫cpwdT • So, hda = cp,dat which assumes a reference state of 0 °F or 0 °C – Tables A4 • Note different reference • hw = cpwt + hg0 • h = cp,dat + W(cpwt + hg0) Or you can use: • h = cpt + W∙hg0, cp = cp,da + Wcpw cp = specific heat h = enthalpy T = absolute temperature t = temperature W = humidity ratio Subscripts: w is water vapor, a is dry air, g is saturated water vapor

26. Adiabatic mixing • Governing equation External heat

27. Sensible heating

28. Dehumidification by Cooling

29. Real Dehumidification Process

30. Transport of saturated air Mold in a duct tsurface < tdp Condensation

31. Humidification hw Specific enthalpy of water added to system hg Specific enthalpy of saturated water vapor

32. Summary • Describe psychrometric quantities • Given any two psychrometric quantities, calculate any other quantity • Use Tables A4 or psychrometric charts to look up psychrometric quantities • Calculate psychrometric quantities at non-standard conditions