Objectives Finish with Heat transfer Learn about Psychometrics Psychometric chart

Forced Convection External turbulent flow over a flat plate Nu = h m L/k = (Pr ) 0.43 (Re L 0.8 – 9200 ) (µ ∞ /µ w ) 0.25 External turbulent flow (40 < Re D <10 5 ) around a single cylinder Nu = h m D/k = (0.4 Re D Re D (2/3) ) (Pr ) 0.4 (µ ∞ /µ w ) 0.25 Use with care Re L = Reynolds number based on lengthQ = heat transfer rate (W, Btu/hr) Re D = Reynolds number based on tube diameter A = area (m 2, ft 2 ) 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) h m = mean convection heat transfer coefficient (W/m 2 /K, Btu/hr/ft 2 /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) H = plate height (m, ft) T = temperature (°C, °F) Q = heat transfer rate (W, Btu/hr) g = acceleration due to gravity (m/s 2, ft/min 2 ) T = absolute temperature (K, °R) Pr = Prandtl number ν = kinematic viscosity = µ/ρ (m 2 /s, ft 2 /min) α = thermal diffusivity (m 2 /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

Short-wave & long-wave radiation Short-wave – solar radiation <3  m Glass is transparent Does not depend on surface temperature Long-wave – surface or temperature radiation >3  m Glass is not transparent Depends on surface temperature

Radiation Equations Q 1-2 = Q rad = heat transferred by radiation (W, BTU/hr) F 1-2 = shape factor h r = radiation heat transfer coefficient (W/m 2 /K, Btu/hr/ft 2 /F) A = area (ft 2, m 2 ) T,t = absolute temperature (°R, K), temperature (°F, °C) ε = emissivity (surface property) σ = Stephan-Boltzman constant = 5.67 × W/m 2 /K 4 = × BTU/hr/ft 2 /°R 4

Combining Convection and Radiation Both happen simultaneously on a surface Slightly different temperatures Often can use h = h c + h r

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

Relative Humidity Φ = x w /x w,s = P w /P ws 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

Dew-point temperature, t d Temperature at which condensation will form Under appropriate surface conditions Vapor is saturated Φ = ? W s (P, t d ) = 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 W s for calculations Subscripts: a = dry air, s = saturated air v = v a +µv as h = h a +µh as s = s a +µs as

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)

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 = P w + P a R = gas constant P = pressure V = volume T = absolute temperature W = humidity ratio Subscripts: w is water vapor, a is dry air

Calculation of psychometric quantities For an ideal gas, h da = ∫c pa dT, h w = ∫c pw dT So, h da = c p,da t which assumes a reference state of 0 °F or 0 °C – Tables A4 Note different reference h w = c pw t + h g0 h = c p,da t + W(c pw t + h g0 ) Or you can use: h = c p t + W∙h g0, c p = c p,da + Wc pw c p = 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

Adiabatic mixing Governing equation External heat

Sensible heating

Dehumidification by Cooling

Real Dehumidification Process

Mold in a duct Transport of saturated air t surface < t dp Condensation

Humidification h w Specific enthalpy of water added to system h g 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