Forced conviction heat transfer
AHMED ABDELHAMEED NEMR DEPARTMENT: MECHANICS REG:!"#$%&
ABSTRACTThe o'(ective of this e)*eri+ent is to ,nd the +ain contri'-tors to heat transfer in the s.ste+/ 0ater is heated and the ener1. is transferred in t2o 2a.s thro-1ho-t the s.ste+/ The s.ste+ is r-n for a *eriod of $" +in-tes3 in 'oth free and forced convection/ The heat *rod-ced '. the 'oi4er 2i44 re+ain constant thro-1ho-t the e)*eri+ent and the act-a4 ener1. 1athered 2i44 'e a res-4t of the condensed 2ater ca*t-red in the three di5erent vesse4s/ The theoretica4 and e)*eri+enta4 data 2as deter+ined thro-1h +eas-re+ents ta6en in the e)*eri+ent '. ther+oco-*4e3 sca4e and 2ater draina1e for the forced and free convection tria4s/ The stea+ condensed on the o-ter s-rface of the inner t-'e as 2e44 as the inner s-rface of the o-ter t-'e/ 0hen theoretica4 va4-es for forced convection 2ere ca4c-4ated 7#8!9; 2as co+*ared to the ##" 9 for the e)*eri+enta4 va4-es3 ro-1h4. #<= error 2as e)*erienced/
Contents ABSTRACT>///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
INTR?D@CTI?N>/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// $
Methodo4o1. E)*eri+enta4 S.ste+>///////////////////////////////////////////////////////////////////////////////////// ! Theor.////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// <
Res-4ts///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// &
Conc-4sion>//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// !
INTRODUCTION-
The e)*eri+enta4 s.ste+ -ses a 'oi4er 2hich s-**4ies heat to the 2ater to create stea+/ Heat is 4ost in the s.ste+ and ca4c-4ations are sho2n 4ater in the re*ort to ana4.e this for the t2o tria4s in the e)*eri+ent3 forced and free convection/ Convection refers to the transfer of ther+a4 ener1. in the +eans of di5-sion/ As a -id +oves aro-nd the 'o-ndaries of an o'(ect3 2ith a 1iven ve4ocit.3 an a+o-nt of heat ener1. 2i44 'e transferred/ It is -sed in +an. *rocesses3 s-ch as coo4in1 a circ-it 'oard or 6ee*in1 a roo+ coo4 d-rin1 a hot s-++er/ The -id3 2hich co+es in at a certain te+*erat-re3 2i44 e)*erience the chan1e in te+*erat-re/ The o'(ect is 'ein1 coo4ed 2hi4e the -id 6ee*s o2in1/ This *rocess re*eats over and over a1ain3 6ee*in1 the o'(ect at a desired te+*erat-re/ A reservoir in the s.ste+ 2as ad(-sted 'et2een forced and free convection 4eve4s/ This +eans that the *ress-re head is 'ein1 chan1ed/ The forced convection set-* creates a *ress-re head ca*a'4e of +ovin1 2ater thro-1h the s.ste+ 2ith a ve4ocit./ The free
convection set-* does not circ-4ate as +-ch ne2 2ater into the s.ste+/ The forced convection set-* res-4ts in an increase in dissi*ated heat in the e)itin1 of the -id into the draina1e tan6/ This res-4ts in a 4ar1er tota4 heat transfer for the forced convection than the free convection/ In the ne)t section of the re*ort the *roced-re -sed to co+*4ete the act-a4 e)*eri+ent is sho2n/ After that a 1enera4 -nderstandin1 of the e-ations and +ethodo4o1. -sed 2i44 'e e)*4ained/ Fina44.3 a series of sa+*4e ca4c-4ations are sho2n that sho2 ho2 achievin1 the hc convection heat transfer coecient 2as *ossi'4e and 2hat conc4-sions can 'e +ade thro-1h these res-4ts/
Methodology & Experimentl System-
The e-i*+ent -sed for this e)*eri+ent is 'asica44. one *iece e-i*+ent 2hich inc4-des di5erent co+*onents/ An e4ectric 'oi4er is the drivin1 force of the e)*eri+ent/ The 'oi4er is set to a constant o-t*-t 7"" 2atts; and as a res-4t it heats the 2ater and t-rns it into stea+/ This stea+ is fed into a condensin1 to2er/ This to2er is co+*rised of a c4osed (ac6et and a centra4 sin14e a4-+in-+ t-'e/ Coo4in1 2ater *asses -*2ard tho-1h the inside of this condenser t-'e3 ca-sin1 the stea+ to condense on the o-tside s-rface/ Stea+ a4so condenses on the inside s-rface of the (ac6et as heat esca*es o-t into the roo+/ A 'oi4er s-**4. tan6 is -sed to *rovide and +aintain a constant 4eve4 in the 'oi4er this ins-res that the +ass 2ithin the s.ste+ re+ains constant d-rin1 the e)*eri+ent 714ass t-'e;/ Coo4in1 2ater is *rovided '. reservoir that a44o2s the e)*eri+ent to 'e *erfor+ed 2ith either free or forced convection/ A44 the co**er>constantan 7t.*e T; ther+oco-*4es are +onitored -sin1 a hi1h i+*edance +i44ivo4t+eter/ T-'e 2a44 and she44 2a44 condensates are co44ected se*arate4. fro+ drain t-'es *rovided3 and coo4in1 2ater o2 thro-1h the condenser t-'e is co44ected in the 2ei1h tan6 +o-nted on the sca4e/ 0hen *erfor+in1 the e)*eri+ent +an. 2ater 4eve4s needed to re+ain constant in the s.ste+/ The 1ro-* +e+'ers 2ere 1iven di5erent res*onsi'i4ities s-ch as3 +aintainin1 the 14ass t-'e 2ater hei1ht3 +aintainin1 reservoir hei1ht 7forcedfree settin1;3 as 2e44 as 6ee*in1 trac6 of the start and ,nish 2ater 4eve4s/
Theory-
0hen ana4.in1 convection heat transfer coecients3 three di+ension>4ess va4-es +-st 'e ac-ired/ To deter+ine 2hat n-+ero-s constants are the initia4 conditions +-st 'e 6no2n so ta'4es can 'e -ti4ied/ Nusselt Number:
Nu =
hc D K
Prandtl Number:
Pr =
Cpμ K
,
Grashof Number:
D ρ g ( ∆T ) 2
Gr =
2
2
μ
Reynolds number3 for interna4 o23 is o'tained '. the fo44o2in1 e-ation:
ℜD=
ρUD μ
These e-ations are cr-cia4 to ca4c-4ate to deter+ine 2hat t.*e of o2 e)ists in the s.ste+/ In order to -se the correct heat transfer e-ation the t.*e of o2 +-st 'e 6no2n to 'e 4a+inar or t-r'-4ent/
Types of Convection observed-
Forced convection occ-rs 2hen the -id o2s across the 'o-ndar. of an o'(ect3 2ith the +ove+ent ca-sed '. e)terna4 forces/ Heat transfer coecient for the forced convection de*ends on the re4ationshi* 'et2een N-sse4t n-+'er3 Prandt4 n-+'er and the Grasho5 n-+'er ac-ired for free convection/ The re4ationshi* is e)*ressed in the fo44o2in1 e-ation:
hc D K
( )
m =α DG m ∧ n=exponents experimentally acquire
μ
Free convection occ-rs 2hen the -id is a44o2ed to o2 '. +eans of '-o.anc. forces/ This convection +ethod occ-rs 2hen the te+*erat-re di5erences e)ist 'et2een the t2o ends of the air/ 0hen the end *art to-chin1 the hot o'(ect contacts the o'(ect3 the -id 'eco+es 2ar+er and 4ess dense/ The air +oves -* and the co4der air +oves in to re*4ace the 2ar+er air/ The co+'ination of the varia'4es in order to o'tain the heat transfer coecient for the free convection *rocess is: n Nu= ! ( Pr x Gr )
Heat transfer in condensation, because a phase change is involved, requires complex analysis. Condensation takes place when vapor is cooled down. Once this occurs, heat is transferred in a fundamentally different manner than when heat is added or taken away from a fluid without such phase change. When vapor is condensed, it lets go of considerable amounts of energy. he condensed fluid becomes a barrier, in the form of a liquid film which either completely or partially covers the cooler surface. !f the drainage of the fluid is done from vertical or inclined surface, the drainage will be naturally faster than a hori"ontal surface. he film will be thinner. !f the vertical height is great, the accumulation of condensate fluid at the lower portion of the surface will thicken the film and make the lower portion less effective than the upper transmitting heat.
In order to ac-ire an even +ore acc-rate res-4t3 the heat transfer that occ-rs 2hen heat is re4eased d-rin1 the condensation of the va*or +-st a4so 'e ta6en into acco-nt/ This va4-e can 'e easi4. ca4c-4ated '. o'tainin1 the 4atent heat of va*oriation va4-e/ Neverthe4ess3 as the condensate is coo4ed 'e4o2 T sat3 the e-ation +-st 'e +odi,ed to:
h#fg h=
fg
+ $.%& CT
Tpl'
sat
− (s
Settin1 -* a44 e-ations to1ether3 the co+'ination of the rate of heat transfer and the heat
transfer coecient for+-4as3 the fo44o2in1 e-ation is o'tained/
.
Qconden =hA Ts ' sat T − mh s( =
#
fg
?nce ever. va4-e has 'een o'tained3 the heat transfer coecient for the free and forced convection heat transfer *rocesses can 'e o'tained/ The theoretica4 va4-e for the free convection is e)*ressed as:
k + ρ ) h fg Do µ ∆ T
.)*
h = C
The theoretica4 va4-e for the forced convection is e)*ressed as:
h=C
k Di
.&
ρ VDi ., µ ( -r )
In order to deter+ine the heat transferred a+o-nt3 t2o e-ations are needed/ The e-ations 2i44 ta6e into acco-nt the 1ains and 4osses in the s.ste+/ The ,rst e-ation needed is the heat transferred fro+ the stea+3 2hich is e)*ressed as fo44o2s:
QSteam
= VSteam hfg ρ
The second e-ation needed is the heat transfer that occ-rs in the 2ater/ The
e-ation is e)*ressed in the fo44o2in1 +anner:
QWater =W(
(Cp ) ) ( T ) ∆Water
Water
Therefore3 in order to ac-ire the tota4 a+o-nt of heat transferred3 the t2o e-ations +-st 'e co+'ined/ The tota4 a+o-nt of heat transferred is e)*ressed in the fo44o2in1 +anner:
QLosses
= QSteam − QWater
In order to ,nd the heat transfer coecient3 the transfer heat a+o-nt +-st 'e o'tained/ F-rther3 the resistance +-st 'e ta6en into acco-nt/ The resistance va4-e 2i44 1ive -s the rate at 2hich the heat is 'ein1 transferred3 2hich 2i44 s.+'o4ie the overa44 heat transfer coecient/ Heat F4o2 Thro-1h a *i*e Forced convection
cμ .4 ¿ " ρ#D .8 ¿ ¿ μ " ∁ h= ¿
Nat-ra4 Convection
3
(
2
$ ρ % ∆ Tg cμ n )( )¿ 2 " μ " h =∁ ¿ $
Condensin1 Stea+ 3
2
" ρ h !g Dμ ∆ T ¿ ¿ h=∁¿
Res!lts A44 ca4c-4ations are 'ased on data co44ected fro+ the tenth to ,fteenth +in-tes of the e)*eri+ent/ The data 2as avera1ed over the ,ve +in-te ti+e di5erence and -sed to co+*-te e+*irica4 and e)*eri+enta4 va4-es/ The e)ce4 co*ies 'e4o2 sho2 the avera1e te+*erat-res and vo4-+e2ei1ht of 2aterstea+>condensate co44ected/
Forced Convection
Free Convenction
Heat Transfer Coecient, Forced Convection, Inner
h 'Forced ( =C
K ρ ×V × Di ÷ Di µ
$.&
Cp × µ K ÷
$.,
hiforced heat transfer Co efficient of F?RCED convection C is a constant "/""#$ +ean avera1e ve4ocit. of -id in +s
Do o-ter dia+eter of inner t-'e
Do inner dia+eter of inner t-'e
( + ( )) 3 1 2 4 32
& 0.0254 =0.02064 m
()
3 & 0.0254 =0.01905 m 4
1 acce4eration d-e to 1ravit. in +secsec &/8 +s# 6 Ther+a4 Cond-ctivit.3 in 0+J 9 C* s*ecific heat in 661 6 Ther+a4 Cond-ctivit.3 in 0+K9
iscosit. in 61+Js Densit. of 0ater in 61+$
JPro*erties in red 2ere fo-nd in 2ater *ro*ert. ta'4es at at+os*heric *ress-re and Tav1 T# TO# Tav1 $!/&&<<
μ
"/"""O#!"O 61+Js3 C* !/O8 661
6 "/%##&OO!$ 0+J9 0# %/#< 4'+Q +ass of 2ater that *assed thro-1h the inner *i*e in a ,ve +in-te interva4
%.)*lbs #$ .,*,kg / lb m ´
=
*min#% $sec/ mi n
= $.$$0,,010)kg / s
Q +ass o2 rate
)
Ai
=
π Di
=
,
π
× '$.$0$*( ) ,
= $.$$$)&* +# Q Cross sectiona4 area of inner t- 'e
m ´ #= = ρ&'
0.00945 994
"g m
= 0.0023
hi
!orce
hi
!orce
(
3
"g s
=0.0333
& 0.000285 m
0.623 0.01905
)(
2
m s
994 & 0.0333 & 0.0195 0.000724
)( 0.8
4178 ( / "g ℃& 0.000724 0.623
)
0.4
) $!/"8
2
m K
Heat Transfer Coecient; Condensing Steam; Outer Surface; Inner Tube 3
1 4
2
" & ρ &h !g h =c & $ & μ & ∆ T
[
o
]
J Pro*erties -sed in this ca4c-4ation 2ere ta6en at T,4+ Ts-rface Tstea+ ECEPT hf1 ta6en at Tstea+ Ts-rface is the avera1e inner *i*e o-ter s-rface te+*erat-reQ T8 T& Tstea+ is the avera1e te+*erat-re of condensin1 stea+ Q T"
T s=
T 8 +T 9
=
T !ilm
2
=
92.58946154 + 80.441 =86.51 ℃ 2
T sur!ace+ T steam 2
=
86.515231+ 103.546 2
=95.031 ℃
T Tstea+ Ts-rface 8/<# C
"g 3 &%/!OO&"< m3 3
) 6 "/%OO"##OO m∗℃
μ
"g "/"""#&"&!< m∗s 3 hf1
( #3#!O3!
2
0.677 & 961 & 2,247,415.8
ho =1.666 &
[
0.635 & 0.000290945 & 8.521
1/ 4
)
=6303.14
2
m *℃
]
Heat Transerred; Forced Convection em!irical calculations"
R=
$.$)$%, m ln $.$0$*m + + × = W W $.$$$)&* )+& ,*&.$% %+$+., m2 m) K
+ T lmt =
∆ T ¿ −∆ T out ∆ T¿
ln ∆T out
´= ,
68.273 0.09308
=
( 91.05 −49.5 )
$.$0$* m÷ ÷ W $.$)$%, m÷ ÷ ) m K
$.$0+$&
K W
=68.273 K
ln 91.05 49.5
=733.34 )atts∨
( s
Tota4 heat added to 2ater in a ,ve +in-te interva4Q
´ &∆t =746.7
( & 300 secons=220.01 "( s
#$!erimental : Heat Transerred; %osses due to condensin& steam on inner 'urace o ()T#R Tube; Forced Convection 3 "g "( 6 m qloss =m steam & h!g =25 m$∗10 m$ & 961 m3 ( at T 4 ) & 2,239 Kg ( at 100 ℃)=53.8 "( −
#$!erimental: Heat Transerred; Forced Convection q trans!erre=m´ - C p ( T 2−T 7) &∆time
q trans!erre=6.25 l.s& 0.454
"g ( & 4178 & ( 24 ℃) & 300 s =284 "( l.s "gK
0hen a44 the data 2as co44ected the heat transfer coecient 2as a'4e to 'e so4ved for/ Based on o-r data 'et2een the ti+e *eriod of " and < +in-tes the heat transferred for the free convection 2as 8%/< 9 2hi4e for forced it 2as ##" 9/ Thro-1h the theor. that 2as *revio-s4. ta46ed a'o-t it 2o-4d 'e a 4o1ica4 h.*othesis to ass-+e that the forced convection 2o-4d have a 1reater heat transferred/ This is 'eca-se a -id is 'ein1 forced thro-1h havin1 a o2 rate that is constant4. i+*4e+entin1 ne2 coo4er -id to the s.ste+/ Therefore3 the ne2 -id has a 1reater di5erence in te+*erat-re and creates a 1reater heat transfer/
Con"!lsionThe stea+ condensed on the o-ter s-rface of the inner t-'e as 2e44 as the inner s-rface of the o-ter t-'e/ This 2as the *ri+ar. +ode of heat transfer in the e)*eri+ent/ The e+*irica44. ca4c-4ated res-4ts varied '. ro-1h4. #<= 2hen co+*ared to the e)*eri+enta44. ca4c-4ated res-4ts/ This can 'e attri'-ted to the e)*eri+enta4 +ethods/ The e)*eri+ent had its do2nfa44s that co-4d have *oor4. a5ected o-r res-4ts and therefore3 o-r ca4c-4ations/ The +eas-re+ent s.ste+ of ,44in1 -* 'ea6ers see+ed fair4. -nre4ia'4e/ Since the tria4s 2ere $" +in-tes 4on1 often ti+es the 'ea6ers 2o-4d 'eco+e f-44 and re-ire e+*t.in13 in 2hich 2ater 2as not 'ein1 ca-1ht and +ass 2as 4ost/ In addition3 there 2as *ress-re acc-+-4atin1 inside of the c.4inder itse4f that 2as not acco-nted for/ This *ress-re 2as ass-+ed to 'e at+os*heric 2hen in rea4it. it 2as *ro'a'4. hi1her/
