Convection on a Tube. Outside and Inside. Nusselt_Coefficient_Tout_and_Array

8/12/2019 Convection on a Tube. Outside and Inside. Nusselt_Coefficient_Tout_and_Array

1/109

Resume of Excel Fu

Outside tube convection

Ambient air a.- Outside naturalNatural_convection_array_horizontal_tube_in_still_air_Material_dn_tsurf_tamb

Natural_convection_Nusselt_horizontal_tube_Material_dn_tsurf_tamb

Natural_convection_coefficient_horizontal_tube_in_still_air_Material_dn_tsurf_tamb

b.- Outside forcedForced_convection_array_tube_in_air_Material_dn_ !mh_tsurf_tamb

Forced_convection_Nusselt_tube_in_air_Material_dn_ !mh_tsurf_tambForced_convection_coefficient_tube_in_air_Material_dn_ !mh_tsurf_tamb

c.- Outside combinedCombined_Convection_array_horizontal_tube_Material_dn_ !mh_tsurf_tamb

Combined_Convection_Nusselt_horizontal_tube_Material_dn_ !mh_tsurf_tamb

Combined_Convection_Coefficient_horizontal_tube_Material_dn_ !mh_tsurf_tamb

"elv # $%&'() "

* # +',-..) m/s0


2/109

Rev' c1c' $('

ctions for Convection in Tubes

3nside tube convection

Air d1.- Air laminar average

Avera*e_4aminar_Convection_Array_Air_Material_dn_5chOr6N_4m_t7all_tin_6bar_!*s

Avera*e_4aminar_Convection_Nusselt_Air_Material_dn_5chOr6N_4m_t7all_tin_6bar_!*s

Avera*e_4aminar_Convection_Coefficient_Air_Material_dn_5chOr6N_4m_t7all_tin_6bar_!*s

d2A.- Air turbulent local4ocal_Turbulent_Convection_Array_Air_3nside_Tube_Material_dn_5chOr6N_tair_6bar_m!*s

4ocal_Turbulent_Convection_Nusselt_Air_3nside_Tube_Material_dn_5chOr6N_tair_6bar_m!*s4ocal_Turbulent_Convection_Coefficient_Air_3nside_Tube_Material_dn_5chOr6N_tair_6bar_m!*s

d2B.- Air turbulent average and outlet temperatureForced_Convection_Avera*e_Array_tout_Air_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_6bar_m!*s

Forced_Convection_Avera*e_Nusselt_tout_Air_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_6bar_m!*s

Forced_Convection_Avera*e_Coefficient_tout_Air_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_6bar_m!*s

8ater e1.- Water laminar average

Forced_4aminar_3nterior_Array_8ater_Material_dn_5chOr6N_4m_t7all_tin_9m&hForced_4aminar_3nterior_Nusselt_8ater_Material_dn_5chOr6N_4m_t7all_tin_9m&h

Forced_4aminar_3nterior_Coefficient_8ater_Material_dn_5chOr6N_4m_t7all_tin_9m&h

e2A.- Water turbulent LocalForced_Turbulent_4ocal_Nusselt_8ater_3nside_Tube_Material_dn_5chOr6N_tbul!_ts_9m&h

Forced_Turbulent_4ocal_Coefficient_8ater_3nside_Tube_Material_dn_5chOr6N_tbul!_ts_9m&h

Forced_Turbulent_4ocal_Array_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_9m&h

e2B.- Water turbulent average and outlet temperatureForced_Turbulent_Avera*e_Nusselt_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_9m&h

Forced_Turbulent_Avera*e_Coefficientt_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_9m&h

Forced_Turbulent_Avera*e_Tem:erature_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin_9m&h

*'; Forced inside 8ater a:or


3/109

$'$-(2

Ref ( Mills


4/109

a.- Natural convection on a horizontal pipe e posed to ambient conditions !tep"ise sol - Array (Nu, he, Ra) 6i:e :ro:ertie

- Nusselt diameter "dn"- Convection coefficient or nominal rnside diamet

5elect diameter and shedule or nominal

:ressure> accordin* selected material

6i:e data Area of secti6i:e Material Carbon steel A #

dn # ($ in ?nit outside su

6i:e surface tem:erature As #

##$!%& 'C d # Ambient air tem:ereature As #

$.', @C ilm tem era

!olution using functions

Nusselt> convection coefficient and Reynolds'

For function used> see Note (

Array function

Nu # *A+ . ;he # A4?EB 8/ m0D!

Ra / *A+ . - 0 ansion vo

1in2le functions (for ideal 2as

Nu / *A+ . - 3eta /

he / A4?EB 45(m678)3eta /

Note (

9 Natural_convection_array_horizontal_tube_in_still_air_Material_dn_tsurf_tamb Mat> d$ Natural_convection_Nusselt_horizontal_tube_Material_dn_tsurf_tamb Mat> dn> ts> te

& Natural_convection_coefficient_horizontal_tube_in_still_air_Material_dn_tsurf_tamb M

Ro:s :ith i e data! ;o not delete Carbon steel

!ize 5C /6N !ize 5C

(/ $ ) (/ $ ) &/ 2 (- &/ 2 (-( $- ( $-

d e #

d e #

ts #

tamb #

tfilm /

tam3 /

t s /

tfilm /

< film8 /

< film8 /

< film8 /

Carbon steel


5/109

( (/ $ &- ( (/ $ &-$ 2- $ 2-& .- & .-2 ,- 2 ,-) (-- ) (--. ($- . ($-

, (2- , (2-(- (.- (- (.-($ 5TG ($ 5TG(2 H5 (2 H5(. HH5 (. HH5(, - (,$- - $-$$ - $$$2 - $2$. - $.$, - $,&- - &-&$ - &$&2 - &2&. - &.&, - &,2- - 2-2$ - 2$22 - 222. - 2.2, - 2,- -

- -


6/109

ution Air_:ro:erties_array_out:ut_t t> accordin* material> t # 9#$!%#& @C

and schedule "sch" # $ *A+ . 8/ mD" essure "PN"! %p $ *A+ . !I/ !*D"er &r $ *A+ . ;

A4?EB mm *A+ .A4?EB m *A+ . 6aDs

n *A+ .A4?EB m0 *A+ .

rface area

Grashof num3er*A+ . m65m Gr / 2 7 3eta 7 (A3s(ts - tam3)) 7 d = > 5 *iscCinem = #A4?EB m65m 2 / ?!%@$$& m5s6

3eta / #!& -@> 958ure ts / ##$!%& 'C

tam3 / #$!% 'C

#$!% 'C *A+ . m5s6

##$!%& 'C *isc8inem / *A+ . m65s

9#$!%#& 'C Gr / *A+ . -

>??!? & 8 Raylei2h num3erRa / Gr 7 Pr

lume coefficient Gr / *A+ . -

s) Pr / *A+ . -

Ra / *A+ . -

>??!? & 8#!& -@> B958

> ts> te

DoduleE aF utsideFNaturalFConvat> dn> ts> te

1tainless steel H;P 9@@ Daterialdn 1ch ;n Bmm 6N 5% I@1 #& % H;P P 9@@

$ !*/m &

m $/s

m $/s

7 d e 7 9

(t am3 J t s) 5 #

d e #

tfilm J # >!9&

9 5 < film8


7/109

1'2 %@1 ># 9@ (') I@ 9#!&1 &@ 9$ eatin* or coolin

1 1') $> #@ 91 1'2 & 2 ?@ C

2 1'2 99@( 9#&

( 1'2 9I@ Anne BI 9$@ JNusselt number & 9%@$ #@@ J3nside convection fo% ##& JFollo7in* relation is

9@ #&@ JThis relation may *i9# #%@9I >9& NuG # -'-$& D Re 9$ >&&9% I@@ J6etu!ov eLuation' T#@ I&@ Nu6 # f / , D Re## &@@#I &$@ JPnielins!i (+%. ; A>@ $>@ JThe accuracy of this

9@ is im:roved> in relati%@@?@@ NuP # f / , D Re ;

9@@@ Thefriction factor 7ill9#@@ instead of 6etu!ov f9I@@9$@@


8/109

Rev. cjc. 21.02.2014

NusseltB9 , q! I!% , a2e #?I

Nu # -'&. -')(, D Ra (/2 / ( -'))+/6r +/(. 2/+

Ra / *A+ .Pr / *A+ .

Nu / *A+ . -

Convection coefficienthi # Nu D ! / d

Nu # A4?EB ;

! # A4?EB 8/ mD"

d # A4?EB m

hi # A4?EB 8/ m0D!

eat loss :er meter of :i:e

9 # As #

As # *A+ . m65m

hi / *A+ . 8/ m0D!

ts # ##$!%& 'C

#$!% 'C9 # *A+ . 45m

?se Mills I), a2e I>$Gata and results in Annex K'

Ra3s Bmm Ref@!9

@!@9@!@@ B , !&

As 7 hi 7 (t s - t am3 ) D d

tamb #

96 1010


9/109

* of flo7HorC

-'2@!>

r fully develo:ed turbulent flo7 in smooth :i:es'

recommended by Gittus and Koelter' EL' ,;%- f /

(--- D 6r / ( ($'% D f / , -') D 6r $ / & ;(

be calculated usin* Colebroo! eLuation

rmula


10/109

Anne0 A

Exam:le 2'.> :a*e &--

A horizontal steam :i:e has an outside

$$.',)

$.',)&-- mm

)-- "

&-- @C

?sin* EL' 2',%

Result'

Ra # ('2(E -, ;

Nu # 2$'+ ;

h / I! > 45(m678)

K / %?# 8/m

Anne0 LB9@ , q! (?!>I), a2e I>$

@!9 m

9$& 'C

#> 'C

ResultRa / &!@ > J@$ -

Pr / @!$? -Nu / #>!> -h / !#? 45(m678)

diameter Qd eQ> an outer surface

tem:erature QTsQ and is located in still air

at tem:erature QT amb Q

ts #

tamb #

d e #

Ts #

Tamb #

d e /

tsurface /

tam3 /


11/109

tion for smooth tu3es, a2e # @, or B& q! (%-$&), a2e II9


12/109

b.- * terior forced convection on apipe e posed to ambient conditions !tep"ise sol - Array (Nu, he,Ra) 6i:e :ro:ertie- Nusselt diameter "dn"- Convection coefficient or nominal r

nside diamet5elect diameter and shedule or nominal


6i:e data Area of secti

6i:e Material 5tainless steel A #dn # -'$) in ?nit outside su

8ind velocity As #v # &. km5h d #

6i:e surface tem:erature As #($,'2 'C

Ambient air tem:ereature ilm tem era

$.'$ @C


Nusselt > convection coefficient and Reynolds'

For function used> see Note (

Array functionNu# *A+ . ; 0 ansion vohe / A4?EB 8/ m0D! (for ideal 2as

Re / *A+ . - 3eta /

1in2le functions 3eta /Nu / A4?EBhe / A4?EB 8/ m0D!

Note (

9 Forced_convection_array_tube_in_air_Material_dn_ !mh_tsurf_tamb Mat> dn> !mh>$ Forced_convection_Nusselt_tube_in_air_Material_dn_ !mh_tsurf_tamb Mat> dn> !m

& Forced_convection_coefficient_tube_in_air_Material_dn_ !mh_tsurf_tamb Mat> dn>


!ize 5C /6N !ize 5C

(/ , )5 (/ $ ) (/ 2 (-5 &/ 2 (-

&/ 2-5 ( $-

d e #

d e #

ts #

tamb # tfilm /

tam3 /

t s /

tfilm /

< film8 /

< film8 /

< film8 /

Stainless steel


13/109

(/ $ ,-5 ( (/ $ &- &/ 2 - $ 2-( - & .-

( (/ 2 - 2 ,-( (/ $ - ) (--$ - . ($-

$ (/ $ - , (2-& - (- (.-

& (/ $ - ($ 5TG2 - (2 H5) - (. HH5. - (,, - $-

(- - $$($ - $2(2 - $.(. - $,(, - &-$- - &$$$ - &2$2 - &.&- - &,- - 2-- - 2$- - 22- - 2.- - 2,- -

- -


14/109

Air_:ro:erties_array_out:ut_t t

ution t # !> @C> accordin* material> # $ *A+ . 8/ mD"

and schedule "sch" %p $ *A+ . !I/ !*D" essure "PN"! &r $ *A+ . ;

er *A+ .A4?EB mm *A+ . 6aDsA4?EB m *A+ .

n *A+ .

A4?EB m0rface area

Forced convection> exterior a tube

*A+ . m65m Avera*e Nusselt number> for 6r -')

A4?EB m65m Churchill and Kernstein :a*e $,%> eLuations 2'%(a > 2'%(b and 2'%(c

ure

Re S (- 2 (I! 9a)

#$!# 'C Nu # -'& -'.$ D Re (/$ D 6r (/& /

9#%!I 'C Nu # A4?EB

!> 'C (- 2 S# Re S 2D(- ) (I! 93)

Nu # -'& -'.$ D Re (/$ D 6r (/& / (

>&@!I& 8 Nu # A4?EB2D(- ) S# Re S )D(- . (I! 9c)

lume coefficient Nu # -'& -'.$ D Re (/$ D 6r (/& / ( s) Nu # A4?EB

>&@!I& 8 Nusselt#!? -@> B958 Nu # *A+ . -

alid for 6r -')

surf> tamb

h> tsurf> tamb b_Outside_Forced_Conv

mh> tsurf> tamb


$ !*/m &

m $/s

m $/s

7 d e 7 9

(t am3 J t s) 5 #

tfilm J # >!9&

9 5 < film8


15/109

1'2 %@1 ># 9@ (') I@ 9#!&1 &@ 9$ eatin* or coolin

1 1') $> #@ 91 1'2 & 2 ?@ C

2 1'2 99@( 9#&






16/109

Rev! cMc! #9!@#!#@9I

Reynolds 0am le !I,Re / sin2 Hil ertv / 9@ m5s Nu /d / *A+ . m5s Constants fro

*A+ . m 5s C / Re / *A+ . - m

Prandtl n ut dataPr / *A+ . - 0terio i e di

*A+ . Ambient air te

6i:e surface te

8ind velocityv #

( -'2/6r $/& (/2 Results

ilm tem erat

-'2/6r $/& (/2 D ( Re / $,$--- (/$ Pro erties at f

6r #

Re / -'2/6r $/& (/2 D ( Re / $,$--- )/, 2/) Nu /

h /

Convection coefficienthe / Nu 7k 5 dNu / *A+ . -k / *A+ . 45(m78)d # *A+ . m

he # *A+ . 45(m678)alid for 6r -')

Ra3s Bmm Ref

@!9@!@9@!@@ B !&

v 7 d 5

/

d e #

tamb #

ts #

tfilm /


17/109

* of flo7HorC

-'2@!>



(--- D 6r / ( ($'% D f / , -') D 6r $ / & ;(


rmula


18/109

B9@ , a2e >>$->>?orrelation, q! ( !)C 7 Re=m 7 Pr=(95>)

>&@!9?>@!$9%

iameter

($'% mm:ereature

$.'$ @Cm:erature

9#%!I 'C

9@ m5s

ure

!> 'C

ilm tem erature

@! -$@ 9 -> !> -%% 45(m678)


19/109


20/109

c.- %ombined convection on a horizontalpipe e posed to ambient conditionsB& , q! (?!I9), Cha ter ?, a2e I% Auxiliary varia Exterior diame

- Array (Nu, he, Ra) - Nusselt - Convection coefficient ilm tem era



6i:e data6i:e Material Carbon steel @ km5h Natural conv6i:e surface tem:erature Nusselt> conve

##$!%& 'C For function u Ambient tem:erature Nu#

$.',) @C hi #

Ra /

Combined convection

Array function*A+ . - +orced conv

*A+ . 45(m678) Nusselt > convFor function u

1in2le functions Nu#

*A+ . - he /*A+ . 45(m678) Re /

Functions used Module c_Outside_Combined_Conv

9 Combined_Convection_array_horizontal_tube_Material_dn_ !mh_tsurf_tamb Mat> dn># Combined_Convection_Nusselt_horizontal_tube_Material_dn_ !mh_tsurf_tamb Mat> d> Combined_Convection_Coefficient_horizontal_tube_Material_dn_ !mh_tsurf_tamb Mat


!ize 5C /6N !ize 5C

(/ $ ) (/ $ ) &/ 2 (- &/ 2 (-( $- ( $-

d e #

d e #

tfilm /

tam3 /

t s /

tfilm /

ts #

tamb #

Nu com3ined /

h e_Combined #

Nu com3ined /h e_Combined #

Carbon steel


21/109

$ 2- $ 2-& .- & .-2 ,- 2 ,-) (-- ) (--. ($- . ($-, (2- , (2-

(- (.- (- (.-($ 5TG ($ 5TG(2 H5 (2 H5(. HH5 (. HH5(, - (,$- - $-$$ - $$$2 - $2$. - $.$, - $,&- - &-&$ - &$&2 - &2&. - &.&, - &,2- - 2-2$ - 2$22 - 222. - 2.2, - 2,- -

- -


22/109

!tep"ise solution les %ombined natural and forced convection

er (.- %ombined natural and forced convection

A4?EB mm

*A+ . mm :ith n > Iure ( see Note ( n / I

*A+ . ; and consider the case :here 3oth effects sA4?EB 8/ m0D! 3e addedE (J) si2nus

*A+ . - *A+ .

Convection coefficientection

ction coefficient and Re' *A+ .

ed> see Note $ k / *A+ . 4 5 (m78)*A+ . ; d / *A+ . m

A4?EB 8/ m0D! *A+ .*A+ . - Com3ined convection

q! (?-I9), B& , a2e I%

!mh> ts> te

> !mh> ts> te

> dn> !mh> ts> te 4ith the e0 onent "n" :ith a value in theran2e of > and I! sed value, n / I


Nu Com3ined / A3s( (Nu Nat )=n (Nu orc )

(tam3 J t s) 5 #

NuCom3ined

/ A3s(( NuNat

)=n O (Nuorc

)=n

Nu Nat / 8/ m $D"

Nu orc / 45(m $D"

Nu Com3ined / 45(m $D"

h e_Conv # Nu Com3ined 7 k 5 d

Nu Com3ined / 45(m $D"

h e_Conv # 45(m $D"

( n

natun

forced combined Nu Nu Nu +=


23/109

(') I@ 9#!&1 &@ 9$ eatin* or coolin

1 1') $> #@ 91 1'2 & 2 ?@ C

2 1'2 99@( 9#&






24/109

Rev! cMc! #9!@#!#@9I

B&

e n-vale

all

Ra3s Bmm Ref@!9

@!@9@!@@ B , !&

n )=(95n)

)=(95n)

Micrec

)nal 1

( )

[ ]

[ ]

[ ]

[ ]

[ ]41

44

1

1

1

1

1

1

4

natural forced combined

nn

natural

n

forced combined

nn

natural

n

forced combined

nn

natural

n

forced

nn

combined

nn

natural

n

forced

n

combined

n

natural

n

n

forced combined

n

natural

n

n

forced combined

nn

natural

n

forced combined

hhh

n

withhhh

hhk d

d k

h

hhk d

d k

h

hhk d

d k

h

k d

hk d

hd k

h

k d

hk d

hk d

h

k d

h Nu

Nu Nu Nu

+==

+=

+

=

+

=

+

=

+

=

+

=

=

+=


25/109

* of flo7HorC

-'2@!>



(--- D 6r / ( ($'% D f / , -') D 6r $ / & ;(


rmula


26/109

*A+ .

*A+ .*A+ .

h com3 / ( h forc=IJh nat =I )=(95I)

h forc / 8/ m $D"

hnat / 8/ m $D"h com3 / 8/ m $D"

soft Editor deuaciones &'-

1

1

nn

nn

[ ]41

44

natural fo rced combined hhh +=


27/109

a2e II9


28/109

d1,nside laminar convection of Air !tep"ise solinside a pipe 6i:e :ro:ertiealid for Fully develo:ed laminar flo7> diameter "dn"

- +aminar flo: Re #>@@ or nominal r

- ully develo ed laminar flo: im lies

3oth, hydrodynamically and thermallyfully develo ed flo:s (Anne0 C) A #

Air flo7 is cooled as it flo7s throu*h a tube 7ith Asumed outlet

constant surface tem:erature'

5elect diameter and shedule or nominal Avera*e bul! t


6i:e data

6i:e Material 5tainless steel

dn # $ in

5ch # ,-5 ; 6i:e len*ht Gensity

4 # #& m6i:e 7all constant tem:erature 6 #

9@@ 'C R #

luid inlet tem erature and ressure() @C

P / $ 3ar (a3s) Air :ro:ertiesDass flo: rate

m # -'--( !*/s # $%p $

?sin* the array function sho7n in Note ( &r $

Array

Nu # *A+ . -

Re # *A+ . *A+ . h / *A+ . 45(m678)

tout / *A+ . 'C "inematic visc

Note 9 Avera*e_4aminar_Convection_Array_Air_Material_dn_5chOr6N_4m_t7all_tin_6bar_!*s Avera*e_4aminar_Convection_Nusselt_Air_Material_dn_5chOr6N_4m_t7all_tin_6bar_!* Avera*e_4aminar_Convection_Coefficient_Air_Material_dn_5chOr6N_4m_t7all_tin_6bar


d i #

d i #

tout_Ass #

tave #

tin #

tout #

tave #

Tave #

#

t7all #

Tave #tin # /

tave #

$

#

Stainless steel


29/109

(/ , )5 (/ $ ) (/ 2 (-5 &/ 2 (- &/ , 2-5 ( $- (/ $ ,-5 ( (/ $ &- &/ 2 - $ 2-( - & .-

( (/ 2 - 2 ,-( (/ $ - ) (--$ - . ($-

$ (/ $ - , (2-& - (- (.-

& (/ $ - ($ 5TG2 - (2 H5) - (. HH5. - (,, - $-

(- - $$($ - $2(2 - $.(. - $,(, - &-$- - &$$$ - &2$2 - &.&- - &,- - 2-- - 2$- - 22- - 2.- - 2,- -

- -


30/109

ution *olume flo: rate> accordin* material> K /

and schedule "sch" m # ('--E;-& !*/s

essure "PN"! $!>#

A4?EB mm K / 9!&% -@I mQ5s

A4?EB m elocity

A4?EB m0 v # 9 / A 9 # ('.E;-2

tem:erature A # A4?EB m0

. @C v # A4?EB m/s Reynolds

m:erature Re #

v # *A+ . m/s

()'- @C d # *A+ . m

(--'- @C *A+ . m0/s

)%') 'C Re # A4?EB -

&&-'. " *A+ .

6 / R D T Nusselt/ average.-->--- 6a Grae num3er

$,%'- I / !*D" G / Re 7 Pr 7 (d5+)

&&-'. " Re / *A+ . -$!># k25mQ Pr / *A+ . -

t ambient :ressure d / *A+ . m

& !& @C + / #& m

*A+ . 8/ mD" G / *A+ .*A+ . !I/ !*D" B9 , a2e # #, q! (I!&@)*A+ . ; Nusselt :itout consideration of*A+ . ro erties variation :ith tem erature*A+ . 6aDs

*A+ . G / *A+ .*A+ . *A+ .

sity at :ressure Q6Q

*A+ . m0/s

s DoduleE d9F orF ntF+aminarFAir!*s

1tainless steel H;P 9@@ Daterial

m 5

# !*/m &

m &/s

v D d /

t in t out_Ass / $

#

!*/m & N @ / >!$$J(@!@$&7G ) 5 (9J@!@I7G =(#5>) )

m $/sm $/s Nu @ /

2300Re


31/109

95% &1 9$ I Car3on steel @!9 95I 9@1 #@ $ 1tainless steel @!@9 >5% I@1 #& % H;P P 9@@ @!@@ 1'2 %@1 ># 9@ (') I@ 9#!&1 &@ 9$ eatin* or coolin* of flo

1 1') $> #@ 9 HorC1 1'2 & -'22 ?@ C @!>

2 1'2 99@( 9#&

( 1'2 9I@ Anne BI 9$@ JNusselt number & 9%@$ #@@ J3nside convection for fully dev% ##& JFollo7in* relation is recomme

9@ #&@ JThis relation may *ives errors9# #%@9I >9& NuG # -'-$& D Re -', D 6r 9$ >&&9% I@@ J6etu!ov eLuation' This relatio#@ I&@ Nu6 # f / , D Re D 6r / ('-## &@@#I &$@ JPnielins!i (+%. ; A modificati>@ $>@ JThe accuracy of this eLuation

9@ is im:roved> in relation to 6etu%@@?@@ NuP # f / , D Re ; (--- D 6

9@@@ Thefriction factor 7ill be calcul9#@@ instead of 6etu!ov formula


32/109

Rev! cMc! #9!@#!#@9I

Correction for ro erties variation Anne C. Outlet temperature :ith the tem erature or a heat e0chan2er :ith constant :all

tem erature, the outlet tem erature

0 onent for viscosity correction can 3e calculated :ith the equation

+aminar flo: of 2asa B9 , q!(I!99), a2e

9@@ 'C>>@!$ 'C

rom


33/109


34/109

Anne0 C! Cen2el and GhaMar, B&ully develo ed laminar flo:or this ty e of flo:, the Nusselt Cen2el and GhaMar, B&num3er is constant! ntry len2ths for laminar fl

@!@& 7 Re 7 d

-Hydrodynamically fully develo ed @!@& 7 Re 7 d

@!@& 7 d 7 Re q! (%-99)d / @!9@I m

Re / *A+ . - ntry len2ths for tur3ulent f

*A+ . m 9!>&? 7 Re=(9

t is 2enerally a2reed that e- !@ -

*A+ . m

Note!


35/109

Petukov equation for smooth tu3esB9 , q! (I!I#), a2e # @, or B& q! (%-$&), a2e II9

f / ( @! ?@ 7 +n(Re) - 9!$I )=-#Re / *A+ .

f / *A+ .


36/109

:

q! (%-99)

7 Pr q! (%-9#)

lo:

5I) q! (%-9>)

ntrance effects for:ithin a tu3e len2th

rodynamic and thermal

tely taken to 3e

9@ 7 d q! (%-9I)

onvection heat transferr in the entrance re2ion!

2th is taken as the

ance, :here the friction

3out #T of the fully


37/109


38/109

Air *as constant

,&(2'2( I/ !molD"

MM # $,'+% !*/!mol

R #

R # $,%'- I / !*D"

R *en

R *en / MM

= Ld

Gz Pr Re

32

04.01

065.066.3

Gz

Gz Nu

++=

Microsof t Editor deecuaciones &'-


39/109


40/109

d2A0urbulent convection of Air inside a pipe alid for Fully develo:ed turbulent flo7> ?sin* the array function sho7n

that is> for Re (->--- Array

+ocal value Nu# A4?EB Air flo7 is heated as it flo7s throu*h a tube hi / A4?EB

7ith constant 7all tem:erature' Re # A4?EB

Calculation is done for a local :oint'

5elect diameter and shedule or nominal sin2 the sin2le functions (N

:ressure > accordin* selected material Nu / *A+ .6i:e data hi / *A+ .6i:e Material G6E 6E(--

dn # &$ mm6N # (. bar !tep"ise solution

4 # #& mFluid data 6i:e :ro:erties> accordin* mate

t # $-- @C diameter "dn"and schedule "6 # # 3ar (a3s) or nominal ressure "PN"!m # -'--, !*/s A4?EB

A4?EB Air *as constant A # A4?EB

,&(2'2( I/ !molD"MM # $,'+% !*/!mol Gensity

R # r # 6 / R D TR # $,%'- I / !*D" 6 # $-->---

R # $,%'-T # 2%&'()

9!I >

Note ( 4ocal_Turbulent_Convection_Array_Air_3nside_Tube_Material_dn_5chOr6N_tair_6bar_m!*s

Note $ 4ocal_Turbulent_Convection_Nusselt_Air_3nside_Tube_Material_dn_5chOr6N_tair_6bar_m!*

4ocal_Turbulent_Convection_Coefficient_Air_3nside_Tube_Material_dn_5chOr6N_tair_6bar_m

Note & Pnielins!y eLuation reLuires that Qthe friction factor must be calculated from EL' 2'2$ Q > :a

Ro:s :ith i e data! ;o not delete Carbon steel 1tainless steel

!ize 5C /6N !ize 5C dn(. 2 ) 95%$- . (- 95I$) , ( $- >5%

d i #

d i #

R *en

R*en / MM

/

HDPE PE100


41/109

2- ($') $ 2- ('))- (. & .- 1.& $- 2 ,- 1 1')%) - ) (-- 1 1'2+- - . ($- 2

((- - , (2- 2 1'2

($) - (- (.- (

(2- - ($ 5TG ( 1'2(.- - (2 H5 I(,- - (. HH5 &$-- - (, $$$) - $- %$)- - $$ 9@$,- - $2 9#&() - $. 9I&)) - $, 9$2-- - &- 9%2)- - &$ #@)-- - &2 ##).- - &. #I.&- - &, >@%(- - 2-,-- - 2$+-- - 22

(--- - 2.($-- - 2,(2-- -

(.-- -


42/109

Convection co

in Note ( Air ro erties (from *LA functions) hi #

t # $-- @C Nu #

; 6r # A4?EB ; ! #8/ m0D! *A+ . d #

A4?EB *A+ . Pa s hi #9!&

riction facto

ote #) *A+ . m0/s f /

- ! # A4?EB 8 mD! Re /45(mQ78) C: # A4?EB !I / !*D" f /

olume flo7 rate Nusselt Pni Rho # 9!I > k25mQ

ch" 9 # @!@@&I mQ5s or accuracy,elocity Nu /

mm v # 9 / A f /m 9 # )'2E;-& Re /m0 A # A4?EB m0 Pr /

v # A4?EB m/s Nu /Reynolds *A+ .

Re #6a v # *A+ . m/s Convection coI / !*D" d # *A+ . m hi #" *A+ . m0/s Nu #k25mQ Re # A4?EB - ! #

d #hi #

at> dn> 5chOr6N> t> 6bar> m!*s

Mat> dn> 5chOr6N> t> 6bar> m!*s Module d$_For_3nt_Turbulent_Air

!*s Mat> dn> 5chOr6N> t> 6bar> m!*s

e $%-' f # -'%+ D 4n Re ; ('.2 ;$

H;P 9@@ Daterial1ch n Bmm 6N Ra3 Ref &1 9$ I Car3on steel @!99@1 #@ $ 1tainless steel @I@1 #& % H;P P 9@@ @ B , !&

#

# !*/m &

# /

#

m &/s

v D d /

#


43/109

I@ 9#!&&@ 9$ eatin* or coolin* of flo7$> #@ 9 orC& -'2?@ C @!>

99@

9#&9I@ Anne B9$@ JNusselt number 9%@#@@ J3nside convection for fully develo:ed##& Follo7in* relation is recommended b#&@ on :a*e $%2' This relation may *ive#%@>9& NuG # -'-$& D Re -', D 6r n>&&I@@ J6etu!ov eLuation' This relation mayI&@ Nu6 # f / , D Re D 6r / ('-% ($&@@&$@ JPnielins!i (+%. ; A modification of$>@ JThe accuracy of this eLuation at lo79@ is im:roved> in relation to 6etu!ov e%@@?@@ NuP # f / , D Re ; (--- D 6r / (

9@@@ Thefriction factor 7ill be calculated u9#@@ instead of 6etu!ov formula


44/109

Rev! cMc! #9!@#!#@9I

fficient Anne0 CNu D ! / d

-'- ;

A4?EB 8/ mD"A4?EB m

A4?EB 8/ m0D! -Hydrodynamically fully develo edB& , q! (%-9I)

(Note >) 9@ 7 d

(@! ? 7 +n(Re) - 9!$I) = (-#) d / *A+ . m

*A+ . *A+ . m*A+ .

-


45/109

turbulent flo7 in smooth :i:es' B& Uunus A! Cen2el and Afshin S! GhaMar y Gittus and Koelter' EL' ,;%- f / *A+ .

($'% D f / , -') D 6r $ / & ;( sin* Colebroo! eLuation

;.) for smooth tubes'


46/109

Cen2el and GhaMar, B&ntry len2ths for laminar flo: ;ata for e0am le $-9, Pa2

@!@& 7 Re 7 d q! (%-99) ( sin2 ;ittus and Loelter e@!@& 7 Re 7 d 7 Pr q! (%-9#) Pi e data

3nterior diameter

di # #&

ntry len2ths for tur3ulent flo: Fluid data

9!>&? 7 Re=(95I) q! (%-9>) t # #@@

t is 2enerally a2reed that entrance effects for 6 # # tur3ulent flo:, are confined :ithin a tu3e len2th 9 # (%'.%of 9@ diameters and the hydrodynamic and thermal Flo7 reLuired to ontain a vel

entry len2ths are a ro0imately taken to 3e v # 9@9@ 7 d q! (%-9I) eatin* or coolin* of flo7

orC # HNote!Nusselt num3ers and thus convection heat transfer Result for the Nusselt B#coefficients are much hi2her in the entrance re2ion! Nu / I9!$%

Results usin2 ;ittus and L and data from e0am le $-9

Nu / I@!$#hi / $@!9

+hF+am

/

+tF+am /

+tF+am / + hF+am 7 Pr

+hF


47/109


48/109

#%>, B#

quation)

mm

'C

3ar (a3s)

city

m5s

elter


49/109


50/109

d2B0urbulent convection of Air inside a pipe sin2 the sin2le functionsalid for Fully develo:ed turbulent flo7> Note #that is> for Re (->--- Nu / *A+ .

Air flo: is cooled as it flo:s throu2h a tu3e hi / *A+ .

utlet tem erature :ill 3e calculated5elect diameter and shedule or nominal !tep"ise solution

:ressure> accordin* selected material 6i:e :ro:erties> accordin* mate

6i:e data diameter "dn"and schedule "

6i:e Material Carbon steel or nominal ressure "PN"!dn # ( in A4?EB

5ch # 2- ; A4?EB

4 # & m Area of i e section6i:e 7all tem:erature A # A4?EB

(-- 'CFluid data Asumed outlet tem:erature

$-- @C 1 ). 26 # # 3ar (a3s)m # -'--% !*/s Avera*e bul! tem:erature

Air *as constant

,&(2'2( I/ !molD" $--'-

MM # $,'+% !*/!mol (-2'+R # ()$')

R # $,%'- I / !*D" 2$)'.

!olution using functions Air densityNusselt number 6 / R D T?sin* the fuction sh7on in Note ( 6 # $-->---

Nu# A4?EB ; R # $,%'-

Re # A4?EB A4?EB T # 2$)'.(

hi / A4?EB 8/ m0D! 9!$Itout / A4?EB @CNote ( Forced_Convection_Avera*e_Array_tout_Air_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tin

Note $ Forced_Convection_Avera*e_Nusselt_tout_Air_3nside_Tube_Material_dn_5chOr6N_4m_t7all_

Forced_Convection_Avera*e_Coefficient_tout_Air_3nside_Tube_Material_dn_5chOr6N_4m_t7

Anne #!- Ro:s :ith i e data! ;o not delete Carbon steel 1tainless steel

!ize 5C /6N !ize 5C dn (/ $ ) ) 95%

:ith constant surface tem eratre "t :all "

d i #

d i #

t7all #

tin # t out_Ass #

tave # t in t out_Ass / $

R *en t in #

tout

#

R*en / MM t ave #

Tave #

/

/

Carbon steel


51/109

( $- ( $- >5%( (/ $ &- &- 1'2$ 2- $ 2- (')& .- & .- 12 ,- 2 ,- 1 1')) (-- ) (-- 1 1'2

. ($- . ($- 2

, (2- , (2- 2 1'2

(- (.- (- (.- (

($ 5TG ($ 5TG ( 1'2(2 H5 (2 H5 I(. HH5 (. HH5 &(, - (, $

$- - $- %

$$ - $$ 9@

$2 - $2 9#$. - $. 9I$, - $, 9$&- - &- 9%&$ - &$ #@&2 - &2 ##&. - &. #I&, - &, >@2- - 2-2$ - 2$

22 - 222. - 2.2, - 2,- -

- -


52/109

*olume flo: rate riction factor (Petukov)K / f / ( @! ?@ 7 +n(re) - 9

- m / @!@@ k25s Re / *A+ .

45(m678) 9!$I k25mQ f / *A+ .

K / I!#% -@> mQ5s Gnielinsky equation requires the use

of Petukov equation B9 , a2e # #

*elocity Nusselt Pnielins!y eLuation

rial> v # 9 / A EL' 2'2) > 6a*e $%- Ann

ch" 9 # 2'$,E;-& alidity ran*e

A # A4?EB m0

mm v # A4?EB m/s EL' 2'2) > :a*e $%-

m NuP # f / , D Re ; (--- D 6r / ( ($'% D f / , -')

Air :ro:erties at ambient :ressure The friction factor must be calculated usinm0 9!& @C 6etu!ov eLuation

# $ *A+ . 8/ mD" for smooth tubes EL' 2'2$ > :a*e $%-%p $ *A+ . !I/ !*D" f # -'%+- D 4n re ; ('.2 ;$ EL' 2'

@C &r $ *A+ . ; For accuracy> see Annex $*A+ .

*A+ . 6aDs Nu # EL' 2'2) *A+ . f # A4?EB

'C *A+ . Re # A4?EB

'C "inematic viscosity at :ressure Q6Q 6r # A4?EB'C *A+ . m0/s Nu # A4?EB" A4?EB

Reynolds

Re # Convection coefficient

v # *A+ . m/s hi # Nu D ! / d

6a d # *A+ . m Nu # A4?EB

I / !*D" *A+ . m0/s ! # A4?EB" Re # A4?EB - d # A4?EB

k25mQ *A+ . hi # A4?EBA4?EB _6bar_m!*s Mat> dn> 5chOr6N> 4m> t7all> tin> 6bar> m!*s

in_6bar_m!*s Mat> dn> 5chOr6N> 4m> t7all> tin> 6bar> m!*s DoduleE d#F orF ntF dn> 5chOr6N> 4m> t7all> tin> 6bar> m!*s

H;P 9@@ Daterial

1ch Bm 6N


53/109

I@1 #& % H;P P 9@@ @ B , !&%@1 ># 9@

I@ 9#!&&@ 9$$> #@&

?@99@9#& Anne 29I@ JNusselt number 9$@9%@ J3nside convection for fully develo:ed turbulent flo7 in s#@@ Follo7in* relation is recommended by Gittus and Koelte

##& on :a*e $%2' This relation may *ives errors as lar*e a

#&@

#%@ NuG # -'-$& D Re -', D 6r n>9&>&& J6etu!ov eLuation' This relation may *ives errors less thI@@ Nu6 # f / , D Re D 6r / ('-% ($'% D f / , -') D 6I&@&@@ JPnielins!i (+%. ; A modification of 6etu!ov eLuation'&$@ JThe accuracy of this eLuation at lo7er Reynolds numb$>@ is im:roved> in relation to 6etu!ov eLuation :a*e 229@%@@ EL' 2'2) > :a*e $%-?@@ NuP # f / , D Re ; (--- D 6r / ( ($'% D f / , -')

The friction factor must be calculated usin* :etu!ov eLfor smooth tubes EL' 2'2$ > :a*e $%-'

f / ( @! ?@ 7 +n(re) - 9!$I )=(-#)


54/109

Rev! cMc! #9!@#!#@9I

Anne C. Outlet temperature Anne0 C!$I )=(-#) or a heat e0chan2er :ith constant :all

tem erature, the outlet tem erature

can 3e calculated :ith the equation

B9 , q!(I!99), a2e

-HydrodynaB& , q! (%-9I

ex K

d /

D 6r $ / & ;( -


55/109

ooth :i:es'r'


56/109

Cen2el and GhaMar, B&ntry len2ths for laminar flo:

@!@& 7 Re 7 d q! (%-99)

@!@& 7 Re 7 d 7 Pr q! (%-9#)

ically fully develo ed

9@ 7 d ntry len2ths for tur3ulent flo:

*A+ . m 9!>&? 7 Re=(95I) q! (%-9>)

*A+ . m t is 2enerally a2reed that entrance effects for tur3ulent flo:, are confined :ithin a tu3e len2th

ully develo ed of 9@ diameters and the hydrodynamic and thermal

entry len2ths are a ro0imately taken to 3e9@ 7 d 9@ 7 d q! (%-9I)

*A+ . mNote!Nusselt num3ers and thus convection heat transfer

& m coefficients are much hi2her in the entrance re2ion!

*A+ .flo: is

*A+ .

*A+ .flo: is

*A+ .

inar flo: is

*A+ .

nar flo: is *A+ .

Anne0 >ully develo in2 len2th for tur3ulentfl d

+hF+am /

+tF+am /


+hF


57/109

+5d / 9@A coordin2 B9 , a2e# #E4hen no lar2e scale eddies are resent

+5d / 9@ -9&4hen lar2e scale eddies are resent

+5d / >@ - I@

+et9& 7 d

d / *A+ . m

*A+ . mPi e len2th

+ / & m+en2th ercenta2e no develo ed

*A+ .

*A+ . T


58/109

;ata for e0am le $-9, Pa2e #%>, B#( sin2 ;ittus and Loelter equation)

Pi e data

3nterior diameter

di # #& mmFluid data

t # #@@ 'C

6 # # 3ar (a3s)

9 # (%'.%Flo7 reLuired to ontain a velocity

v # 9@ m5s

eatin* or coolin* of flo7orC # H

Result for the Nusselt B#Nu / I9!$%

Results usin2 ;ittus and Loelterand data from e0am le $-9

Nu / I@!$#hi / $@!9


59/109


60/109

e1.- Average laminar convection of sin2 sin2le functions"ater inside a pipe Nu / *A+ .

hi / *A+ .

alid forFully develo:ed laminar flo7> - +aminar flo: Re #>@@

- ully develo ed laminar flo: im lies3oth, hydrodynamically and thermally !tep"ise solutionfully develo ed flo:s (Anne0 C) 6i:e :ro:erties> accordin* mate

8ater flo7 is cooled as it flo7s throu*h a tube diameter "dn" @

7ith constant surface tem:erature' or nominal ressure "PN"!A4?EB

5elect diameter and shedule or nominal A4?EB

:ressure> accordin* selected material A # A4?EB

6i:e data Asumed outlet tem:erature

6i:e Material 5tainless steel .(

dn # & in Avera*e bul! t

5ch # ,-5 ; 6i:e len*ht ()'-

4 # #@ m .-'&-6i:e 7all tem:erature constant &%'%

9@@ 'C &(-',-

luid nlet tem erature and ressure 4ater ro erties ( unction a

() @C t / > !*olume flo: rate # $ A4?EB

9 -'$) mU/h %p $ A4?EB

&r $ A4?EB

?sin* the functions A4?EB

Array function A4?EBNu # *A+ . - A4?EBRe # *A+ . *A+ . A4?EB

hi / *A+ . 45(m678) &sat $ A4?EBtout / *A+ . 'C

orcedF+aminarF nteriorFArrayF4aterFDaterialFdnF1ch rPNF+mFt:allFtinFKm>horcedF+aminarF nteriorFNusseltF4aterFDaterialFdnF1ch rPNF+mFt:allFtinFKm>horcedF+aminarF nteriorFCoefficientF4aterFDaterialFdnF1ch rPNF+mFt:allFtinFKm

Ro:s :ith i e data! ;o not delete Carbon steel 1tainless steel

!ize 5C /6N !ize 5C dn

d i #

d i #

tout_Ass #

tave # t in t out_Ass / $

tin #

tout #

tave #

t7all # T ave #

tin #

$

Stainless steel


61/109

(/ 2 (-5 &/ 2 (- 95I &/ , 2-5 ( $- >5% (/ $ ,-5 ( (/ $ &- 1'2 &/ 2 - $ 2- (')( - & .- 1

( (/ 2 - 2 ,- 1 1')

( (/ $ - ) (-- 1 1'2$ - . ($- 2

$ (/ $ - , (2- 2 1'2& - (- (.- (

& (/ $ - ($ 5TG ( 1'22 - (2 H5 I) - (. HH5 &. - (, $, - $- %

(- - $$ 9@($ - $2 9#(2 - $. 9I(. - $, 9$(, - &- 9%$- - &$ #@$$ - &2 ##$2 - &. #I&- - &, >@- - 2-- - 2$- - 22- - 2.- - 2,- -

- -


62/109

elocity Correction for ro erties variat - v # 9 / A :ith the tem erature! B9 , q! (45(m678) 9 # -'----%

A # A4?EB m0 0 onent for viscosity correctiv # A4?EB m/s +aminar flo: of liquid

Mass flo7 rate 9@@m # K 7 Rho > !

rial> 9 # $!?II -@@& rom :ater functions

Rho # *A+ . *A+ .

m / *A+ . k25s *A+ .mm Reynolds rom h

H;P 9@@ Daterial1ch Bm 6N !$$J(@!@$&7G ) 5 (9J@!@I7G =(#5>) )

Nu 3 /

2300Re


63/109

9@1 #@ $ 1tainless steel @I@1 #& % H;P P 9@@ @ B , !&%@1 ># 9@

I@ 9#!&&@ 9$ eatin* or coolin* of flo7$> #@ 9 orC

& -'2?@ C @!>

99@9#&9I@ Anne B9$@ JNusselt number 9%@#@@ J3nside convection for fully develo:ed turbulent flo7 in smooth :i:es'##& JFollo7in* relation is recommended by Gittus and Koelter'@ JThe accuracy of this eLuation at lo7er Reynolds numbers9@ is im:roved> in relation to 6etu!ov eLuation :a*e 22(> EL' ,;%-%@@?@@ NuP # f / , D Re ; (--- D 6r / ( ($'% D f / , -') D 6r $ / &

Thefriction factor 7ill be calculated usin* Colebroo! eLuation

instead of 6etu!ov formula


64/109

Rev! cMc! #9!@#!#@9I

Anne0 C! Cen2el and GhaMion Anne C. Outlet temperature ully develo ed laminar floI!>%) or a heat e0chan2er :ith constant :all or this ty e of flo:, the N

tem erature, the outlet tem erature num3er is constant!

n can 3e calculated :ith the equationB9 , q!(I!99), a2e -Hydrodynamically fully de

'C @!@& 7 d 7 Re'C d / *A+ .

Re / *A+ .

Pa s *A+ .

Pa s iquids -


65/109

on :a*e $%2

Petukov equation for smooB9 , q! (I!I#), a2e # @, o

f / ( @! ?@ 7 +n(Re / *A+ .

f / *A+ .

;(


66/109

ar, B&

sselt Cen2el and GhaMar, B&ntry len2ths for laminar flo:

@!@& 7 Re 7 d q! (%-99)elo ed @!@& 7 Re 7 d 7 Pr q! (%-9#)

q! (%-99)

m - ntry len2ths for tur3ulent flo:

m 9!>&? 7 Re=(95I) q! (%-9>)

t is 2enerally a2reed that entrance effects forq! (%-9#) tur3ulent flo:, are confined :ithin a tu3e len2th

of 9@ diameters and the hydrodynamic and thermal

m entry len2ths are a ro0imately taken to 3e - 9@ 7 d q! (%-9I)

m

Note!

Nusselt num3ers and thus convection heat transferm coefficients are much hi2her in the entrance re2ion!


67/109

h tu3esr B& q! (%-$&), a2e II9e) - 9!$I )=-#


68/109

= Ld

Gz Pr Re

32

04.01

065.066.3

Gz

Gz Nu

++=

Microsof t Editor deecuaciones &'-


69/109


70/109

e2A.- Local turbulent convection of"ater inside a pipe !tep"ise solution

+ocal value 6i:e :ro:erties> accordin* mate

diameter "dn"and schedule "

alid for Fully develo:ed turbulent flo7> or nominal ressure "PN"!

that is> for Re (->--- A4?EB

A4?EB

8ater flo7 is heated as it flo7s throu*h a tube A # A4?EB

7ith constant 7all tem:erature Qt7Q Rabs # -'(

Calculation :ill 3e done for a local oint!Film tem:erature


:ressure > accordin* selected material $.',)6i:e data ..'+

6i:e Material Carbon steel 2.'+dn # $ in

5ch # 2- ; 4ater ro ert (from *LA functiRabs # -'( mm t # 2.'+

4 # #& m 6r # A4?EBKul! fluid tem:erature *A+ .

tb # #$!%& 3ar (a3s) *A+ .8all surface tem:erature

ts # ..',) @C *A+ .4ater flo: rate ! # A4?EB

9 # $,'$% mU/h C: # A4?EB

!olution using functionssin2 sin2le functions (Note9)

Nu / A4?EB ;h / A4?EB

Forced_Turbulent_4ocal_Array_8ater_3nside_Tube_Material_dn_5chOr6N_tNote ( Forced_Turbulent_4ocal_Nusselt_8ater_3nside_Tube_Material_dn_5chOr6N

Forced_Turbulent_4ocal_Coefficient_8ater_3nside_Tube_Material_dn_5chO

orcedF


71/109

( (/ $ &- &- 1'2$ 2- $ 2- (')& .- & .- 12 ,- 2 ,- 1 1')) (-- ) (-- 1 1'2. ($- . ($- 2

, (2- , (2- 2 1'2(- (.- (- (.- (($ 5TG ($ 5TG ( 1'2(2 H5 (2 H5 I(. HH5 (. HH5 &(, - (, $$- - $- %$$ - $$ 9@$2 - $2 9#$. - $. 9I$, - $, 9$&- - &- 9%&$ - &$ #@&2 - &2 ##&. - &. #I&, - &, >@2- - 2-2$ - 2$22 - 222. - 2.2, - 2,- -

- -


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v # 9 / A B9 , q! (I!I&), Pa2e # @ (Ann

ch" 9 # -'--%+ Ran2esE

A # A4?EB m0

mm v # A4?EB m/s Nu / (1ee Anne0 L"m f / *A+ .

m0 Reynolds Re / *A+ .

mm Re # Pr / *A+ .

v # *A+ . m/s Nu / *A+ .d # *A+ . m *A+ .

*A+ . m0/s

@C Re # A4?EB - Convection coefficient@C *A+ . hi # Nu D ! / d

@C Nu # A4?EBRelative ru2osity ! # A4?EB

ns) Rrel / Ra3s 5 d d # A4?EB@C Ra3s / @!9 mm hi # A4?EB ; d / *A+ . mm *A+ .Pa s Rrel / *A+ . -

riction factor! B9 , q- I!I#, a2e # @m0/s Gnielinsky, smooth tu3es8 mD! f / f(Re)!I / !*D" Re / *A+ .

f / *A+ .

bul!_ts_9m&h _tbul!_ts_9m&h Module e$_For_3nt_Turbulent_8ater 6N_tbul!_ts_9m&h

tsFKm>h

H;P 9@@ Daterial1ch n Bmm 6N


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%@1 ># 9@I@ 9#!&&@ 9$ eatin* or coolin* of flo7$> #@ 9 HorC& -'2?@ C @!>

99@9#&9I@ Anne B9$@ JNusselt number 9%@#@@ J3nside convection for fully develo:ed turbulent flo7 in smooth :i:es'##& JFollo7in* relation is recommended by Gittus and Koelter'@ JThe accuracy of this eLuation at lo7er Reynolds numbers9@ is im:roved> in relation to 6etu!ov eLuation :a*e 22(> EL' ,;%-%@@?@@ NuP # f / , D Re ; (--- D 6r / ( ($'% D f / , -') D 6r $ / & ;(

9@@@ Thefriction factor 7ill be calculated usin* Colebroo! eLuation9#@@ instead of 6etu!ov formula


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Rev! cMc! #9!@#!#@9I

Anne0 CCen2el and

e0 L) ntry len2ths

-Hydrodynamically fully develo ed - B& , q! (%-9I)

- 9@ 7 d ntry len2ths

- d / *A+ . m

- *A+ . m t is 2enerallytur3ulent flo

-


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Petukov equation for smooth tu3esB9 , q! (I!I#), a2e # @, or B& q! (%-$&), a2e II9

f / ( @! ?@ 7 +n(Re) - 9!$I )=-#Re / *A+ .

f / *A+ .

:a*e $%2


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Exam:le ,'&> :a*e &,. 4ater flo:s throu2h a tu3e :ith

7all surface tem:erature constant

(-- @C

di # )- mm

4 # .'- mm

m # @!#& !*/s

9& @C

& @C

Result

h / &$ 8/ m0D"

t7all #

tin /

tout /


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*2b.- Average turbulent convection of"ater inside a pipe

sin2 the sin2le functions sho:n in

alid for Fully develo:ed turbulent flo7>

that is> for Re (->--- Nu / *A+ .

8ater flo7 is cooled as it flo7s throu*h a tube hi / *A+ .

tout *A+ .Outlet tem:erature 7ill be calculated

5elect diameter and shedule or nominal !tep"ise solution

:ressure> accordin* selected material6i:e data 6i:e :ro:erties> accordin* mate6i:e Material G6E 6E(-- diameter "dn"and schedule "sch

dn # .& mm or nominal ressure "PN"!

6N # (. bar A4?EB

4 # m A4?EB6i:e 7all tem:erature Area of i e section

$- 'C A # A4?EBFluid data

,- @C Asumed outlet tem:erature9 # $,'$% mU/h 42.4)


3nterior turbulent convection ?sin* the array function sho7n in Note (

Nu# A4?EB ;Re # A4?EB A4?EBhi / A4?EB 8/ m0D!

tout / *A+ . 'C

Note 9 Forced_Turbulent_Avera*e_Array_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7all_tinNote # Forced_Turbulent_Avera*e_Nusselt_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7all_ti

Forced_Turbulent_Avera*e_Coeff ic ien t_tout_8ater_3nside_Tube_Material_dn_5chOr6N_4m_t7a

Forced_Turbulent_Avera*e_Tem:erature_tout_8 ater_3nside_Tube_Material_dn_5chOr6N_4m_t

Anne #!- Ro:s :ith i e data! ;o not delete Carbon steel 1tainless steel

!ize 5C /6N !ize 5C dn(. 2 (/ $ ) 95%

7ith constant surface tem:eratre Qt 7all Q

d i #

d i #

t7all #

tin #

tout_Ass #

HDPE PE100


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$) , ( $- >5%&$ (- ( (/ $ &- 1'22- ($') $ 2- ('))- (. & .- 1.& $- 2 ,- 1 1')%) - ) (-- 1 1'2

+- - . ($- 2

((- - , (2- 2 1'2($) - (- (.- (

(2- - ($ 5TG ( 1'2(.- - (2 H5 I(,- - (. HH5 &$-- - (, $

$$) - $- %

$)- - $$ 9@

$,- - $2 9#&() - $. 9I&)) - $, 9$2-- - &- 9%2)- - &$ #@)-- - &2 ##).- - &. #I.&- - &, >@%(- - 2-,-- - 2$

+-- - 22(--- - 2.($-- - 2,(2-- -

(.-- -


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ReynoldsNote # Avera*e bul! tem:erature Re #

v # *A+ .

,-'- 'C d # *A+ .

45(m678) )$') 'C *A+ .

'C ..'& 'C Re # A4?EB&&+'2 " *A+ .

4aterF ro ertiesFarrayFout utFt (t) riction factor (Petukov)

t / $$!> 'C f / ( @! ?@ 7 +n(re) - 9rial> # $ A4?EB 8/ mD" Re / *A+ .

" %p $ A4?EB !I/ !*D" f / *A+ .&r $ A4?EB ; Gnielinsky equation requires t

mm A4?EB of Petukov equation B9 , a2e

m A4?EB 6aDs Nusselt Pnielins!y eLuation A4?EB B9 , q! (I!I&), Pa2e # @ (Ann

m0 A4?EB *alidity ran2e&sat $ A4?EB bar

or accuracy, see Anne0 #@C Dass flo: rate Nu / or equation, see

m / f / *A+ .

K / @!@@ %& mQ5s Re / *A+ .A4?EB Pr / *A+ .

m / *A+ . k25s Nu / *A+ .*A+ .

*elocity Convection coefficientv # 9 / A hi # Nu D ! / d9 # %',)E;-& Nu # A4?EB

A # A4?EB m0 ! # A4?EB

v # A4?EB m/s d # A4?EB

hi # A4?EB

9m&h Mat> dn> 5chOr6N> 4m> t7all> tin> 9m&h *A+ .n_9m&h Mat> dn> 5chOr6N> 4m> t7all> tin> 9m&h

ll_tin_9m&h Mat> dn> 5chOr6N> 4m> t7all> tin> 9m&h Module e$_For_3nt_Turbulent_8ater

all_tin_9m&h Mat> dn> 5chOr6N> 4m> t7all> tin> 9m&h

H;P 9@@ Daterial1ch n Bm 6N Ra3 Ref &1 9$ I Car3on steel @!9

v D d / tave # t in t out_Ass / $

tin #

tout # #

tave #

Tave #

$ !*/m &

m $/s

m $/s

K 7

$ !*/m &

m &/s

4 15Re10

200Pr 5.0


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I@1 #& % H;P P 9@@ @ B , !&%@1 ># 9@

I@ 9#!&&@ 9$$> #@&

?@99@9#&

9I@ Anne 29$@ JNusselt number 9%@#@@ J3nside convection for fully develo:ed turbulent flo7 in s

##& Follo7in* relation is recommended by Gittus and Koelte

#&@ on :a*e $%2' This relation may *ives errors as lar*e a

#%@>9& NuG # -'-$& D Re -', D 6r n>&&I@@ J6etu!ov eLuation' This relation may *ives errors less thI&@ Nu6 # f / , D Re D 6r / ('-% ($'% D f / , -') D 6&@@&$@ JPnielins!i (+%. ; A modification of 6etu!ov eLuation'$>@ JThe accuracy of this eLuation at lo7er Reynolds numbe9@ is im:roved> in relation to 6etu!ov eLuation :a*e 22%@@

?@@ NuP # f / , D Re ; (--- D 6r / ( ($'% D f / , -')9@@@ The friction factor must be calculated usin* :etu!ov eLu9#@@ for smooth tubes EL' 2'2$ > :a*e $%-'9I@@ f / ( @! ?@ 7 +n(re) - 9!$I )=(-#)9$@@


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Rev! cMc! #9!@#!#@9I

Anne C. Outlet temperature Anne0 Cor a heat e0chan2er :ith constant :all

m/s tem erature, the outlet tem erature

m can 3e calculated :ith the equation

m0/s B9 , q!(I!99), a2e

- -HydrodynamiB& , q! (%-9I)

d /

!$I )=(-#)

-


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ooth :i:es' B& Uunus A! Cen2el and Afshin S! GhaMar

'


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Cen2el and GhaMar, B&ntry len2ths for laminar flo:

@!@& 7 Re 7 d q! (%-99)

@!@& 7 Re 7 d 7 Pr q! (%-9#)

cally fully develo ed

9@ 7 d ntry len2ths for tur3ulent flo:

*A+ . m 9!>&? 7 Re=(95I) q! (%-9>)

*A+ . m t is 2enerally a2reed that entrance effects for tur3ulent flo:, are confined :ithin a tu3e len2th

lly develo ed of 9@ diameters and the hydrodynamic and thermalentry len2ths are a ro0imately taken to 3e

9@ 7 d 9@ 7 d q! (%-9I)

*A+ . mNote!Nusselt num3ers and thus convection heat transfer

m coefficients are much hi2her in the entrance re2ion!

*A+ . lo: is

*A+ .

*A+ . lo: is

*A+ .

ar flo: is

*A+ .

ar flo: is *A+ .

Anne0 >ully develo in2 len2th for tur3ulent

+hF+am /

+tF+am /


+hF


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+5d / 9@A coordin2 B9 , a2e# #E4hen no lar2e scale eddies are resent

+5d / 9@ -9&4hen lar2e scale eddies are resent

+5d / >@ - I@

+et9& 7 d

d / *A+ . m

*A+ . mPi e len2th

+ / m+en2th ercenta2e no develo ed

*A+ .

*A+ . T


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;ata for e0am le $-9, Pa2e #%>, B#( sin2 ;ittus and Loelter equation)Pi e data

3nterior diameter

di # #& mm

Fluid data

t # #@@ 'C

6 # # 3ar (a3s)

9 # (%'.%

Flo7 reLuired to ontain a velocityv # 9@ m5s

eatin* or coolin* of flo7orC # H

Result for the Nusselt B#Nu / I9!$%

Results usin2 ;ittus and Loelterand data from e0am le $-9

Nu / I@!$#

hi / $@!9


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&/ , 2-5 ( $- >5% (/ $ ,-5 &- 1'2 &/ 2 - $ 2- (')( - & .- 1

( (/ 2 - 2 ,- 1 1')( (/ $ - ) (-- 1 1'2

$ - . ($- 2$ (/ $ - , (2- 2 1'2& - (- (.- (

& (/ $ - ($ 5TG ( 1'22 - (2 H5 I) - (. HH5 &. - (, $, - $- %

(- - $$ 9@

($ - $29#

(2 - $. 9I(. - $, 9$(, - &- 9%$- - &$ #@$$ - &2 ##$2 - &. #I&- - &, >@- - 2-- - 2$

- - 22- - 2.- - 2,- -

- -


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m # -'--% !*/s

ch" %I#!@ 0 onent for viscosity correcti

K / %!>9 -@$ mQ5s +aminar flo: of oil 1A &@

mm >@@m elocity $?!%$ #@?%#m0 v # 9 / A rom ) )

Nu @ /

2300Re


93/109

I@1 % H;P P 9@@ @ B , !&%@1 9@

9#!&9$ eatin* or coolin* of flo7#@ 9 orC

-'2

C @!>

Anne BJNusselt number

J3nside convection for fully develo:ed turbulent flo7 in smooth :i:es'

JFollo7in* relation is recommended by Gittus and Koelter' in relation to 6etu!ov eLuation :a*e 22(> EL' ,;%-

NuP # f / , D Re ; (--- D 6r / ( ($'% D f / , -') D 6r $ / &Thefriction factor 7ill be calculated usin* Colebroo! eLuation

instead of 6etu!ov formula


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Rev! cMc! #9!@#!#@9I

Anne0 C! Cen2el and Ghaion Annex C. Outlet temperature ully develo ed laminar flo

or a heat e0chan2er :ith constant :all or this ty e of flo:, the Ntem erature, the outlet tem erature num3er is constant!

n can 3e calculated :ith the equation

B9 , q!(I!99), a2e #&@! Also, see 1heet -Hydrodynamically fully de

8 @!@& 7 d 7 Re8 d / *A+ .%, Re / *A+ .

Pa s *A+ .

Pa sinar flo:, -


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on :a*e $%2

Petukov equation for smooB9 , q! (I!I#), a2e # @, o

f / ( @! ?@ 7 +n(Re / *A+ .

f / *A+ .

(


96/109

ar, B&

sselt Cen2el and GhaMar, B&ntry len2ths for laminar flo:

@!@& 7 Re 7 d q! (%-99)

elo ed @!@& 7 Re 7 d 7 Pr q! (%-9#)

q! (%-99)

m - ntry len2ths for tur3ulent flo:

m 9!>&? 7 Re=(95I) q! (%-9>)

t is 2enerally a2reed that entrance effects forq! (%-9#) tur3ulent flo:, are confined :ithin a tu3e len2th

of 9@ diameters and the hydrodynamic and thermal

m entry len2ths are a ro0imately taken to 3e - 9@ 7 d q! (%-9I)

m

Note!

Nusselt num3ers and thus convection heat transfer

m coefficients are much hi2her in the entrance re2ion!


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h tu3esr B& q! (%-$&), a2e II9e) - 9!$I )=-#


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0am le I!9, B9 , a2e #Avera2e heat transfer coefficientAssum tionE 8m # -'--% k25s

Results

Re # I !#

Nu / !@9Corrected Nusselt

Nu / I!%?

Convection coefficienthi # $$!? 45(m678)

utlet tyem erature>$> 8

t7alls #

tinlet #

toutlet #

= Ld Gz Pr Re

32

04.01

065.066.3

Gz

Gz Nu

++=

Microsoft Editor deecuaciones &' -


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Interior convection with saturated water and saturated vapor

4aterFunction Forced_Convection_water_inside_pipe_di_Rabs_t_m unction orce

I#%!& mm

Ra3s / @!9 mm Ra3s /9 >!& 'C

m / &9@!@ k25min m /P /

dm / di59@@@ m dm /dm / @!I#%I$ m dm /

Rho: / *A+ . Vk25m> Rho: /Pr / *A+ . - Pr /

*isc8inem / *A+ . m65s *isc8inem /

k / *A+ . 45(m7k) k /

m / &9@!@ k25min m /ms / %!& k25s ms /A / @!9II# m6 A /

q / *A+ . mQ5s q /v / *A+ . m5s v /

Rrel / @!@@@#> - Rrel /

Re / *A+ . - Re /f / *A+ . f /

Nu / ((f 5 %) 7 (Re - 9@@@) 7 Pr) 5 (9 J 9#! 7 (f 5 %) = @!& 7 (Pr = (# 5 >) - 9)) Nu / ((f 5 %) 7f / *A+ . f /

Re / *A+ . Re /Pr / *A+ . Pr /Nu / *A+ . Nu /

h / Nu 7 k 5 d h /Nu / *A+ . Nu /k / *A+ . 45(m7k) k /d / @!I#%I$ m d /h / *A+ . 4 5 (m678) h /

d i # d i #

ti # ti #


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s BkS5(k278)


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References


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B$ htt E55:::!youtu3e!com5:atchWv/afv# 92S83A

B Productos P CC, &E lectronic coolin2H Phtt E55:::! ath:ays!cu!edu!e25ec5te0t- df5 artT#@3-?! df


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B9@ undamentals of heat ans mass transferrank P! ncro era;avis P! ;e 4ittSohn 4iley and 1ons! 9?%9

B99 Heat transferAdrian LeManSohn 4iley X 1ons, nc! 9??>

B9# htt E55:::me!nchu!edu!t:5 nter5html5la35la3&9$5HeatT#@ 1team velocitiesn2ineerin2 tool3o0htt E55:::!en2ineerin2tool3o0!com5flo:-velocity-steam- i es-dF>%$!html

B9I Convection coefficient values

B9& 0am le ro3lem

B9$ utlet tem erature of an heat e0chan2er :ith constant surface tem erature;erivation of equation

B9 Advanced Heat and Dass 99@5+ecture9?! t


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Convection on a Tube. Outside and Inside. Nusselt_Coefficient_Tout_and_Array

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Transcript of Convection on a Tube. Outside and Inside. Nusselt_Coefficient_Tout_and_Array