correlaciones tc por conveccion

8/14/2019 Correlaciones TC Por Conveccion

1/12

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.


3/12

- -3

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


4/12

- -4

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


5/12

- -5

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


6/12

- -6

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)


7/12

- -7

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


8/12

- -8

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)


9/12

- -9

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


10/12

- -10

( )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


11/12

- -11

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


12/12

- -12

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

Natnl. Heat Mass Transfer Conference, Indian Inst. Technol Bombay,Vol. I, Paper HMT-11-75

(1975).

Stephan, K.: Wrmebergang und Druckabfall bei nicht ausgebildeter Laminarstrmung in

Rohren und ebenen Spalten. Chem.-Ing.-Tech.31, 773-778 (1959).

Stephan, K.: Chem.-Ing.-Tech.34, 207-212 (1962).

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.

correlaciones tc por conveccion

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