Objectives Heat transfer Convection Radiation Fluid dynamics Review Bernoulli equation flow in...
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Transcript of Objectives Heat transfer Convection Radiation Fluid dynamics Review Bernoulli equation flow in...
Objectives
• Heat transfer• Convection
• Radiation
• Fluid dynamics• Review Bernoulli equation
• flow in pipes, ducts, pitot tube
l1k
1, A
1k2
, A2
l2
l3
k3,
A3
A2
= A1
(l1
/k1
)/A1
R1
/A1
Tout
Tin
(l2
/k2
)/A2
R2
/A2
(l3
/k3
)/A3
R3
/A3
1. Add resistances for series
2. Add U-Values for parallel
l thickness
k thermal conductivity
R thermal resistance
A area
Convection and Radiation
• Similarity• Both are surface phenomena• Therefore, can often be combined
• Difference• Convection requires a fluid, radiation does not• Radiation tends to be very important for large
temperature differences• Convection tends to be important for fluid flow
Forced Convection
• Transfer of energy by means of large scale fluid motion
In the following text:
V = velocity (m/s, ft/min) Q = heat transfer rate (W, Btu/hr)
ν = kinematic viscosity = µ/ρ (m2/s, ft2/min) A = area (m2, ft2)
D = tube diameter (m, ft) T = temperature (°C, °F)
µ = dynamic viscosity ( kg/m/s, lbm/ft/min) α = thermal diffusivity (m2/s, ft2/min)
cp = specific heat (J/kg/°C, Btu/lbm/°F)
k = thermal conductivity (W/m/K, Btu/hr/ft/K)
h = convection or radiation heat transfer coefficient (W/m2/K, Btu/hr/ft2/F)
ThAQ
Dimensionless Parameters
• Reynolds number, Re = VD/ν
• Prandtl number, Pr = µcp/k = ν/α
• Nusselt number, Nu = hD/k
• Rayleigh number, Ra = …
What is the difference between thermal conductivity and thermal diffusivity?
• Thermal conductivity, k, is the constant of proportionality between temperature difference and conduction heat transfer per unit area
• Thermal diffusivity, α, is the ratio of how much heat is conducted in a material to how much heat is stored
• α = k/(ρcp)
• Pr = µcp/k = ν/α
k = thermal conductivity (W/m/K, Btu/hr/ft/K)
ν = kinematic viscosity = µ/ρ (m2/s, ft2/min)
α = thermal diffusivity (m2/s, ft2/min)
µ = dynamic viscosity ( kg/m/s, lbm/ft/min)
cp
= specific heat (J/kg/°C, Btu/lbm/°F)
k = thermal conductivity (W/m/K, Btu/hr/ft/K)
α = thermal diffusivity (m2/s)
Analogy between mass, heat, and momentum transfer
• Schmidt number, Sc
• Prandtl number, Pr
Pr = ν/α
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 careRe
L = 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)
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
For an ideal gas
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)
Forced Convection Boiling
• Example: refrigerant in a tube• Heat transfer is function of:
• Surface roughness• Tube diameter• Fluid velocity• Quality• Fluid properties• Heat-flux rate
• hm for halocarbon refrigerants is 100-800 Btu/hr/°F/ft2
(500-4500 W/m2/°C)
Nu = hm
Di/k
ℓ=0.0082(Re
ℓ2K)0.4
Reℓ = GD
i/µ
ℓ
G = mass velocity = Vρ (kg/s/m2, lbm/min/ft2)
k = thermal conductivity (W/m/K, Btu/hr/ft/K)
Di
= inner diameter of tube( m, ft)
K = CΔxhfg
/L
C = 0.255 kg∙m/kJ, 778 ft∙lbm/Btu
Condensation
• Film condensation• On refrigerant tube surfaces• Water vapor on cooling coils
• Correlations• Eqn. 2.62 on the outside of horizontal tubes• Eqn. 2.63 on the inside of horizontal tubes
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)
Blackbody
• Idealized surface that• Absorbs all incident radiation• Emits maximum possible energy• Radiation emitted is independent of direction
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
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
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
Combining Convection and Radiation
• Both happen simultaneously on a surface• Slightly different
temperatures
• Often can use h = hc + hr
Fluid Flow in HVAC components
Fundamentals: Bernoulli’s equation Flow in pipes:
• Analogy to steady-flow energy equation
• Consider incompressible, isothermal flow
• What is friction loss?
gD
LVf
2
2
2
2V
D
Lfp friction
[ft]
[Pa]
Summary
• Use relationships in text to solve conduction, convection, radiation, phase change, and mixed-mode heat transfer problems
• Calculate components of pressure for flow in pipes and ducts