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155 views27 pagesPart 9 Heat
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© © All Rights Reserved
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/ 27
5S lect ~=Guvectlon “Feral ‘Sheet No{_) Forced convection
|.Consider steady, lamina, two-dimensional flow over an eotbernal plate. Does the thickness of
coe, tousiary ayer Increare or decrease with (a) datance fom the leading edge, W) fie
stream velocity, and (c) kinematic viscosity?
‘two-dimensional flow over an isothermal plate, Does the wall shear
with distance from the leading edge?
low with constant properties and =
that both the average friction and
2+ Consider steady, laminar,
stress increase, decrease, or remain constant
3- Consider steady, laminar, two-dimensional, incompressible
Prandil number of unity. For a given geometry, {sit corre to say
heat transfer coelficients depend on the Reynolds number only?
4-0 flow in a journal bearing can be treated as parallel flow between two large isothermal plaiey
vate thoving at a constant velocity of 12 m/s and the other stationary. Consider such #
vaiform specing of 0.7 mm between the plates, ‘The temperatures of the upper and
lower plates are 40°C and 15 ely. By simplifying and solving the continuity,
vo eeahun, and chergy equations, determine (a) the velocity and temperature distributions in the
oO) the maximum temperature and where it occurs, and (c) the heat ux from the oil to each
plate.
|5- A 6-cav-tiameter shaft rotates at 3000 rpm in a 20-cm-long bearing with a uniform clearance of
0.2 mm. At steady operating conditions, both the bearing and the shaft in the vicinity of the oil g=p
tre at 50°C, and the viscosity and thermal conductivity of lubricating oil are 0.05 Ne/m? and 0.17
Wim K. By simplifying and solving the continuity, momentum, and energy equations, determine
(@ the maximum temperature of oil, (2) the rates of heat transfer to the bearing and the shaft, and
(© the mechanical power wasted by the viscous dissipation inthe oil.
6 A S-covdiameter shaft rotates at 4500 xpm in a 15-cmlong, 8-cm-outer-diameter cast iron
pearing (& #70 Wim K) with a uniform clearance of 0.6 mm filled with lubricating oil (n=0.03 N
w/m? and k = 0.14 Wim K). The bearing is cooled externally by'a liquid, and its outer surface is
aitntained at 40°C. Disregarding heat conduction through the shaft and assuming one-dimensional
Tent transfer, determine (a) the rate of heat transfer to the coolant, (8) the surface tensperatare ofthe
shaft, and (c) the mechanical power wasted by the viscous
dissipation in oil.
10°C flows over a 6-m-long flat plate whose temperature is 30°C with a velocity of
the total drag force and the rate of heat transfer over the entire
7-Engine oil at 8
‘3 mvs. Determine
plate per unit width.
& The local atmospheric pressure is 83.4 kPa. Aira his pressure and at 30°C flows with a velocity
arb ls over a 2.5m X Bema fat plate whose temperature js 120°C. Detenmine the rate of heat
oe from the plate if the ai flows parallel othe (2) &-m-long side and (b) the 2S-m side.
wind at 55 kan/h is blowing parallel toa 4-m-high and 10-m-long wall
'S°C and the surface temperature of the wall s12°C, determine the
9-During a cold winter day,
‘What would your answer be if the wind velocity was
of a house. Ifthe air outside is at
rate of heat loss from that wall by convection.
doubled?
10- Air at 15°C flows over a 3-m-long flat plate at 2 ms. Detemine the local fiction and heat
10 coefficients at intervals of 0.5m, and plot the results against the distance from the Leading
edge. -
_ @
17-A desktop computer is to be cooled by a fan. The electronic components of the computer
consume 80 W of power under full-load conditions. The computer is to operate in environments at
temperatures up to 50°C and at elevations up to 3000 m where the atmospheric pressure is 70:12
KPa The exit temperature of tir is not to exceed 60°C to meet the reliability requirements. Also,
tverage velocity of air is not to exceed 120 m/min atthe exit of the computer case, where the fan is
im talled to keep the noise level down. Specify the flow rate of the fan that needs to be installed
and the diameter of the casing of the fan. ——__
to be heated by saturated steam at 1 atm in a double-pipe heat exchanger to
"The inner and outer diameters of the annular space are 3 cm and 5 cm,
{with a mean velocity of 0.8 mis. The inner tube may be assumed to be
Suter tube is well insulated, Assuming fully developed flow for oil,
to beat the oil to the indicated temperature. In reality, will you
18. Oil at.10°C is
temperature of 30°C.
respectively, and oi enters a
Fsothermal at 100°C, and the
determine the tube Tength required
need a shorter or longer tube? Explain.
1b- Hot water at 90°C enters « 15-m section ofa cast iron pipe (k =52 Wm °C) whose inner and
oe Het wer cure 4 and 4.6 em, respectively, at an average velocity of 0.8 m/s. The outer surface
eee Shove emissivity is 07, is exposed to the cold air at 10°C in a basement, with 8
Of the wa eansfer coefficient of 15 Whit °C. Taking the walls of the basement to be at 10°C
reel (a) the rate of heat loss from the water and (b) the temperature at which the water
eaves the basement.
120- The velocity profile in flly developed laminar flow in a circular pipe, in m/s, is given by We
(1 1007) where r isthe radial distance from the centerline of the pipe in m. Determine (a) the
radius ofthe pipe, (6) the mean velocity through the pipe, ad (c) the maximum velocity in the
pipe.
21- A house built on a riverside is to be cooled in summer by utilizing the cool water of the river,
which flows at an average temperature of 15°C. A 15-m-long section of a circular duct of 20-em
diameter passes through the water. Air enters the underwater section of the duct at 25°C at
Velocity of 3 m/s. Assuming the surface of the duct to be at the eroperature of the water, determine
the outlet temperature of air as it leaves the underwater portion of the duct. Also, for an overall fan
cfficiency of 55 percent, determine the fan power input needed to overcome the flow resistance in
this section of the duct.
‘22- Hot air at 60°C leaving the furnace of a house enters a 12-m-long section of a sheet metal duct
of rectangular cross section 20 cm X 20 om at an average velocity of 4 m/s. The thermal resistance
Of the duct is negligible, and the outer surface of the duct, whose emissivity is 0.3, is exposed to the
Cold air at 10°C ia the basement, with a convection heat transfer coefficient of 10 W/m? °C. Taking
the walls of the basement to be at 10°C also, determine (a) the temperature at which the hot air willl
leave the basement and (B) the rate of heat loss from the hot air in the duct to the basement.
report
4+ Design an experiment to measure the viscosity of liquids using a vertical funnel with a
Sindrical reservoir of height & and a narrow flow section of diameter D and length L. Making
appropriate assumptions, obtain a relation for viscosity in terms of easily measurable quantities
such as density and volume flow rate.
2- A facility is equipped with a wind tunnel, and can measure the friction coefficient for flat
surfaces and airfoils. Design an experiment to determine the mean heat transfer coefficient
for a surface using friction coefficient data. Ca
ESIC For sendy meo-timensiona Now ove
‘Goce! fat plate in thea ivetin. the Dosndary ute
(oncliioes for be velocity component wad ea
Setempeatare [atthe plate surface andattbe este
tf be bownaay layer are expresied 25 (lon
Atyeo: ats.0)eQ we.0) 7 TO) A
As yoo: oe n)een Teed Te
‘6.32 Anindegenden vaabe ta makes t possible anforming 3 set f pata teresa ios
CECE SEET Siterentt cnn called similarity variable A siilty sans 0 1
ae ne ree larental eqanions if there is funtion that remains wechanped (s0ch 23
‘oo-dimensonal velocity profile on iat pst
(2% ovng en tine noni ew ng aber et et
eee eee ace) increases with Gisance frm te leading edge, b) decreazes with fee-Sraiy
elociy. cd (e} td increases with Liners wisesity
® 64C During steady, laminar, wo-Cimersional flow over an istherms! pute, the wall shear Sess
ecreaaes with Sizance free the leading 2a
GSC A major advartege of rondiaesionslising the convection equations i the sieniican reduction in
tre nanter of parame [the orginal problem involves 6 parsmesers (LV. Ta Tx va butthe
eee Saliaed protien involves jst 2 parsmesers (Re, and Pri. Nendimensionsization ase resus
Rliearty parameters touch as Reyeols and Prandi pumbers) tht enable us to group the resis of 3
[Eipe numberof experiments and o fepon them converiestly in terms of such parsers
® 60 For stcty, mina two Ciensins.incompresibe flow wih consant properties anda ran
eee toni sad a given geomeny, yem itis corect to say that both the average friction snd heat
TEnUEr coufficiente depend on the Reynolss number only since C, = f4(Rey.) Sad Mu= gy(Rey.PP)
from non-dimersionalized momentum and crergy equations.
PROPRIETARY MATERIAL, ©2207 Te Cine Compic in. Lied rn pric el ten eon
eee eT ERTN ifjou ea maten wing ts Manas youre wing tho! perme on
29 Pol ow afi between plas omer he ety
8 lc fume the elo an inet shins,
and the heat fluy are to be determined. i m= . =
ina pFESSINTE Whstince wth gomant ~~ == ———
The plates are large so that hee Is naval
Properties The propsmics il athe average temperate of (40*15972 = 27.5% are (ole AID)
ASO1MS Wim and y= 0.605 kylos= 0.405 Nei?
Anat (a) We take the saris tobe te No. direction, und yi the normal teton, “his is pale),
owe Rete two plates and thus = Then the continuity equation reduces 1a
tame
arg ractante! | TE yo atne
inthe Now direstion be, ity profile remain
‘uachanged). Noting that w = ny)» = 8 and
EP 1é¢ = 0(iNow is maintained bythe motion ofthe eee i On
‘epper plate rather than the pressure gradien
‘momentum equation (Eq, 6-28) reduces 19
smameninm: — fu Sty St) Se 2h 0
UE a ar a
‘This isa second-order ordinary differential equation, and iniepratng it twice gives
More Crees
‘The Maid velocities at the plate surfaces mest be equalto the vlacies ofthe ploes because ofthe nip
fe condition, Therefore. the boundary conditions are (0) 0 and w= F’-and appsing them gives the
r velocity distribution to be
: wort
Frictional heating due to viscous dissipation inthis ease is significant because athe high
Viscosity of ol and the large plate velocity. The plates are isothermal and thee is nochange in the Now
: Girection, and thus the temperature depends ony only, T= Ty). Also. w = udy) and ¥ = 0. Then the energy
equation with dissipation (Eqs. 6-36 and 6-37) reduce to
& eu)!
page 04 Ea 2)
since Qu/y="'1L Di
itt
| “Applying the boundary conditions 110) = T, and TIL) = T: gives the temperature uistibution to be
Bat yyy wey :)
TW
J eevee
Tine tn Sel te
J (8) The temperature gradient is determined by direnatng Ty wth respect toy
. “The location of maximuin emperaturcis determined by setting dTldy = 0 und solving for y
PROPRIETARY MATERIAL, ©2007 The McGraw Comprise. Limited sition pied oly taba
ag Cnr ior coure preparation Ifyou fen sent ong his Manual, you ae sigh wihow permission 12
ABA Wat) sy {eases
or tae oe 7”
_The minimum temperature Is the value of temperature at thisy: wae in
ho! (40=15°C
yea e22=F 2) (0.0007 mY (0145 Win Or cimeyiamisF 2
4 4 we i} aon {' TososNetm? Ki2misi* 2
= 0,0003791m = 03791 a
ren :
Tae
(40-15 rc (0.605 N-s/m? M12 més}? 0.000379) m (0.0003791 mi
0.0007 m_ cqg0ns7s] mi} “210.145 Wim-*C) 0.0007 m_ (0.0007 m)”
swae
doen ie tm he tion as
ar
(40=157C_(0.605 Nea!" X12 m9D®
"0.0007 m 710.0007 m)
(0.145 Wim.7C) 6.742108 Wim?
Tana?
“Et
(4o=15PC , 0608N-sni 2m (1 + wim?
4O=197°C , (0605 N-ven?M12m/5)" (1) 5744
‘0.0007 m CC
= 40.145 win 20)
“pivcusion A vemperature is of about 76°C confinms out suspicions sss dissipation is very
Hes a8 275°C but ihe vil temperature tumed nt 1 Be
on temperature eleultions should
‘Significant, Calculations are done using oil proper
si gher. Therefore. knowing the sons dependence of ise
be repeated using pt
ropertes atthe average temperature of shout 65
‘e207 Te ere Comp. me, Linel ri oe rt noche ond
207 det cng You Em a Fm es
(641 The il ina journal Rearing i considred. The velocity and temperature distributions the masimum
“enperatre he rae of heat transi. and the mechanical power wastedin vl ae toe determine.
“Assumptions \ Steady operating cendiions eve 2 Oil an incompresible sUREaNGE with COAT
properties. 3 Body forces suchas gravity are negligible.
Properties The properties of wil at SO°C are given to be
B=017WinK and y= DOSNim?
nals (a) Oil Ra in journal bearing sm
‘ee spprosimated ss parallel Mow between 3000 rpm
too large plates wth one plate moving and
the other stationary. We the the x-axis to be Oi
the Mow direction andy tobe the normal
Uirection, This is parallel low between two
plotes and thus y =f. Then the con
Eiuation reduces
en
are
Continue ° ae)
“Therelore. the s-component of velocity does not change in the flow di
‘mains unchanged). Noting that u = u(y) v = O.and @P/ @& =0(flow is maintained bythe motion ofthe
Upper plate other shan the pressure gradient. the s-momentom equation reduces 0
‘This is second-order ordinary differential equation, ad integrating ittwice gives
wvr=Cier
“The Muid velocities atthe plate surfaces must be equal othe velocities f he ples because of the noslip
condition. Takingyf = O at the surface ofthe bearing, the boundary conditions are(0) =O and uL)= I.
‘and applying them gives the velocity distribution tobe
wet
“The plates ure izotherml and there is no changein the flow direction. and thus the temperature
depends om vonly. 7= TW) Also. u = i4v) and v =O, Then the energy equation wth viscous dissipation
reduce 10
owe: tof) — Giede]
shy band integrating wi
since Qu f2y =1°1L. Dividing both
A(t) seve,
“Applying the boundary conditions 710) = Ty and TIL) = To gives he temperature distribution tobe
Ty
respect toy.
(03007 The McGraw-Hill Companies. ne. Lie rho permite also aches end
ing it without permis
rs
a a edne prepravon 1fyouaressuden using this Man, ote
emperture is determined hy seting THA = 0 and saving fOr
‘The lasation of manimum
: 1
ata
rerefre maximum terperature wil cur mid plar inthe il The velocity andthe sfee area
isle) ga NYS wOR
106399, noma evn
4 Db nang = £40.06 0.20) = 0.0377 9?
‘The mavimom temperatures
T. sraraer oe (2. wuzt)
5 ule e
wot asa asa meas? (IW Jase
© ROT Win-) CIN,
(8) The rates oF heat wansfer are
a ad a
a a (-0)2 a
So nn Oe
3) (ODSN-sin? 19.425 m/s)
iw.
= (000377 41
+ 210.0002 m) 7) Hdd
a we? ws
| ate (2) -
2 ake] seg ales -8, = ar9
(6) Therefore. rates of heat wansfer af the rwo plates are equal in magnitude bul opposite
mechanical power wasted is equa the rat of heat transfer.
Wyaa == 2419=838W
sign. The
FHOPRIETARY MATERIAL ©2007The MeGromHll Const Line nisin
‘aciesforcoune esa Ifyou ares ween wing hsm you sean or peomon aM ro
are piven to bek #016 Win K and j1= 03 Non, the thermal
f= 79 Wim K.
Properties The properties
Crisereity of beating is given to Re
“anarss (a) Ot low in journal beating om
parallel ow between 500%9m
Siorprosinaes 3
ro lurge pater with one plat moving sn
cRET datos We eke ibe rasta be Tom
Eine acon and tn Be te normal ise
Breton, Theis paral low betwen
SineSpaimare © Then he cnt
Eien ees ———e|
9 so
oso emo
‘enti: $+ =
< =e
joes not change inte flow direction (he. the velocity praile
Se ad GP oe =O {flow is mained by the motion ofthe
momentum equation resuces 0
“Theretore. the component of velocity
‘emains unchanged). Noting that w = Wh
Toner plate rather than the pressure gradient the
semomemum: of w+ » 2)
Aa ey,
“This is second-order ordinary differential equation, and integrating
Maes
the uid veloc at the plate surfaces must he enualto he veostes of the paws Pecoue of te o-
vid estore. the Noundary conditions areu(0)™ Oand w(L)= Fad plying tem Eves he
jribution to be
we
sin
senor nous S wh
vr exoea nostril 2
“peace telethon cine ene
Le efter htt
ame
on
since du [221° Dividing bth sides by and Interating twice ve
(ry Cy
yee 2 (tr) sees
vor fle)
Applying the wo boundary conditions give
iGraw Hin Cononies I. Lied ibis perme ony others and
“PROPRIETARY MATEIIAL ©2007 Te M ;
PRLETABY SA IAN yu sue cngihs Mama youve wing en emo,
ea Thebes fin we spe meee is
ae
ol
ee
Neng ss hea ser slang he shat i nepiipibie al the hen eevee in he il ig tensed wo the
gat ind Seree often mes
(003N-vo HILTOS! sey gy
aed, tao Sw onsets
On Aig toe = rats ISH —
(oy Teint cauivsien to te rte cf heat ler trmugh the cylindrical sieeve by conduction, wtich is
apes 3
cr
BOIS -O.
nr ET) © owiecy
70,70} wa ate) (58 ee
tick piece the mrtice temepeamere ofthe shafts he
Taare
The mechacical power weed by te viscous Gexipein iil is equivalent the nae of hem generation.
= O-1835 0
aby MATEDIAL ©2007 The cere tt Comanche, Lind erent mone 2A
rien Uh yon es se ny Sot Mach yu ewig whos RON, oe
4.9 Ava esl of steamtnng ition drag Increases) pressure dng decent ond 0 8
ZAC As 2 et Roya nombre general ssc but increase ot very Tow Rey name
Sere Tran domlnaes a for Reyrolds numbers = ———
rn he surace othe body.
pr vlociy tor tec 9
fies the Mul tream detaches
hud lowing over & curved srtace aa Ng
nctcact he dag coeliclent Gras.
“10 At suit high veloc
aled seperation is caused by 8
Stivers pressure gradient) Separation
vera Mat plate. Is proportions 0
edie equivatent othe mean ition
ne resistance in uid Nos
mn seeticlen represents
‘oefient fora Mts
ing om the pate. THESE
2.1e The fi
the drag free a
tvelicent
-pA2€ The ition and the heat transer cet
13 The average friction and heat ramfer coe ice
FEAR Tg thc fal rction and Beat tansler cet
ihe engin of the plat.
sents change wi position in laminar ow over 3 Meta
sin fow overa fat plate are determines
ms over he entire pte and en
‘ PCs oy cot ge
A setsanteshiceae 7
1 Reynolds number is Reg * 5108.3
7 “Assumptions 1 Steady operating conditions exist 2 The ei
Radiation effects ae negligible.
a, The poperiscf engine iat thei empertre of 7+ To¥2 = (80430V2 58°C are (Tle
AB)
oe pene kgm? v= 7.045107 m2
= O.1414WimsC Pr=1551
‘ “Analysis Noting that L* 10 m, the Reyoolds
fhumber atthe end ofthe plate is
t 0m) ' t= 10m
HL, 2S misKlOm_ 5 s49x10 _ = SH
i re, =the i
© 7015x107 mils
theciteal Reynolds number.
and the dg force per
“Thus we have laminar flow over the entire plate. The
nit width are determined from
shih i less than
average Iretion coefficient
Fa, 24 BE oconontt SESE =t8 8
similarly, the average Nusselt mumberand he heat ansfer coe hen a determined using the laminar
Tow relations fora Mat plate,
sia = oaet? re? a3 94108 98551 = 4879
net hw - MAME asi 6478 win?sC
‘The rate of heat transfers then determined from
Q HAA Te =T,) = (6475, Wit CX 10>
[Newion's law of ewoting to be
1m? Y80-30)'C = 3.24x 10" W = 32.4KW
diario emit els 0 veh md
pnoraucTaBy MATERIAL ©2007 The Mcronil oopms amid
PROPRIETARY ATE pe siete ha Moma cute wig wit mn
\\ serait wie fee brat
Se soa conditions exis 2 The etical Reynolds number is Re
Se a ge FO
werner
18 asain
Toiazsirs
= ror anidea gate eral conduit and he Prana
unter are independent of pressure bt the Hneraic
TENG ey oporton othe pressre With ese
LSalon ne popes ofa a 08 atm and atte ln
‘Srp or ani ae (able AIS)
4003917 imc a
"= (2046107 2/0425 = 2486 «10° m7
a 5e108.3
pe ananray
ares tna
rr=0766
Anais a) be sie ows pallet heim ig the Reynolds meter in his eave becomes
| te, =f eatin)
: Fate mis
f hich is ereater than the eiteal Reynolds number Thus we aye cumbia laminar and turbulent How
; Ung he proper rein for Nusselt amar the verge Peat wafer enelTicler andthe eat Wane ate
se dtemined he
=1onsio®
awn 037 Re, 2719 =0037. 93110 /* 4711066)" #2957
ak aye DENT WHE 57) 01008 Win? 1C
4, =k =(25m48m)= 20m?
= Ady —T,)~ (10.05 Win? *CH20m? K120-
orc o1ns00W = tRs0KW
(ores om prlel othe 25 male. Reel nami
oy PE ASSO gor4yigh
7 Fab wh
ich gree hn hers Ree ber Th we hve combi ania bet he
ig the pope ton fr ans number te erg eer cient fea arr ale
sedhemned nbe
pete ouae,*-r7090 =[onnnGoren ih -mngaie” 84
gg 202917 Win,
ohne (615.1) = 7.177 Win? 3
ie 25m
Q =A (T, 7.) (9.177 Wi? 220m? (120-30"C = 12820 W = 12.92KW
{PROPRIETARY MATERIAL 02207 The MeGrwil Cong. Lined ain permits ny ees nd
‘deat coe peeton you oe sen ang Sa ana ove cingeoowpemee
pea ”
uta wind a Bowing rate oe walof ite, The ah a om a wot i18
FRACS TS HUTSTINE, * 5410S
gas wah contant pRETICS.
“assumpotons 1 Seay pering COMTT
SSE ere are vcpigite Airis an teat
Peps epee
SScnesests Messin
Paoaness wie nose
eatanant ws =
peer =
amt ti fire porate 19 whe 10. ide
pe Repos somber in his ase fs Wt
ve feast 000/3600%SKIOM _y o§1 5107
ham he critical Reynoits number. Ths
Se Nese number beat rater coe
th i erent have combined laminar and wurhulent fom.
ing Semen vyiclem ad them Peat wronsfer Fe BF
Soumined ote
neath = 007 anos"? «136104
= riper”? = [0057L081«10"
9.92428 wins 1
= LORE WIRE (5560108) = 32.43 Wh °C
«Tom
ve = (emt) = 40m?
Qe AT =7,1 (3245 Wi? SKA WIE SPE = ORD W = 9.08
the wind velocity is doublet
ey wth 0000/3600. NIOM) 9695107
Tad 107 ts
obi is greater than the ertical Reynolds number Thos
Tione ne proper relation for Nusselt mumber. he averse
se determined 10 Be
neath = oosRe,"
we have combined lsminar and turbulent love.
Nesttanater coefficient andthe heat wansfr rte
3a4x10*
siype!? = 0.037(2.162«10" P* —871K0.73400"*
rot an ROLAREWARE (2 sph t0 = 57.KB Wi TE
L Tom
= Ae tT=7,9= (57E Wim? PCO I2-SPC=162IO 621k
secqnica, re Limed ein permite al teers 2nd
peopmicrany MATIBIAL ©2507 Te Meee it
ERO RIETARY SATE yu ea eet as Ma Yee Bie ARPS 7
Sopa
CVEDG EE aeration tae
pane Air Ooms ver realreywetepeay
TisScmined and ploued agies te 6
aie . soe The cri Reypots mambots ey
saan ry Se ial gs wth COAT OPTS
asst roe popnien ost nim and oF ae (Table RISE)
1 201433 NF
= 0.1588%107 7/5
peor2t
nao stn Rie Res eters el
ree CTRAIN) aoe! _ ee
t ra, =the TEN
we GASHEIO A,
510.3
10. Therefore. the Now is laminar The lal Nusselt number fs
swbich is fess than he eitial vale of 5
2
“The local est transfer andftion coeficlens a
mene hae
yb y= HOUSBNATE gaan Bw
ar 6
eee _jameenie
eaoes107
interval, The results re
a HT
i Tr ieee G x cote
i, I 7 aa005 2s] loo
2 | osse7 =
ih 3 [_asie9 24 locos
[nasa z,4
s) aor 2
eo] 30r6 Er 7
Team [eonnres]
wf es foo] Cy lone
| o5ean | 00010se
70] ome ‘0.001 oF . : ' ae
xt)
PROPRIETARY MATERIAL, ©2007 The MeGroi Comparie ne. Lined ib
nc. Line aban pried only
EAOPRIETARY MATERIAL 02017 ounatinalyorwecig eae NGS Risto ot
m3
OD) wre rcrvoistascniy 110m there ner om bt ae feo
Tinitcain unk tsb seca
Seaty porting condition exist 2 The crcl Reymlds momber nite S103 Ale —
simeribe ene srace Because o he onan
engine ok
Properies The eoretes fs at am andthe fil hroam
ware are ane AS)
Anatysis hie Nows parallel to he 04 m se The
‘Repos mtr in his casei
Tat 180100073400) e/SKO.80 9 76108
STE
ice! Reynolds number sn she flow i lminar + wrtent Butte Noo is
Bo ee ccaue ef the corsa apation ofthe engine Nock. Using
Tene heat wranafrcoeicint, and hebeat ener ae are
snbich is greater shan thei
SSomed foe trator over
ine proper veteions she Russel nm
Socrmined tobe
dv = AL a0.037 Re, Pr”? =0.03719.376x10°Y40.7202)"" = 198
rok Nig SOO WHO 1044) 69.78 Win? 2C
z o8m
eb =(0.8myU4m)= 032m?
(7 —7,) = (69.78 Wh? $CXO32m71(100~201°C = 1786
ome
‘The radiation heat transfer from the same surface is
Oras = 4,978 Tor!)
=(0.95N0.32e07 95.6710
“Then the total rate of heat tansfer from that surface becomes
1706 4198) = 1984.
wim? #1004 273 Ky “25-4273 Ky] = 198.
(ee wl? pgatsees
Jo Sa parses ¥" \
plok =" Bahu
Pood qr ®
Kp des
: Gor< Gane * Qx OX?
iene Lind abt ermine ono each od
rl you ae ug wou emis.
IETARY MATERIAL, ©2007 The McGaveh
Das Torcowse preparaion Ifyovareasiden ns cu sheet of platicThe ae of eat arses fom the plate set
1.38 Arles oth ies
fee determines ‘i
Jo. 2 The ete! Reynolds number fey = $410.3
mptons 1 Stenty peratine condiin
i a gible Ais on deal gat wh const properties
ata sa aa mate iy mgeriae /
; ‘none wine ee
" wet av6n10! mss Digest
paren ee eee
Anata The with ofthe cooting eon
{STs determined ten
Way =[AS/60)msK20) = 05m
The Reynods numbers
FLOM 4996108
+ Ta96H 107 m2
seh sess han the ities! Reynolds number. Thusthe Now is
| finer ow for Nusselt number, he average heat traefer coefiint an the
Aetemined 1 be
2h wo,664 Re"? Pri? m0. 499 210°)"9(0,7202)" = 259.3
laminar. Using the proper relation
rest wane ate 2
ne
guy 2.02808 Wi
Se $9.3) = 6.07 Win
4 wi (a59.) 607 Win 26
’
4, =2LW #202 mxOSm)e 12M?
noe = Ad Fy =T,)=(607 Wim? CK.2 m?490-30"C = 437 W
(03007 The McGraw Hil Copies Ine. roto peri nly ta aches 2nd
eee er. Ifyou ates sen win this Manel ou ate win it witout pessoa, ns
surface ofthe passenger eat of in
pvr fhe ep surace tate deli,
“Assumptions 1 Sieaay operating conditions et
Aacintlon heat exchange withthe suroundings is ne
PC are (Table Ax)
Properties Te properties oft 33 .
f = 0.02588 Wh "C oe gt aan
no annett at syle ALLL LS
proms? =
“Anatase rate of comvecon hes ans 0 Ne WP
nae ar a rust be ena othe sar radiation
anaes ote sme surface inorder to rea 287 5
steai condo The Reynolds numer is
a, a PE = BzHONO ABE 9 grentt
wT g0RRIO™ 2/5
critical Reynolds nu
Tor Nussch number
bined laminar and wrbutent fom,
ner, Thus we have 2 7
Mee ircfet andthe eat transfer rae
The average Feat raster
2x10"
ariype'? =f0.03719.674 «10897 -A71]0-72R2I"™
ty SEISEE SIO 212 +10") 239.21 Wi 2c
_The ewittrium temperureof top suri ashen deemined ytakingconvesion sd iat heat
Teen equa to cach wher
4 200 Wim?
wag) eT Teo arc +
0 jaw
Gna = doe
sorngaqe mre 050 mtn nti eno ein
A 0207 ee or yomemogsone ot
soto eles Tha vate of eat Tos fom he
in is incident he "mer ei ows through Reo
rer ctlency. ad be wermpeatre i
Sedctrmined
mmberis Rey = S107 3 Mest
Reynolds 2
exis. 2 The estes!
era Sey apemtig conn .
serio | Sey a pepe mein Asan el wi
ee ene pe
Tr vcyepeiertara he imienpei of ofelgiees
rans wine os
eriammate? oth = Lb ll
foams = al
apo sig wind wa ass? 8
eget tet atctaen
ery, tet 3eBRIEN yoo
ee, Using he Nusselt number relation for combined
cubic is geater than he erica Reyrols nk
Ticient ie determined tobe
TSminar and turbulent flow, the average heltranser eae
v= ajoasrnatt-emin tos seat HOE «TE
ot yn ARSE WINE yp asad WiC
“Then the rate heat los fram the collet by convection is
our =Ad,{ Ta =T,) = (07.83 Wim $0241.22 YBS-287C = 279 W
“The rae of heat loss from the collector ty radiation is
nay * 407-4 Teen)
(oom aetant 5470" Win? sofose 2 Ky-(-102736)]
pana
and
rns = Que + Oma = 42794782 1169W
(8) The netrate of heat ransferred to the water is
Oar = Que Qa = 81 Sn
= (088.212 m? 1.700 Wie? 1-1 169.
= 1478-1169 =309W
Om 309.0
Pat 3M 0209
% @, ew"
(c) The temperature rise of water as it lows through the collector is
Qu 3004W
Bey” UoKpsnainogec)
ny = tie ATT
(©3007 The McGraw-Hill ompenies, In, Limite inttaion perme ony wo chery and
RIETARY MAL
dent wig thi Man YOu wing it wih permission
‘uate for couse preparation Ifyou ae
8 2
‘1:23 Wate a preented hy exhaust uses na ibe anh The neo eat ae epee oof
“Rit uch anne tempers ta watered
steady operating conditions ens2 For eshout gases operisaeune
vied hus ve meaniemperaire snl kon. We eva teat
Ihe chesbed ler and Ue (Table A= 13
‘Properties The est temperate of
ropes tthe assumed mean tempera of 28°C (wil
1= 04108 Wink p= 047d hyn!
er Pr=oeose
5 pen 2.76010" Kans Pie Pg sare OT154
the deny oar a he nex vemperatare of 307C ore nthe mag late aetaton whe lS
ae cine bea woter os RO" 144197 KIC (Tele AD
n= 06138 pm’
_ styl (a) Ws given that D= 0.021 m.$; = 5) = O08 rewre
s ent ONS Then te masimu veloc and he .
Ronmaus number bated onthe maxim Westy iaaet,
fod
— 300°C
Sry g 28 ca Semis) = 6.102
aD (067g WENGE NOON. 545 > oOo
276x107 ky
“4 “The average Nusselt mamber i determined using he —
i Peover eision fom Table F210 be
wreomnef =a Oo a, 0
10.27.3132) (0.6946 "(0 6946/07150)" #3746
since =the venge Nose umber nd est anf coef rl be bes inthe ie bak
: ‘come
Noe, # Nay #3746
i Mant _ 37.4640.08108 Win-*C) ha?
} n= Magat masmnere in ra win?
‘Te tal numberof whesis N= NxM 16x8= 128 For aunt ube enh =
Tree tanh mes lowe at ofa evaluated thee ate
“tp = NeDL=128e(0.021my m= 8443
‘Ly=(06158hghm? 4S 548 YOO8 mT) «1774s
sure dtlerence ane ate of eat rnser sme
imbthe het waster
: nmin, = PM Sy
“Then the fui ext temperature, thelog mean tempers
“tant o-oo
(7-1)
Tin T= TIAT, =F WN
Qe Ad, ATia = (732 Win? *CKEAASM XIB677C) = 115430W
‘e007 The MeGreillConoves, ne. Lil una ported ely tebe and
ng ht Mal, yu ewig wb eri.
ear ET Apuepepron Wf youxe 3 wwden
" 5 \9 ane
uty
140
(2) Foe Wisin arangament te hak he ton efficent eomeponing Kay 3132 an SD =
$2134 fehomtp nara) Ule Alan y= | orthe gure amangement Ten the prestre Sop
‘rssh he hn Rees
74 1” (6.102 ers)®
arene ot Hayy BE Heaait ef
im
jt )a sea ro
: Je
Teme
(The emperaure rte of waters
o uisasaw
Wome gear WRPEKSISTERE
Discusion The arthmctic mean fui temperature i 7+ 7.) = (300 + 237V2 = 269°C. which is
‘scent close othe assumed vale of 280°C. Therefore, therein need io repeat calculations.
0* epee Tome —t Tone
460
PROPRIETARY MATERIAL © 2007 The McGraw-Hill Compaen.
ca for course preparation you res den wins his Mana yous ung it wine perce
Linde dsrbaion permite ony wench and tyes
acts oo
ade © +193 The plumbing tym of» pan ivales tome secon of ame pe enPuerd os SES
1 Tree wna te nad eet cy pa alsin prevew Feezing of weet ns PST
Tsp wn med wi ec us rar wer ren comoons he ASTM
2 Meat waster
‘ vewmpwons | Heat arf a tact fat cone rated weno SES SOO
semen | He ee cal erm sbout ere an a0
Scene re cant 4 The weve nie pm 2 ae
Se eee comac emce he mete write 6 The convection HTS mene
the pre nese
promos Te eral Conacvitics Age given 1
TEC er ites asulanen The density and
Ung € (Table A)
dnarais The tet rads of tbe pipe
AnD Ghaauianca er 33cm Weletn
ae oe pe the omount of heat a met be tered rom
“Srermned tobe
: a pv = tart) = (0000 kn? 03m) (Hey) = 2827
TOE ar Cian naxe 8 ne CHI OFC 1773
te pipe amd A= 0035
be #= 0.16 Wien fo past
1H im an
pect heat of wer 2 B= am
125.0 cmand the vter ads ofthe pipe and thus te inne
Se trans of insulation. Conserng 21-0
he nner a2 coals From 15 100°C
t Cons
“Then the average rte of et Wransfer
: dorng 60 becomes
Qua 1773005
= Peat eomw
an = = a 60055
0 Pew Re Re :
; “The individual thermal resistances are
i Ini i) 14 093/003)
Boge EE OTL —
on St Fanewinecxray
Indesleg) Wey 0033)
Aan = MEH) 5 MLO — a 381/008
Sie = ages winsome! met
a 1 1 1
cet Re = Rae =
Rem = Fay GOW CHEE) me) SRS
-then the rte of average heat transfer from the water can be expressed as
Tee Tu (5-107 eae
S 3 on w=
oe 821 W To opans a SSla(r, 10.033) +1 AIRES CW
-eretore. the minimum thickness f fiberglass needed opretet he pipe fom ering
pany -1p2 350-0.033 = 3.467 m
sebch soo are Installing chick nsltion sot pnt, however and hus oer sae
Jrotection methods should be considered.
IAL, 2007 The MeGnweilCompenic n.Lid bation permite vy ech nd
AERIAL Tye nc singh Mame ou ew Hh Pm,
hector coe
u 1
15 Design and Essay Problems
ena.
fr, The flow rate ofthe f20
{4115 A conpue cooked by a an lowing sit rough heen ofthe come The fs
‘dhe diameter ofthe casing ofthe fan ae to be spe
“sumption | Steady ow conditions ens. 2 Meat ux is uiformly dsr
‘Constant properties
Properties The relevant progenies of ar ae (Tables Act and A-15)
ep = 1007 seg "6
2 a0.287LPam"EK
Anelyss We need to determine the flow rte of sir forthe
trued. 3 Air isan ideal yas with
‘ont ease scenario. Therefore, we assume the init bee
temperature of arto be SO"C, the atmospheric pressure be “yi <> 7
50.12 Pa, and disregard any heat transfer from the outer
surface ofthe computer ease. The mass flow rate of ait as
Fepuired to absorb ata nate of 80 W ean be determined
From °
rh ° 00 isa Bdiiat
ee oe Fa) Waar IG "CKeO=5OFC
60°C. Then the density of air entering the fon and the
eM =
4 Inthe worst cate the exhaust fn will handle ir
5 ‘volume Now rate becomes
pw) Jor2KPa
BT ~ (ORT KPa ag KXCOFITR
pn 0007844 kaIe
2” 07337 kgm
Foran average velocity of 120 m/min,
determined from
0.7337 kgm?
= 0.01083 m/s = 0.6497
the diameter of the duct in which he fan installed can be
[0.6497 PF
Set? = 008s m=8.3.em
ow
baa D es
ROPRIETARY MATERIAL © 007 he McGineil Como re Ui rb
an mit ty ete
“educator for course preparnivon. Ifyou ares stent using this Manual, you are using i withunt permission. ee
Ce 166
(sro sti: Tegan
SEX, Assmpin1 Srey opera sonny es 2 Them the ade are smooth,
‘Properes The prestics fia the avernbe te
Aeonperatre of (1S*25V2=20°C are (Table AL? rw
esate a &
‘catowmee vec (€))]
qusinee wet
nap he mow mea emt i
Gus
san ptng tb eg’ ye LEE (Ot W OSOEDEEN,
5 2c 25=157C = PHO
Qe mc 7, 7,010 5022 bys 9R I
ar1$0,6 10 be Nay = $364, Then he beat
( seem poe rind om ae 45107
ea nee gen men enrtaee
nab ny SEMIN soy asosewinice — ¥ + od
“ by nhs -b,x0t5m-008m=0020
ieee
| arg Bala EB a pee
yet) (=)
te) ol oo=ts
enn anne wei erin fo
rs
= 290m?
asi
co WOT, (40.34 Win!
“Then the tube length becomes
293m?
AUR)
4, ADL —+h = <3LIm
‘0.007 The MeGrowillCorpetics tc, Lite nba permed ly teches and
PROPRIETARY MATES po 8 xen ing Hs Mona, wg with Femson, “9
ecified bet
cei expe weld ir with 25
ue cot oni ee th eat empath we 9M
2 porter se
EEE Recercetcen Te eof eto
i “determined
‘ are smooth,
= ven ame tle ow
0) oe ssh coh: 4 significantly since the pipe is not very Fong.
oe Sees :
ce ean ngs oem
sore maamarenienaed
pipe 0326110" aang ing °C
; jaa Then low eo wate
ne kg #143 ODED
They ert
Teen 2mnya0en
, en aus, 2000 e.a9
i ¥ 0326x10% mie
ie irae on 1008 Teton fw it he le ey eg it
TL Tiapstaoorm soem
charac oan te al eg pp Tene wean ae iy veo
i Weicnteenwe pe Theis Rewer oem aah nd es
! rote cn) 0085 da ae ody carob 808. Tene ae am
I €,
(120i
isease ae roughly
1 tecomer
| a= Ae cas pmo!” =0,125x00324147.24001 96" = 737.
: = = SEES Wl 7371) 12-40 Wim? *C
0m
be and thas henner urfice temperate ofthe
lmperatre. Also, we exes the pipet be nearly sate
fince is made of hin metal (we check inter) Then th ate ef eat less ome pipe wil ete
‘tthe convection tnd radiation fam the utr srts ot ntempertare of MPC, a i eermined tobe
4, Ogt = #0045 mK 15mm) =2 1682 Teno Chott) OX0L Wtce J
carpe area aaa ee rere Cher SENT
Poa = et00T Ta UA Pores ml
210.772.1682 867010" wink hfooszT 63! -toe2730*)o9e2W wat aR
: Ons Qon Ons 8192+ OW AR
i (ans frpeset itl masse BB ET en BR)
detes-1)—+0 of Dre BY nee Ta a
3 i Tass esnaz0E TREO
'Theresult jf our assumption thatthe eperatue drop of witer is eligible Also, he thermal
ritanee ofthe pipe and temperstre dap scent are St :
i fg, lB!) WABI) a
i om ait” FE wimCKISm) SMO CW
BT pe * Qo ge = BOB WH2 SHO" CHW) 2 O09
hich justifies ou assumption thatthe temperature drop across the pipe ineligible.
{EROPRIETAMY MATERIAL, ©2107 Te McG Hl Congo, Lmid ston min
‘Son fren repsation yu ae Pie wing ht Ma you meng co eee on RT aNd (Be wre me vec rt my serceys wrt finn cor Pea Ta neater
NS acta nd tte manaones cocey ae be meme
Assumplions Toe Yow wendy. eczar. n fly erin,
Anatpas Tee velocity ecie a iy dele amet fiw a eT ES
5)
‘The velocity profile inthis case gives by
wn=ai-ier)
Compating the two relations above gives he pipe iat Be
(raxima veloezy, 2a the mena webct 12
wort al!
crm Comp ine en poe ty tee ot
‘TPOPSIETABY MATERIAL, 92007 De
Ore eT ners cy Namal ee ESS 233
(Pease cens sen et nanan hes enpne ste he
heat os ret be determined.