correlaciones tc por conveccion
TRANSCRIPT
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Convective Heat Transfer Correlations
Bernhard Spang
Email: [email protected]
Web: http://chemengineer.miningco.com
1 Forced Convection Flow Inside a Circular Tube
Re
Pr
=
= =
=
u D
c
k
hD
k
m
p
Nu
All properties at fluid bulk mean temperature (arithmetic mean of inlet and outlet temperature).
Nusselt numbers Nu0from sections 1-1 to 1-3 have to be corrected for temperature-dependent
fluid properties according to section 1-4.
1-1 Thermally developing, hydrodynamically developed laminar flow (Re < 2300)
a) Constant wall temperature
Nu0
0 8
0 467
3657
019
1 0117
= ++
.
. (Re Pr )
. (Re Pr )
.
.
D
LD
L
(Hausen)
b) Constant wall heat flux
Nu0=+ 7.
1-3 Fully developed turbulent and transition flow (Re > 2300)
a) Constant wall heat flux
Nu02 3
2 3
8 1000
1 12 78
1
1=
+ +
(Re ) Pr
. (Pr )/
/
DL
(Petukhov, Gnielinski)
where=
1
182 164 2( . log Re . )
b) Constant wall temperature
For fluids with Pr > 0.7 correlation for constant wall heat flux can be used with
negligible error.
1-4 Effects of property variation with temperature
a) Liquids, laminar and turbulent flow
Nu Nu0w
=
0 14.
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at mean fluid temperature, wat wall temperature
b) Gases, laminar flow
Nu = Nu0
c) Gases, turbulent flow
Nu Nu=
0
0 36
T
T
m
w
.
Temperatures in Kelvin
2 Forced Convection Flow Inside Concentric Annular Ducts, Turbulent (Re > 2300)
Do
Di
Dh=Do-Di
Re=
u Dm h
Nu=h D
k
h
All properties at fluid bulk mean temperature
(arithmetic mean of inlet and outlet
temperature)
a) Heat transfer at the inner wall, outer wall insulated
Nu
Nu tube=
0 86
0 16
.
.
D
D
o
i
(Petukhov and Roizen)
b) Heat transfer at the outer wall, inner wall insulated
Nu
Nu tube=
1 014
0 6
.
.
D
D
i
o
(Petukhov and Roizen)
c) Heat transfer at both walls, same wall temperatures
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Nu
Nutube
=
+
+
086 1 014
1
0 84 0 6
. .
. .
D
D
D
D
D
D
i
o
i
o
i
o
(Stephan)
3 Forced Convection Flow Inside Non-Circular Ducts, Turbulent (Re > 2300)
Equations for circular tube with hydraulic diameterDh = 4 cross sectional area
wetted perimeter
Re=
u Dm h
Nu=hD
k
h
4 Forced Convection Flow Across Single Circular Cylinders and Tube Bundles
l D=
2
Re lmu l=
Nu lhl
k=
D= cylinder diameter, um= free-stream velocity, all properties at fluid bulk mean temperature.
Correction for temperature dependent fluid properties see section 4-4
4-1 Smooth circular cylinder
Nu Nu Nul o l lam l turb, , ,.= + +0 32 2
(Gnielinski)
where Nu l lam l, . Re Pr= 06643
( )Nu l turb
l
l
,
.
. /
. Re Pr
. Re Pr=
+ 0037
1 2 443 1
0 8
0 1 2 3
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10 < Rel< 107
0.6 < Pr < 1000
4-2 Tube bundle
Transverse pitch ratio aS
D
Q=
Longitudinal pitch ratio b S
D
L=
Void ratio
= 14a
for b > 1
= 14ab
for b < 1
Re ,
lmu l=
Nu0,bundle=fANul,0 (Gnielinski)
Nul,0according to section 4-1 with Re ,l instead of Rel.
Arrangement factorfAdepends on tube bundle arrangement.
a) In-line arrangement fb a
b aA
= +
+1
0 7 0 3
0 71 5 2. ( / . )
( / . ).
mu
D
s L
Qs
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b) Staggered arrangement fb
A= +12
3
um
s Q
s L
4-3 Finned tube bundle
Rs
r
D
( ) ( )AA
S S
S D S S D r
o
e
Q R
Q R Q
= + +
( )
2
( )( )
A
A
r r D
D SGo R= +
+ +
+1
2
a) In-line tube bundle arrangement
Nu l o lo
e GO
A
A
A
A,
.
. .
/. Re Pr=
0 26 0 60 6 0 15
1 3 (Paikert)
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b) Staggered tube bundle arrangement
Nul o l
o
e GO
A
A
A
A,
.
. .
/. Re Pr=
0 45 0 60 6 0 15
1 3 (Paikert)
4-4 Effects of property variation with temperature
a) Liquids
Nu Nu
Nu Nubundle bundle
l l o
w
w
=
=
,
.
,
.
0 14
0
0 14
at mean fluid temperaturewat wall temperature
b) Gases
Nu Nul l o
m
w
T
T=
,
.0 12
Nu Nubundle bundle=
0
0 12
,
.
T
T
m
w
Temperatures in Kelvin
5 Forced Convection Flow over a Flat Plate
T
uL
Tw ReL
L
u L
hL
k
=
=
Nu
All properties at mean film temperature
T T Tm w= + 2
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a) Laminar boundary layer, Tw= const.
NuL lam L,/ /. Re Pr= 0664 1 2 1 3 (Pohlhausen)
ReL< 2105
0.6 < Pr < 10
b) Turbulent boundary layer along the whole plate,Tw= const.
( )NuL turb
L
L
,
.
. /
. Re Pr
. Re Pr )=
+ 0037
1 2 443 1
0 8
0 1 2 3(Petukhov)
c) Boundary layer with laminar-turbulent transition
Nu Nu NuL L lam L turb= +, ,2 2
(Gnielinski)
6 Free Convection
All properties at ( )T T TM w= + 1
2
Gr
Nu
=
=
L g T T
h L
k
w
3 2
2
L= characteristic length (see below)
Nu0 "Length"L
Vertical wall 0.67 H
Horizontal cylinder 0.36 D
Sphere 2.00 D
For ideal gases: =1
TM(temperature in K)
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Nu Nu
Gr
= +
+
o
Pr
( (.
Pr) )
/ /
300
105 9 16 16 9
16
(Churchill, Thelen)
valid for: 10-4< GrPr < 41014
0.022 < Pr < 7640
and Tw= const.
7 Film Condensation
All properties without subscript are for condensate at the mean temperature
T T Tm w s= +3
4
1
4
Exception: D
= vapor density at saturation temperature Ts
7-1 Laminar film condensation
a) Vertical wall or tube
Nu= =
hH
k
h g H
T T k
D
s w
09433 1 4
.( )
( )
/
(Nusselt)
Tw= mean wall temperature
b) Horizontal cylinder
Nu =
=
h D
k
h g D
T T k
D
s w0728
3 1 4
.
( )
( )
/
(Nusselt)
Tw= const.
7-2 Turbulent film condensation
For vertical wall
Re = C Am
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( )Re
( );
/
/=
=
h H T T
hA
g k H T T
h
s w s w
1 3
5 3
Recrit= 350
turbulent film: C m= =3 10 3 23 ; / (Grigull)
8 Nucleate Pool Boiling
( )q h T T w s= Tw= temperature of heating surface
Ts = saturation temperature
a) Heat transfer at ambient pressure
Nu = =
hd
kqdk T
hdd
A A
s
A
A
01
0 674 0156 2
2
0 371
2
0 350
0 162.
(Pr )
. . . .
.
(Stephan and Preuer)
' saturated liquid
'' saturated vapor
Bubble departure diameter dg
A o= 0851
2.
( ' ' ' )
Angle o = /4 rad for water
= 0.0175 rad for low-boiling liquids= 0.611 rad for other liquids
b) Water, 0.5 bar
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List of Symbols
cp specific heat capacity at constant pressure
D, d diameter
g gravitational acceleration
h mean heat transfer coefficienth enthalpy of evaporation
H height
k thermal conductivity
L lengthq heat flux
T temperature
u flow velocity
thermal diffusivity coefficient of thermal expansion
dynamic viscosity kinematic viscosity density
surface tension
Subscripts
h hydraulic
i inside
m mean
o outside
s saturationw wall
Dimensionless numbers
Gr Grashof number
Nu mean Nusselt number
Pr Prandtl number
Re Reynolds number
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References
Churchill, S.W.: Free convection around immersed bodies. Chapter 2.5.7 ofHeat Exchanger
Design Handbook, Hemisphere (1983).
Fritz, W.: In VDI-Wrmeatlas, Dsseldorf (1963), Hb2.
Gnielinski, V.: Neue Gleichungen fr den Wrme- und den Stoffbergang in turbulent
durchstrmten Rohren und Kanlen. Forschung im Ingenieurwesen41, 8-16 (1975).
Gnielinski, V.: Berechnung mittlerer Wrme- und Stoffbergangskoeffizienten an laminar und
turbulent berstrmten Einzelkrpern mit Hilfe einer einheitlichen Gleichung. Forschung im
Ingenieurwesen41, 145-153 (1975).
Grigull, U.: Wrmebergang bei der Kondensation mit turbulenter Wasserhaut. Forschung im
Ingenieurwesen13, 49-57 (1942).
Hausen, H.: Neue Gleichungen fr die Wrmebertragung bei freier und erzwungener Strmung.
Allg. Wrmetechnik9, 75-79 (1959).
Nusselt, W.: Die Oberflchenkondensation des Wasserdampfes. VDI Z. 60, 541-546 and 569-575
(1916).
Petukhov, B.S.: Heat transfer and friction in turbulent pipe flow with variable physical properties.
Adv. Heat Transfer6, 503-565 (1970).
Petukhov, B.S. and L.I. Roizen:High Temperature2, 65-68 (1964).
Pohlhausen, E.: Der Wrmeaustausch zwischen festen Krpern und Flssigkeiten mit kleiner
Reibung und kleiner Wrmeleitung.Z. Angew. Math. Mech.1, 115-121 (1921).
Shah, R.K.: Thermal entry length solutions for the circular tube and parallel plates. Proc. 3rd
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(1975).
Stephan, K.: Wrmebergang und Druckabfall bei nicht ausgebildeter Laminarstrmung in
Rohren und ebenen Spalten. Chem.-Ing.-Tech.31, 773-778 (1959).
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Stephan, K. and P. Preuer: Wrmebergang und maximale Wrmestromdichte beim
Behltersieden binrer und ternrer Flssigkeitsgemische. Chem.-Ing.-Tech.51, 37 (1979).
VDI-Wrmeatlas, 7thedition, Dsseldorf 1994.