Objectives

Finish with Heat transfer

Learn about Psychometrics• Psychometric chart

Forced Convection

• External turbulent flow over a flat plate• Nu = hmL/k = 0.036 (Pr )0.43 (ReL

0.8 – 9200 ) (µ∞ /µw )0.25

• External turbulent flow (40 < ReD <105) around a single cylinder• Nu = hmD/k = (0.4 ReD

0.5 + 0.06 ReD(2/3) ) (Pr )0.4 (µ∞ /µw )0.25

• Use with careReL = 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 numberµ∞ = 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)

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)

Pr

TgHTHgRa

/T 2

33

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)

Phase Change –Boiling

• What temperature does water boil under ideal conditions?

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)

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

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

4ATQemited

Short-wave & long-wave radiation

• Short-wave – solar radiation• <3m• Glass is transparent • Does not depend on surface temperature

• Long-wave – surface or temperature radiation• >3m• Glass is not transparent • Depends on surface temperature

Radiation Equations

2

2

2

1

211

1

42

411

21111

)(

AA

F

TTAQ

2

2

2

1

211

1

3

2

2

2

1

211

1

21

42

41

111

4

111

)()(

AA

F

T

AA

F

TTTT

havg

r

tAhQ rrad

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

Combining Convection and Radiation

• Both happen simultaneously on a surface• Slightly different

temperatures

• Often can use h = hc + hr

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 saturationma = mass of dry airmw = mass of water vapor

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

W

Ws

622.0

622.0

x = mole fractionP = pressureμ = degree of saturationW = humidity ratio

Dew-point temperature, td

• Temperature at which condensation will form• Under appropriate surface conditions

• Vapor is saturated

• Φ = ?

• Ws(P, td) = W

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

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

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)

Ref: Tao and Janis (2001)

Ref: Tao and Janis (2001)

Ref: Tao and Janis (2001)

Ref: Tao and Janis (2001)

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%

Alternate calculation for W

• PV = mRT (IGL)

• What do we know about R ratio?

• P = Pw + Pa

w

a

a

w

TRVP

TRVP

a

w

R

R

P

P

m

mW

a

a

w

w

w

w

PP

PW

622.0

R = gas constantP = pressureV = volumeT = absolute temperatureW = humidity ratio

Subscripts: w is water vapor, a is dry air

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 heath = enthalpyT = absolute temperaturet = temperature W = humidity ratio

Subscripts: w is water vapor, a is dry air, g is saturated water vapor

Adiabatic mixing

• Governing equation hmQhmoutin

External heat

Sensible heating

tcmQ p

Dehumidification by Cooling

Real Dehumidification Process

Mold in a duct

Transport of saturated air

tsurface < tdp Condensation

Humidification

hw Specific enthalpy of water added to system

hg Specific enthalpy of saturated water vapor

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