CSVTU code: NlEt,L7 t2_B. Tech. (Seventh Semester) Examination Feb. 2012

Sub.iect: Heat and Mass TransferMax marks: 80

Min F4ss Marks: 28Tirne: Three Hours

Note: All questions corrJ: equul murks. L,se of HMT datn book and steom lobles is permitted,Assume suitable duto if any. Solve any two portsfrorn all cluestions exceptfroru question No.4.

'{u. Consicler a long cyhncler of insrcle raclius rr, outsicle laclius 1': ?ncl lerrgth L. Let insille

tempelatule be Tr anci oritside temperalure be Tz. Derive the tempelalure distribution anel ireat

transfer equafion. 08

1 b. A hollow sphere 10 cm I.D. ancl

W /n K is usecl as a container for

temperatures are 300 "C and 100 .C

sphere.

30 c.m. O.D. of rnaterial having thermal conductivity 50

a liquid chemical mixture. Its ilner and outer surface

respectively. Determine the heat flow rate through the

08

t/L c. An exteriol wa1l of a house mav be approximateei 0.1 m laver of common brick (k = 0.7

!V/m "C) follor.r'ecl bv a 0.0-l m lave.r of gvpsum plaster (k:0.48 \N/rn,'C). \,Vhat thickness of

rock wool insulalion (k:0.065 W/m.C) shouicl be aciclerl to recluce the heat loss or (gain)

tirrough the wall by 80 percent. 0B

2 a. Nichrome wire having lesistiviiy of 100 pO-cm is to be used as a heating elernent in a 10 kW

lreater'. The nichrome surface ternperature should not exceecl 1220 "C. Take -currounding air

temperalule 20 uC, outside surface coefficient 1.15 kW/m2K, thermal conciuctivity of nichrome

77 \N / m K. Fincl what cliameter Nichrome wire is necessarv for 1 m long heatel and tire rate of

current flow-

u|'b.Derive expression for temperatule clistribution ir'r u ,trulgtrt fin of

insuialecl tip.

,_y'4.. Atr aluminium plate of 400 rnm x 400 inlr x 4 mm at

oxvgen at -183 oC. Derive the expression for the time

reach a temperafure of -70.rC. Assume convective heat

C,.= 0.8 kI/kgoC, density p:300 kg/rn:.

08

rectangular profile for

08

200 oC is i;ucl,-lenlv quenclrcd in liqi-ricl

required and the trme for the plate to

transfer coefficient 20000 kJ/mz-hr oC ,

08

.-{a. Distinguish between nafural ancl forced convection. Define Revnolels, Nusselt ancl Stanton

numl-rer. 08

3.b. Air isflowingover afiatplate2miongancll mwidewithavelocityof 3m/sat20.C.if p

:1.77 kg/tr,:., ancl r,= 1.5 x 1g-s vnzf s, calculate (i) bounclary thickness at the tlailing etlge of the

plate ancl the total drag folce on the both sides of the piate. Also calculate the mass flow rate of

the air "vhich

enters the boundary laver between r = 30 cm and r = 80 cm. 08

3 c. A 30 cm long glass plate is hung vertically in the air at

maintainecl at 77 uC. Caiculate the bounclary laver thickness at

air is biown at 4 m/s over the similar plate the eslimate the

trailing eclge.

27 nC while its temperalure is

the trailing eclge of the plate. If

boundarv laver thickness at its

08

ldr(4 Discuss the factors affecting nucleate boiling.

(ii) Differentiate betr,r,een fiim n,ise anci elrop wise conclensalion

;!,b.Derive expressi.on for LMTD for the parallel flow heat exchanger'

&. Derive ihe expression for equivaient emi.ssivity for raciiant heat exchange

long concenh ic cyiindels.

04

04

08

belween inriniie

08

,4. Uotoil with a capacity rate of 2500 lV/k flows through clouble pipe heat exchange. It enters

at 360 "C and leaves at 300 .. Cold fluid enters at 30 .C ancl leaves at 200 nC. if the overail heat

lransfer coefficient is 800 Wf m2K, determine ihe heat exchanger area requirecl for (a) parallel

flow and (b) counter flow. 08

5 c. A 30 mm cleep pan is filled witir water to a level of 15 mm u"O r, exposec-1 to rlrl air at f0,C.

Assumrng the mass cliffusivitlz as 0.25x10-t ^r/s, calculate the time required for all the water Lo

evapolate. 08

CSVTTJ

t:r- ng o s+-

B. Tech. (Seventh Semester) Examination Nov. 2011Subject: Heat and Mass Transfer

Code: ME 11712

Max marks: 80Min Pass Marks: 28Time: Three Hours

Note: Al.l questions csrry equal marks. Use of HMT duta book and steam tables is permitted.

Assume suifable clata iJ'any. Solve {LIJ, trryo pmts from all questions exceptfron question No.4.

08

-lxdettne or explain the fbilovu'ing terms

(i) Thermal conductivity

(iii) Overall heat transfer coefficient.

(ii) thermal diffusivity

ty' A 240 mm steam main,2l0 irr long is coverecl with 50 mm of high temperature insulation\-.-'

(k : 0.092 W/m oC) and 40 mm of low temperature insulation (k : 0.062 W/m "C;. The inner

and outer surface temperatures are measured as 390"C and 40nC respectivel,v. Calculate (i) total

heat lost per hour (ii) the temperature betu'een two layers ol'insulation. 08

. I .. f)erive the expression for the temperature clistribution fbr the hollow spherical conduction

s-ystem lor unifbrm therrnal conductivity. State the assumptions taken. 08

,lt/.{fne temperatures on the two surfaces of a 25 mm thick sfeel'plate, ( k - 48 'Wlm oetraving

a uniform heat generation 30 x 106 W/m3 are 180 oC and 120 oC. Neglecting the end effect.

determine the following:

{i) l'he temperature distribution across plate (ii) the value and position of maximum

temperature (iii) the flow of heat from each surface of the plate. 08

2 tr. Derive expression lbr temperature distributiori in a straight fin of rectangular profile

insulated tip.

-/./\y. A 50cm x 50 cm

temperature is suddenly

temperature of 108 nC.

Take P = 9000 kg/m3, C

lclr

08

copper slab 6,25 mm thick has a uniform temperature of 300 "C. Its

lowered to 36 nC Calculate the time required for the plate to reach the

: 0.38 kJ/kg nC. k: 370 W/m oC and h : 90 W/m2 oC 08

3 a. Using Von Karman integral monrentum equalion ancl cubic velocity profile derive

expression fbr boundary layer thickness. state the assurnptions taken

-;,-dWater at 50 oC enters a L5 cm diarneter and 3 nr iong tube with a velocity of I mls. 'fhe tube

wall is maintained at a constant temperature of 90 "C. Calculate the heat transfbr coefficient ancl

the total amount of heat transferred if the exit water temperarure is 64 "C. 0g

J c l)etermine the rate of heat lclss per rneter length ft'onr 10 cm outside diameter steerm prpe

placeci horizontally in ambient air at 30 "C. T'he pipe has an outsicle wall temperature of 170 "C

and an emissivity of 0.9 0g

tlie

08

t 3-x(i7 Discuss the factors affecting nucieate boiling.

(ii) Diflerentiate,between fllrn wise and drop wise condensation.

4 b. Water (Cp : 42W k.li kg "C) enters a counter flow double pipe heat exchanger

flowing at 0.076 kg/s. It is heated by oii (1880 J/kg "C) flowing ar 0.1-52 kg/s fiom

temperature of 1 16 oC For an overall heat transfer coeft-isient U : 340 W/m2 "C and 1 m2

5a. Write a short note 0n any two;

,(r) vicw lactor ji)).intensity of radiation.(.iii) t;aartrefi cosine tar,v

04

04

at 38 "C

an inlet

area. 08

08

5 tr. The radiation shape factor of circular surface of a thin hollow cylinder of tr 0 cm diameter

and 10 cm length is A.fiffi. What is the shape factor of curved surface of cylinder with itself. 08

5 c. The'"vater in a 5 m x l5 m outdoor su'irnming pool is maintained at a temperature of 27"C.

The average anrbient temperature and reiative humiditv are 27 "C and 40 percent respectively.

Assuming ivind speecl of 2 m/s in the directioii of the long side of the poo[. Estmate the mass

transfer coefficient for the evaporation of water'{from the pool surface. 0g

t."'*lJ"t

CSVTU Code: ME 107122010

Max marks:80Min Pass Marks: 28'fime: Three Hours

Note: All questions carry equal mark* Use af HMT data book and stesm tables is perrnitted.

Assume suitable data if any, Solve uny two partsfrom alt questions exceptfrom question No.4.

I a. Derive three dimensional general heat conduction equafion in Cartesia.n coordinates. 08

I b. A standard cast iron pipe (inner diameter = 50 mm and outer diameter'55 mm) is insulated

with material (K = 0.02 W/!$ nC) Temperature at the interface between pipe and insulation is

300oC. The allowable heat loss from the pipe is 600 W/m length of pipe and for the safefy of the

temperature of the outside surface of insulation must not exceed 1.00oC, (i) determine the

minimum thickness of insulation required, {ii) the temperature of inside surface of the pipe

assuming its thermal conductivity 20 W/m"C ' 0B

1 c. Find the steady state heat flux through the composite slab as shown in the fig. 1 and the

interface temperature. The thermal conductivities of the fwo materials vary with temperature as

follows: Kn = 0.05(1 + 0.0065t) W/m oC, Kn = 0.04 (1 + 0.0076t) W/m "C. 08

'1tf{}"i

t1 *"1

F*ro *{**---" 1".r,*-'9- 5* rrt*i '' lt.l() tllr:r

Fig.1

2a. Acopperbar (conductor) B0mmx 6mmincrosssection (k =370W/rn"C) (Fig.2) islying

in an insulation trough so that heat tlansfer from one face and both the edges is negligible. It is

observed that when a current of 5000 Amp flows through the conductor, the bare surface has

the constant tempelature of 45oC. If the resistivify of copper is 2 x 1"0-s f)m, determine: (i) the

B. Tech. (Seventh Semester) Examination Nov.Sub.iect: Heat and Mass Transfer

'-- ltrtrt'{i:r:i.r

maximum temperafure

center of the bar.

which prevails in the bar and its location (i0 the temperature at the

08

llife $ur'{iiie:

{r '..450'i')

{ llilr;:r:r',":r;:tr.il.:irirrr

{ lr ,,.. j l{i 1l . n"l'i

Fig.2

2 b. Derive expression for temperature distribution in a straigl'rt fin of rectangular profile for

insulated tip" 08

2 c. A stainless steel rod of outer diameter l" cm is originally at a temperature of 320oC is

suddenly immersed in a liquid at L20.C for which convective heat transfer coefficient is 100

W/mzK. Determine the tirne,iequired for the rod to reach a temperalure of 200 oC 08

3 a. Air is flowing over a flat plate 5 m long and 2.5 m wide with a velocity of 4 m/s at 15oC. If

p:1.208 kg/m3 and v = 1,.47 x L0-s m2/s, calculate (i) length of plate over which the

boundary layer is laminar/ and the thickness of boundary layer, (ii) total drag force on

the both sieles where the boundary layer is laminar. 08

3 b. In a tube of 60 mm diameter, water is flowing at a velocily af 1,2 m/s. The tube surface

temperalure is maintained at 70 "C and the flowing water is heated from inlet temperature of 15

nC to an outlet temperature 45 oC. Calculate the following: (i) heat transfer coefficient from the

tube surface to the water (ii) the heat transferred (iii) length of the tube. 08

3 c. A vertical plate measuring 1.80 mm x L80 mm and at 50 oC is exposed to surround.ings at 10

"C. Compare the free convection from this plate with that which would result due to forced

convection over the plate at a velocity equal to twice the maximum veiocity which would occur

in free convection boundary layer.

a. (i) Discuss the factors affecting nucleate boiling.

A'I

Illrrul;rl,:d I. ,-.,_ ililt-! {1, J I

III

m

#{ff ):

tII

iIII

1d

08

04

i:r':;*:"-i; { -"":t-:"p''?/;-'%i.l --jr, "l y ::' 1. i*s l1 *.:1.;.r i*.: i

(ii) Differentiate between film wise and drop wise condensation 04

4 b. Calculate for the following cases, the surface area required for the heat exchanger to cool

3200kg/]rir. of benzene ( Cp = 1..74kJ/kgoC) from 72oC to 42oC. The cooling water (Cp : 4.18

kllkg.,C) at 15 "C has a flow rate of 22AA kg/hr. (i) single pass counter flow (ii) one-shell pass

and four tube passes (iii) cross flow single pass with water mixed and benzene unmixed' For

each configuration, the overa*l heat transfer coefficient may be taken as 0.2BkW/m2 oC. 08

5a. Derive the expression for equivalent emissivity for radiant heat exchange between infinite

long concentric cylinders. 08

5 b. The radiation shape factor of circular surface of a thin hollow cylinder of 10 cm diameter

and 10 cm length is 0.17-1,6. What is the shape factor of curved surface of cylinder with itself? 08

5 c. A 30 mm deep pan is filled with water to a level of 15 mm and is exposed to dry air at 40 nC.

Assuming the mass diffusivitv as 0,25x10o ^t/", calculate the tirne required for all the

water to evaporate. 08

code lvi E o?71 Lcsvtu

b,Twh,(Seventh Sem) Examination Nov-Dec 2009

Subject: Heat and Mass Transfer

Mechanical

Time: Three hoursMax. Marks 80

Min. Marks 28

Note: rtse of HMT data ard stcanr fabresbook is pentdtted: ArI questions carty equar mar*s.

Attenryt arty tzao parts ftom each question eicept question 5' Assume xritable clata if any' -

1 a. A furnace wag is made up of steel plate 10 mm thick (k = 62.8 kJ/m-hr- oc) lined on insid6

with silica bricks 150 mm (k: 7.3|kJ/m-hr- oc) and on outside with magnesia bricks 200 mrn

(k:1g.g4 kJ/m-hr- oc;. The inside and outside surfaces of the wall are attemperatures 650 oc

and tz5 oC respectively. calculate the heat loss from unit atea of the wall. It is required that the

heat loss be reduced to t o tralnu. by means of an air gap between steel and magnesia bricks' Find

necessary width of air gap if thermal conductivity for air is 0'126 KJ/m-hr- oC'

b. A staintess steel wir.e (k : 20 W/m-oC and resistivity: 70 micro ohm-cm) of length 2 m and

and diarnet er 2.5mm is sub merged in fluid at 50 oC and an electric current of intensity 300 amps

passes ti'ough it. If conductance at the wire surface is 4 kw/m2-oc wolkout the steady state

temperaturea+the-centera&d et-!&-surface of the wile -

c. Derive the temperature di.stribution and heat transier: Explession fof-teady-state' heat

e of inner radius rt, temperature Ti and outer radius rz,conductionthroughanhollowsphereofinnerradtus'11

temperature Tz with constant tirermal conductivity material.

2-.a. Afurnace is constructed with 10 cm of fire clay and 50 cm of red brick' The inside surface

temperature is 50 oC. Detesmine the heat loss fi'om 1 nl of the fumace wall,-and the temperature

at the layer interface. Thermal conductivities for the wall material ale:

Fire clay: k:0.28 (1 + 0.000893T) W/m-oc Red brick: k = 0'75 W/m-oC'

b. wrat,is lumped capacity? Derive the expression.for temperature distribution fol a solid

initialty at.a.temperature To which is placed in a convective environment at temperature'

c. ln an experiment to determine the thermal conducti"'ity of a lcng solid 2'5 crrr diameter rod' its

base is praced in furnace with a rarge porlion of it projecti*g into the room air at 22 oc' After

steady state .eonditions prevail, the temperatules at two.points, 10 cm aparl, are found to be i 10 oc

and g5 0c respectiv6iy. Tire convective heat uansfer coefficient betu'1e1 the rqd surface'ald the

surrounding air.is 2g.4 wrnlK. Detennine the thermai conductivity of tire rod material'

?-ro

3 a. Athin flatplate of length l: ! rnand widthb:0.45 m is exposed to a flow of air parallel to

the surface. The velocity and temperature of the free stream flow of air are 2.5 wt/s and 25 oC

respectively. if the temperature at the suface of plate is T, : 95 oC, estirnate the heat loss fi'om

the 50 cm length of plate measured from trailing edge'

b. Air is entering at 7 bar pressue end ternperature 200 oC is heated ai it flows tiuough a tube

with a diameter of 25.4 mm at a velocity of 10 m/s. Calculate the heat transfer per r.urit length of

tube if constant heat flux condition is maintained at the wall and wall temperature is 20 oC above

the air temperature al1 ai.gng the length of the tube. How much would the bulk temperature

increase over 3 m length ofthe tube.

c A square plate 0.5 m x.0.5 m with one surface insulated and the other surface maintained at a

unifonn temperature of 385 K which is placed in a still air at temperature at 315 K. Calculate tire

average heat transfer coefficient for free c.onvection for the following cases: (i) the plate is

horizontal and hot surface faces up (ii) the plate is horizontal and hot surface faces down (iii)

plate is vertical.

4 a. Derive an expression for effectiveness interms of NTU and capacity ratio, forparaiiel flow

heat exchanger.

b. A counter flow heat exchanger, through air 12.5 kg/s of air to be cooled from 540 oC to 146

oC, contains 4200 tubes, each having a diameter of 30 mm. The inlet and outlet temperatures of

cooling water are 25 oC oand 75 oC respectively. if the $,ater side ressistance is negligible,

caiculate the tube length required for the heat exchanger. Use the foliowing properties of air as:

p: 1.009.kg/m3, Cp: 1.0082 KJ/kg oC, p =2.075 x 10's kgims and k = 3.003 x 10-2 Wm oC.

c. Discuss briefly the various regimes in boiling heat transfer.

35. a. (i) Expiain Fick's 1aw of diffusion'

(ii) 02 gas at 25 oC and a preSsure of 2 bar is flowing ttn"ough a nrbber pipe of inside

diameter 25 mm and wall thickness 2,5 nrm. The diffusivity of 02 tluough rubber is 0.21 x 10-e

m2ls and the solubility of Oz in rubber is 3 .1 2 x 1 0' kmolAn3.bar Find ti:.e loss of Cz by diffusion

per meter length of PiPe' 5

b. (i) Calculate the shape factor of a cyliudrical cavity with respect to itself for the figure shown 4

(ii) Define radiosrty and irrradiation. A-

e"s.\i.,F"uE.Teeh" (sev-enth sem.) Exdrninario* Apr*-tui-r" z*f$de

fit f; sE rl '*$ubject: Ftreat and k{ass TrJnsfer

'fime: .t,hree hours Mechanicai Engineering

Max. Marks g0

Note: (Jse of HMT data and steam tabtes book is permitted. o,,Yi}rf;j,Tf;"r# ,u*,morks. Attempt any two partsfrom each question. Asswne suitable data if any.t agyfrngt"is Fourier's law of heat conduction? state the assumptions on which it is based.

6S"r'n"thermal conductivity and overall heat transfer coefficient. 4 + 4.

A2" b' A reactor wall, 320 mm thick is made up of an inner layer of fire brick (k:O.g4wmoc)

-Rs covered with layer of insulation (k:0'16wmoc). The reactor operates at a temperature of1325 oc

and the ambient temperature is 25 oc. Find (i) rhe thickness of fire brick andinsulation which gives minimum heat loss and (ii) the heat loss presuming that theinsulating material has a maximum temperature of 1200 oc.

gc' Derive the temperature distribution for the spherical system under one dimensional steadysipte hegc*99g9!9n.

-8

*ilrli,ili.TH::J:;H:J;:H::ffi ,:i1ru5.'::":fi ;lJ#,::il ':t

mid and quarter planes and (ii) the heat flow rate and temperature gradients at the midanct quarter planes.

gb' Derive the expression for heat clissipation from the fin insulated at the tip. g

0. e . @Asolidcoppersphereof i0cmdiameter(p:g954Kglm3,co:3g3 j/kgK.k:3g6\^,,,/rnK).\P'gYi tntttally at a unifonn temperaturo ti = 250 oc, is suddenly immersed in a weil imrnersed in awell - stir"red fluid immersed which is maintained at a uniform temperatur€ ta : 50 oc.

The heattransfer coefficient between the sphere and the fluid is h : 200 wrn2 K. Determirie thetemperature of the copper block at x:5 min after the immersion. g

' 3A'E*nlain the terms velocity and thermal boundary layers rvith respect to flow over frat\,/plate.Alsodefineq. 4+4

Vr)' Air at atrnospheric pressure and 200 oc flows over a plate with a velocity of 5 m/s. The plate"RF is 15 mrn wide and is maintained at a temperature of 120 oc. calcuiate the thickness ofhydrodynamic and thermal bou'dary layers and the local heat transfer coefficient at a distance

PTO

of 0"5 m from the leading eCge. Assume the flow is cn the one side of tire plate. 'Iake 1p --

0.825 kglrn3,p :24.5 Ns/mz, Pr = 0.7 k: 0.0364 W/m K). gi 1,,

- ,,') ; ,pJvhen 0"5 Kg of water per minute is passed through the tube of 20 mm diameter it is found+.-"e-' to be heated form 20 oC to 50 oC. The heating is accomplished by condensing steam on the

surface of the tube and subsequently the surface temperature gf the tube is maintained at 85 oC"

Determine thr length of the tube required for fully developed flow. Take the thermo-physical

properties of the water at 60 oC as

( p:983"2 kd-', v:0.478 x 10-6 m2ls, co :4"178 kJ/kg K, k = 0"659 W/m K). g

^ h/@hot plate 1.2 mwide, 0.35 m high and at 115 oC is exposed to the ambient still air at 25

@-C.Calculate the following (i) Maximum velocity at 180 mm from the leading edge of the plate

(ii) the boundary layer thickness at 180 mm from the leading edge of the plate (iii) local heat

transfer coefficient at 180 mm from the leading edge of the plate. g

_.,qy,@ A r"eriical flat plate 500 mm high and maintained at 30 oC is exposed to saturated steam at

Watmospheric pressure. Calculate the following (i) the rate of heat transfer (ii) the condensate

gtrt:T rate per hour of the plate width for film condensation. Take properties of water at meanLI;fN'\

hmperature (p: 980.3 kg/m3, p:434x 10-6 kg/ms, h1s= 2257 kJ/kg, k = 0.664 W/m nC ) g

r-$'€xplain briefly film wise and drop wise gondensa!!91! g

t -*{Derive the expression fof rMrn for counter flow heat exchanger arrangement. g

.u-@n a certain double pipe heat'exchanger hot water flows at rateof 5000 kg/hr and gets cooledt.V "

av--- 7' from 95 oC to 65 oC. At the same time 50000 kg4n of cooling water at 30 oC enters the heat_.e*.i vvvrurS YY@r /F.' exchanger. The flow conditions are such that overall heat transfer coefficient remaill constant

at 2270 Wim2 K. Determine the heat transfer area required and the effectiveness, assuming

stream 4re in parallel flow. Assume for both the dtreams Cr: 4.2kJ/kg K. g

c' state Fick's law of diffusion. what are its limitations? Also define Sherwood and schimdt

nos. giving their physical significance. 4+4.

'-l"i t-l."-\

L/\:. )

,, AA\,/ \\

7r

./ cs;v-ru1

t'\0'1 t11 t:{^tt L

1

Code M808712

1

1,.

:i.i:l

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li

t:a

Time: Three hours Max" Marks 80Min" Marks 28

Note: ll|y- of HMT data and svam tAbbs boo! is permitted, All questions cany equal natl's. Atts.mPt

bnyfiDopartsfromeachquestion.Assumentitabbdataif"any,-4 alfyeoomposite wall of the furnace is made up with 120 mm of fire clay [k = 0.25(l+O'0dOOry Wlrn

V.) \ .Cl and 600 mm of red brick ft = 0.08 W/m "-Cl. The inside surface ,"lPtT*t" tt 1.Lt9."".

und.t"

J outside temperatur€ is 40 oC. Determine (i) the temperature at the layer interface and (ii) the heat loss

. for I m2 6f furnaee. ' -. ' 08

-br-€erive the expression for the temperature disfiibutionJrsrler ene dimensional steady state heat

08conduction for the cylindrical system

A cunent of 300 amperes passes through a stainless steel wire of 2.5 mm diameter and k:20 WJm oC'

The resistivity of the wire is 70xl0s f)m and the lgngth of the wire is 2m. If the wlre'is

submerged in a fluid maintained at 50 oC and convective heat transf:r boefficient at the wire surface

is 4000 y1r7# oC, calculate the steady state temperah.re at the center and the surface of wire. 08

Define fin effectiveness and fin efftcienc,y and explain under what conditions the fins are

H Ai'alantinum plate of 400 mm x 400 mm'x 4'mm size'at 20OoC is suddenly dipped into liquid\/'

oxyg.en at -183 oC. Detefinine the tlrc.r required ic."iiio piate to reach a terrrperature of -J0oC. Assunre

6:2a000 kJ/m2-h-"C, cp0.8 kJ/kg oCn and,p=l000 kg/trf. I " Yli 08.i:.. ,i4'

i'r;"gprtriong cylindrical bar ( k-17.4 Wm oC,c = 0,019m2/h) of radius 8o rlrr gornes out of oven at 830'C

" '' ,/ throughout and ii'cooled by quenching it in a large bath of40 oC coolant" The surface coefficient of

heat transfer between the bar surfaOe and the cootpnt is'180 Wm2 oC. Determiire (i) the time taken by

the shaft center to reach 120 "C (ii) the surface temperature of the shaft when its ienter temperature is' f - 'r-:', !20

.C (iiiftemperature gradient at the 9{sr.{e surface.aJ fbe F3l-ne.i[ql4-qJ of..tiinb:" 08

3 a. Explain Reynolds-Colburn analory. 08

B.Tech (Seventh Sem) Examination Nov-Dec 2008

Subiec* Heat and Mass TransferMechanical

b..{anr is to be heated from 15 oC to 65 oC as it flows through a pipe I.D. : 3 cm and length = 5 m.TheV: tube is eQuipped with an electric heater that provides uniform heating throughout the surface of the

tube. The outer surfaee is well insulated, so that in steady operation all the heat generated in the

heater is bansfened to the water in the tube. If the sy-stem is to provide hot water at a rate "f 2W

. determine the power rating of the resistance heater@so estim.glj:tle hl-".ltYtf*etemperatffiti"+"

pipe at the exit" \.J

t**

08

:!

I'1j

ii

/-.\ from the pipe by natural convection.t

I : *F*plain how heat exchangers can be ctassified

i / g#Explain briefly the various regimes of saturated pool boiling.

71 )

16 )Vo 6-m rong:"":t:i ofan a-cm diiameter horizontal hot water-pipe passes through a rarge room wirosefvmperature is 20 "C" If the outer surface temperature of the pipe is 70 'C, determine the heat ioss

08

08

08

-.' " c" A one-shell, two-tube pass heat-exchanger having 3000 thin wall brass tubes of 20 rnm diameter hasbeen installed in a steam power plant with a heat toad of 2.3 x IOs W. The steam condenses at 50 oC

and cooling watei enter the tubes at 20 oc at the rate of 3000 kg/s. calculut"ltlr" overall heat transfer

coefficient, the tube length per pass' and the rate of condensation of the steam. Take the heat transfercoeffiiient for condensation on the outer surfaces of the tubes at 1s500 wr"t& and the latent heat ofthe steam as,2380 klkg. Take properties of fluid as Cp :41g0 Jrkg-K; U - *;;;;;{;i; =0.6t3 Wm lq and Pr:5,83. .''.4:;::x1*x j*::m,:ff :H::H;:l;:***::T;l"i:;:#with respect to itself:08

b' Derive the expressisn for interchange factor for the radiation heat exehange between two infinitecylinder long concentric cylinders. -

;;08c' Air at I atm" and 25 oc" containing small quantities of iodine, flows with a velocity of 5.2f mls inside

a 3 cm diameter tube" Determine mass transfer coefficient for iodine transfer ; ; ";,

;;;;;theweaksurface"Assumethefollowingthermo:physicalpropertiesofair,

D = 0"82 x l0'5m2/s, y= 15.5 x l06rn?/s" 08it:4itilrj

5

A.i.c.T.ilB.Tech. (S1v1nth Sern.) [xarnination Dec, Jan.Subject: Heat and IVIass Transfer

Tirrre: Trrree rrours Mechanical Engineering'

Cirilc {i7'7\)ZZNI24fi7-AB

Max. Marks 100Min. Marks 35

',' Note: use of HMT data and steam tables book is pert*itted. AI! questiotrs esrry equal

.. ' nmrks' Altempt hny twa partsfrom each queslion, Assume suilable dala if atty.* '*' ' I a A furnace wall consists of 200 nrm layer of refractory bricks, 6 mm layer of steelq-ff:t pt"tt i1l:l a 100 mm layer of insulation uri"t u. The maxim*n

-t**p.rature of the wall/'r'/-<)\->'- is 1150"(l o'the furnacc sicle a'd thc

'ri'inr'm temperirture & 4ooc on the€-1)- .utcrttlt":'rl side of the rvall. An accurar.-"r,*rgy [:alri.cc oi,cr.iir* f1mace sliorvs riraLtlte ltcat loss l}om the wall is 400 w/'r'. lt is k'orvn u,u, tir*r* is a thin la1,er of airbetwcetr tlte layers of refractory bricl<s arrclstcel plate.'l"hrr.',,,t ,..,,,au"tivities l.or tlrerruee layers are r.52, 4s and 0.138 wl;;c r"rp".tir"i;"'F;,r;; (i) To horv manymillimelers of insblatiol biicf is the air tafer equivarent? what is ttr" temperature ofthe outer surface of the steel plate? ---J -

*:$",,,Hf'*ri*a:*;H.rtrr#H***ffik = (l + 0.001t) Wrn*dep

Z5;. Bg

i:*E

make calculatiotts for the average thermal r:onciuctjviiy, ilicniral resistrurce anc ireatloss frotu the wall' what would Ie thc tr*orro,ur" at-le0-g1g-<rista'ce from trre wall\j-, surface a1 800oC?

v"' ' \/1 c A steel-pipe (L:.J2wm-deg) of 1{ qr:n outer diamerer and ? nim. radial thiclaress'li*u camies dar"rratJd steam at rzqrJh r"*'i."n provided uffirsbestos insurarion- i*i*-i,' i"ik*il-witn-dg) to checTand nrinirnize ttie rate oisteam .onJ"rrsation. -fhe pipe is

.-'i.,J'*.;"..'*'ln::i irr surroundings at 2i ",q. raking uniiiengtq of pipe carcuiare (i) thickness of' :t ."- asbestos i^sulation for which the rate oisteam condensation i, .ru,-,.,L as that when thetli' pipe is uninsulated, (ii) mass flow rate of condensation rvhen the above insulati*n is!i providcd, and (iii) highest rate of cond,rnsation and the conespo'ding insulationthickness' Take surface conductanc. ; ;i;:;i;L ana .t.un -rio. Lr'-JlWrn2-dqg and500 Wim2_deg respedively hr at IZO.C:Zlllq irtlke.

--"' vrvv s,

:

. 2 a fhe pla'e wail A of thickness 5 cm and thernral conductivity g0 w/m-cieg ancl having'427;"rivolurnckic heat generation of 1.125 ry-id;;i'll'inruru,.d ori one side while the oiherAt- \i sicjc is in contact with surface of anotlier *tutt n. 't'h. wal! tl iiu, nolr*ot generir,,ion is'u/

nrade oi a material of thennal cond'ctivity-ioT wr*.,cleg a'd las a tirickness oi 2.5cm' The non-contact surface-of'rvall B is exposed,o u Joorin#"; at 25oc. {f thet:onve"lir"c l'reat trensfer coefficient bct*.een *olr g and tne nuii'i, roco Wrn2_deg,caisu' 'r it:r'leiature at the insulritecl surface ancl that at ths cooled surfacc of tiris

I

rr0

eillcuJiitd lcmpeiature at the insulateci surtiice aiiri tliai at the i:ucitc,, suriac,; *i.thisconipusite wall.

A curient of 3Oii arlperes passes through a stainless steei wire of 2.5 mrn ciiameterartd k = 20 wh'oc',"fhe rcsistivity of the wirc is 70 x r0's (-lnr a*cj ihe length of rl:er'ire is 2rr; lf thc r'vire is subnrergcci irr a f'lrricl ,rr,,i,,t'i'c,Jir1 5ilo(.urrd er'r,ceii'c Irr:ilt1r'rtsli:r cr'"'"lIicietti iit tltc rvire sirrl.cc is q0d0 w/;;il;:;'J;rcurarc tcr.pcrilrur.e iri r'cccntrc ard ;t tire sudace of wire.

2 c An"aiurninum plate [k = 160. W(ni"oC), p = 2790ke/m3,Co= 0.SS kJi(kg. .C)j ofthickness L = 3 cm and ar a unifonn t.n prrut,o;ii;:;;iib iJruacenly imnrersedat tinre t ='0 in a well=stirred fluic! nrairrtainccl at a_consrant te,-,,'pc:,irlure .j-,,,. -,25oc"ilie hcat t'iusfer c'osfficieut.tctrvecn thc: platc lnti thc flui<j is'ii ,= ;12{.r w/ 1r*2,o{:),IJt{crrrtirte tlle lirne requireci {br the ccntei plate tr-r ielich 50oc. *. ,,-),/ "ifup r,/3 a The temp€rature of air in a reservoir is measurc.f .y-ith the aid of a nrercury-in-glasst' il:etmometr"r placed into 1 steel protective well filled with oil. The ihermometersliows {he remperarure at the encr of the werl g4"c, H;;l;;g;;. ;h; *,"uuffiffi;' crior due to transfer of heat by conduciion along the protective wel"I if theteiuperaturt: at the base of tlie well is 40'c. The well is ri * ro,rg, iis thicknsss is1'5 mm anil thermal conductivity of well material is 55.g wim-ic. h ih*er transfer-V, . co-efficienr betrveen *"f *a ui4 =Z:"S Wl# "C.''<1,.,,94f

:FttI

il|,'t'

I

*tffi, mni thjck stainless sreer prate (q; ryoo kg/m3,.!:1g9 J/kg oc, k:55 \L(rn."c)isrisedtofi;rmtlrenosesett,onoflnissjle'itirei,ii''il:..rr,.--....

)\ of 3O.C \,\,/6en fhe *i.-ir^ Anrn-." .r-_. r- , " irlri*ilii at a urllii;tm lenipgraiure- ^J \ of 30"c' when thc missile enters the rlenscr r,rj*r* oi'rhe !,,*-rpi,"l"l|;'i]#iil;t );;!x"Jg,[: .Tg::"":#i:l:i1*:r:4 f- nose region atralns the varui2150"C; the surface cc'avective heat tra.rsfet ro*rf,"i*ntls estimated as 3395 ,r,il;oC' If the tnaximum metsl te:nperature is not to ***e.c--iffi.e't];.#tJ. Cltntixinrunr 1;ernrissible time in tirese sun"oundi*gs iii; insirie surlace tempeiiltureuniier tiie-qe eon,J itions.

/ " Irjlrd ilr': e:l ;rressictl fi'tr Lhe lroun<j:lrv layc:r thir:knc;;s b ir,:r i; iil:t:lrr. vr:l.ciii 1,r<;iii,:,f tl \.rL'/ U

. A

li:i ijrc i:riiriinl iio*l ovr:r liai piutc:.

-'rLl '4 a A rertical plate is rurder free convection with ambieni still air at 20oc. If the piate is'$f,^q heated from one side and maintained at goo€, \&'o;koJ^ii; j.car heat rransferY-'f ' coefficient at 20 cm fram"thelorvcr.;;-. wtnt wcui<i be the',rrei.age rialue cf\cte- convective coef.ficient over the 20 cm frn![ri

, *yh oj'?l 2 bar ard aOt is heateci as it flows through a 30 mm dian eter rube at a

.#^Ii';,'iy,i:,'1,ft ;s:h;iff H1?:t*1r*x;r;iiffi f #t#5.:Tf*lqF"cahulare rr,. ,;;;;#'i"'u-it tenrpcrarure oo.. o,," m*rer lengrh if tube

:

F.{

i.i.

' 't).f

i i :l-.,t'li\:+

' z .:.!;:

riFf

:;'

,.i!..11.

,.ji::

,:il€

..sril

d':'r;il::-'i,:i:]

l

!

ti'll

a\,l

i

l

ij

;

;- I l-i

4 c A vertical plate 350 mm high and 420 mm wide, at 40oC, is exposed to-galuated-

ste&m at 1 atm. calculate the following: (i) the film thickness at the bottorir of the

o'[i",(iildt-*imum velocity at the 6ouo- of the Pfate; (iii) the total heat flux to

the plate. nrr*" "upour

dgnsliy is small compared to that of the condensate.

,^.r- ) tt(l ct 9l):\l: (\'u*'3;VTwo difhrse ,*flE.r, ir*lft iiqL ot area At and 1 large.disk of ar.ea ez tr? t^t3l*l

to each other and di;ilt;;porrd, i.e., a line joining their centres is normal to' both

\he surfaces. The ;;;-'.1tsi-h; ; r.udiu, R fo{ is-located at a fight,l 3?*-11:smaller disk. Obtai;; .;;t"ssion for the configuratpypor of small disk with

respect to the large disk. Rruldct.LrZa '

\lrpff""ve the expression for LMTD for a counter flow heat exchanger'

\ \_ 7 r,,r, 4"\

ffi", (sp heat = 4 kJlkg K) enters a cross flow exchanger (both fluids unmixed) at

rs'c.and nows "t

tl. r# ItlS. Il l::l'^uiite,:-! tl&g{]"+"fig:t:T,?::-:fr \/^ i0 ;il;;; ;i"i"i tem-p"ratG of 120'C. For an oveiqll heat transfer coefficient

) '^(') ;;0 ffi;]-i;;-K *A * "i"t*g"t sur-ibce area of 249r*, determine the total heat

(,1, \t-' "*r^G-*t-ff"".i"t

t"*pri"tite of air. gow these results would be affected if a 1-

Y' ro lone,slieiG;r arrd ro ,itu" p*rttteat eichanger is emnJolll?, ?fq -, I S

T

--.-:=/

B.Tech (seventh Seni) Exarninatiorl l\q}r'.[}i:{',Z.ix}t{

Subfee* F{eat and k[ass TransferMechanieal

Time:Three howrs Max. Marks 80Min. Marks 28

Note: LIse of HMT data and stenm tables book is permitted. AII questions cnrry equal marks, Attempt

any two parts from eaeh question, Assume suitahle data if any"

,-ptTnecomposite wall of the furnace is made up with 120 mm of fire clay [k = 0.25(1+0.000091) WmoCl and 600 mm of red brick [k= 0.08 W/m oC]. ThE inside surface temperature is 1250oC andthe

outside temperature is 40 uC. Determine (i) the temperature at the layer interface and (ii) the heat loss

CSV U

for I m2 of furnace.

b. Derive the expression for the temperature distribution under one dimensional

lFr"1 r' 1 u)w1 r-7)' .,) .)

C*de &{Htl$"r}?

08

steady state heat

conduction for thecylindrical system 08

\ .-g-- A current of 300 amperes passes through a stainless steel wire of 2.5 mm diameter and k=20 W/m oC.

^ K.<*

@ The resistivity of the wire is 70x10'8 Om and the length of the wire is 2m. I,f the wire is

*i j submerged in a fluid maintained at 50 oC and convective heat transfer coefficient at the wire surface

is 4000 W/m2 oC, calculate the steady state temperature at the center and the surface of wire" 08

2 a. (i) Define fin effectiveness and fin efficiency and explain under what conditions the fins are

effective.

,n:.kb_. An aluminum plate of 400 mm x 400 mm x 4 mm size at 200 'C is suddenly dipped into liquid

?*ff*Y*ygen at -183 "C. Determine the time required for the plate to reach a temperature of -70"C. Assume

h=20000 kl/m2-h-oc, Cp=O.g kJ/kg oC, and p=300p:-r+ 0g

,r"\b LA long cylindrical bar (k=17.4 W/m oC,u : 0.019m?tft-of radius 80 mm comes out of oven ar 830 oC

po\?o' throughout and is cooled by quenching it in a large bath of 40 oC coolant, The surface coefficient of

heat transfer between the bar surface and the coolant is 180 W/m2 oC. Determine (i) the time taken by

the shaft center to reach 120 "C (ii) the surface temperature of the shaft when its center temperature is

120 'C (iii) temperature gradient at the outside surface at the same instant of time. 08

3 a. Explain Reynolds-Colburn anatogy. 08

b. Water is to be heated from 15 oC to 65 oC as it flows through a pipe I.D. : 3 cm and length = 5 m.l'he

tub'e is equipped with an electric heater that provides uniform heating throughout the surface of the

tube. The outer surface is well insulated, so that in steady operation all the heat generated in the

heater is ffansferred to the water in the tube. If the system is to provide hot water at a rate of lA Umin,

determine the power rating of the resistance heater. Alsc estimatE the inner surface temperature of the

r)-- fl-l\tY- tr;1------

pipe at the exit. 08

e " A 5-m long seetior: cf an 8-e m qiiaill,*ter irorizontai hct ""vater-pipe p;).ss€s tiir*ugi, a iirrge l"<;r:r:r iv;r*:s*

iemper*tura is 20 oC. If the outer surface tofirperat$re of the pipe is ?{i oC, deterrnine ti:e !:*at l*ss

u$

08

,, . b. E-x"plain briefly the various regimes of saturated pool boiling.f-*S 0g1i"b x*4'

*"yAreO one-shell, two-tube pass heat-exchanger having 3000 thin wall brass tubes of 20 mm cliameter has

'tdl" been installed in a steam power plant with a heat load of 2.3 x 108 W. The steam condenses at 50 oC

4'^'b:* aand cooling water enter the tubes at 20 oC at the rate of 3000 kg/s. Calculate the overall heat transfer

9ii:E.neffioient, the tube length per pass, and the rate of condensation sf the steam. Take the heat transferlO?Y. coefficient for condensation on the outer surfaces of the tubes at 15500 Wm2K and the latent heat ofthe steam as 2380 kJ/kg" Take properties of fluid as Cp:4180 J/kg-K, p: 855 x 10-6 Nslm2, p:0.613 Wm k, and Pr = 5.83. 08

5 a. Consider a thin hollow cylinder 6 sm diameter and l0 cm length. If the radiant shape factor of the

circular surface is 0.712, make calculations forthe shape factor of the curved surface of the cylinder

with respect to itself. 0g

b. Derive the expression for interchange factor for the radiation heat exchange between two infinite

cylinder long concentric cylinders " -CY-' 08

c. Air at I atm. and 25 oC, containing small quantities of iodine, flows with a velocity of 5.25 m/s inside

a 3 cm diameter tube. Determine mass transfer coefficient for iodine transfer from the air stream to

ffi.k, weak surf'ace. Assume the following thermo-physical properties of air,

D = 0.82 x 10'5 m2ls, v = 15.5 x 10-6-m2/s.

frorn the pipe 'ny naiurai conveeticn. .,r-.o,

4 a" Expiain horv heat exchangers *artbe classifiedp,/ -1V- ,.;1

08

M F-0 Lt ,2 1

l). I r. iScve, rtlr Scrn) Uxaur inatior r .,, .,fl.t.e.:i.,1in200 g_09I .A,I.C.T,E,

Subject: I{eat nntl M:rss-'l:1'un.tnr.l\,lecharr icn I

I'inre : 'I lrrct' horrr.s Max. IVlarksMitr. Mrrlks

U.se o/ HNI'I'd(lrt; urtcl .vrestn tables book i,r perrnittecl. All questirtrts c(r,r.yAitempt (rn)' rwct purrs f'rut ettch questio,. A,ssume suitabre data .i,f any.

'Lrt&ii

!:l;ililt,1

,"1

I00l5

eclttol nrarks

Dcrivs '-'xFrc isiorrs tq'rr' {e'rpc'alurc distributiorr, rrnc{cr orre cJi

r..li<J r r c i i r r r.,,,,., .,,.,,,ffi ,.,k3.i,{, €,9rfrG,,'

@*,"dtip,.M'

irest)rrros lC8 ''L'; 'l'ake 1t - '-;ij0{) l<g/rrr3, g =

v\ .iill "(

Find the tinre at rvhich the slab ternper.ature

0.38 l<J/kg."C. k =, 370 W41,,C., anrl lr : 90

l0

t{)

iorral stearly state lic.ril

IU

iire plare

(l\iDt ? tli

pei'nretel

\\/./nr "C'. y

I tltenstr ":iiit. \vir_it ;.ilo cvlln(rel. sYSleill.

-

'-L'- iUAu'all tr{'ltttttrtc,':isr',,arieof insitjelayerot"silicabrick(k'.i./'vyirrr,,{.) l2.,Jclnthic:k

f \ (6 \rr rrr(rtirruirr'e (,llt,l\

t-9',\--treil nre'/11i1 i'(l ir'l(i ll0oCrespectively.(i)Defelrnine.thearr-rounl o{.hciltl'sspcrlirltr,re\,.:',,r,,,,,,,.,.i'rl,-r.,.,.,,.,.,.,,,1r..-. ,i.1rrctcr. r;i'llie iirr.nirt _ rvitll/,\' l -' I

t{:V [ /' l() ttiirt cr:iblc tvir; is kr be laid in the atrrrosplrere of 2c "c u,ith our siclc hear trarrsl

t0

eri':' I

'[+,1

J#'/ !'r,

u /(,,,}

.j

llt ttc!t'.'.,4a7.,+ )... lt : I : .. ... .' ,......\rj/

: i :'l: ';.'i"'i." 'l '1.: l"') r'111r''1,'^'-: .l',r 1( r'rrr tlri,.t, .r,....! rrlr,trr (l< - ,ii', W,/t,,,,(., IItiivitrg ttltiftrrnt itei:t gelrcrlatiori 30 x 106 W/r,rr, are lg0 oC arrci 120,'C, N*gli:;;.iug tlecncl el'fects, delcrurine tlre foIlorvirrg:

{i.1 tlre tcrnpeirture disrritrution across the

ttraxirrrrutt tenipcr.:rtrrr.c ;lr tlie rrali.

,, v ,r r\/ uw r(llll ilr illg iil.illc)spllefe Ol l{-, .1. 11r1["r'r :.-

c(inllldiclrlt li.' w/rri/ "c]. '["lle sirlllce tcrrrllerature of.cable is likei.,,likei.,, to tre (,i ''C dtre [o hcrrl,t.qcrr';:i\iiii'rrr rvitrrin. witl the rublrer ilrsrrlation, k:0.]5.! wlnr"c, h,<; cirqctrv.,? rf.ycs hc,iv

plate, (ii) the value anJ 1hc, positiorr of

r0hivq'ihe terriper.iitr,rre clisrribirtion lbr a firr t050 r 5r; c!r'r dopi)er. siab 6.25 rr,nr thick is at a uuifornr tentperatur.e of 300 ,,C

sucklenlyils surilc- trrinperatlric Ior,vcreC to 36 .C.

\'' "1'rr\ "i'is r'jrrrrirlr rrJ,'jl,-'rt rrclrt',r flat rrrare it i2t)',(';;r,r ver6ciiv r.r.r'( r,,/,;is I lri; to:lg ltiitl l {) rl , v,'iilr:. Detclnrine tlrc aircr.age liear lrelsli, c,e{l.rc:itlrrllerrgtl: c,l'liic pli,lc. ,\lsu ilnd the l.al.e ol.,lreat tr.arrsfer lretrveetr the pla{.e ancl ailrvictl.lr'r'trre platc 'i.rrce prnp.rti.r.,inirut B0 ocr t. t,* ir.-- o.rrv6. rr - 0 0.1()35- 2. 107 \ l0-i r1.,'1 ,...

I r,ui;rirr li.c. i, .!<l.s-Coibrrr.rr ,rr:.iiog;,.

't1

.*'-

- .1

3c. Watrrr crrter's a l.5c,n dit. anil 3rn long tube n,ith a veh:city,of 1 r'n/s . ''l'he,ttrlre wall is

lrnirirrlrrirrcrl ll! l ooltstallt lslnl)oltturu ol'90 oC Culcttltto tltt" ilie lieat triittsl'er ooeil'tcicnt

ltrtl llrcr trltul urntlurrt ol lrcirl tt'irrtslol if the exit wfitfir tettrpelutttt'o irl 64 "C l0

4 a. A vertical cylinder 1.5 m hilh and 180 mm ih tlihmeter is maintained at 100 "C in an\u

atrnosplrere ol'20 oC. Calculate l,eattibss by natirlal convection from the surface of ttre

\ - t:ylincler. Assunre prrrpcrties ol'air at mean temperatur'e as, p' 1.06 kg/tni, k = 0.01042

r0* nu.V kJ/rnh "C, v : l$.Ql x l0'6 ttr2/s, Cp : 1.004 kJikgoC

H$ l':Ha :iiffi:l*i,,ffiil ;;f.\ - ---1.,--.*L,.r. --4 fD '-1 ' :-----'----T - t 0,tffi\ . .l c. Write a slrt'rrt note on pool boiling ancdforced coirvection boitirp) l0

J-) ,\q-' .qsrcasp'ss=* : hgat\a 2(\ M,\n oil ctioler.for a luhrication system lias to cool 1000 kg/hr of oil having a specifir

., ? ' ' ,'V of,2090 J/lig"C frorn 80oC to,l0"C by 1000 kg/hr of watet'erttcrirrg at 30 "C. Deternritte

_-l ..,' _ n ,/ lhe hcat oxchaltger surlace area for counter flow arranget.ueut i1'the overall heat transfer

ir \L 'r,i..\--:'*, Z 5 , t:oc['[ic:it:tt1 is 24 W/rrr2 "(]. 10

' 'l) )';t4" 1).,]i.r" i!,r- ..x.reqsirrrr {:r-rr'l.MT'l) l'rrr the nalallel flow lreat exchatreer. I tO

l)etennine {he geometrical.factor o1'a bead-shaped. thennocouple to tire inside wall of a

circular cluct. State the assutnptions mads ,-- ' R*Ulj&f+5 ' l0

{

A

_!

ll. .-[i.:.c (. (Ser'errrtlr Scrn) Il,xamitration, Ap'rl, n,l,,,,.r, ,.;llt'u (")"7 V-O2'''

A.l.c.I"l_. / f t'

.Sul:ject: Heat and Mass lf,ransfer

Mechanical

NIotc:

'finre: Three Irours

LIse of ILMT r.ItttrL rtnd :;tantrr

nmrlcs, Attctttpt nttrl l.trtrt pnrtsil)c.finc thc follow ir ri1:

Ma;r. IVlarl<s 100

Itt|tlt:s hook is pernritted. ,+tt q,o}|l,',;'r*j;,:,\i) rrti\r,f:r'o n r etc'l t q t.r t: s l io r r . l\ssr.t rt u: stri. l,nb l c d n trr i,f, arr.r1,

r't.- z-'b(i) T'heunal con(lucti\/i.frr' 11i; 't'her:n.ral dif fusivity (iii) Iiteacil, statec<rrrductio. cnrl (ir') Tlti^sierrt stater collLrLrcti() Lt.zy) 10

llr A stcittrl Lrrtilcr ltu'rrace is utatle oI a la;,111.91 fircclay .12.5 r;rp thi([,, irrrti triayer of recl brick 50 crn thicl<. Ii ttre wall ternp",,urrr," insicJe tlrr: boiierfurnace is 1-100 oC ancl that on thr: ssi1si.1e is 50,,C.1.. defr:r.'rirrc lhr: i11l)ou.tctf heilt loss pel sclLlarc tltr:tct.o1,the f,ru.nircc ur;rll. (kriruclay = 0"S3:t \zV/ryrl(,i(r,r'clbrick:9.71,\r/nri().

10Derive the g,ener:al tiii-ee-tlimensional four:ier,]reaL cr-rncluci-irxr etlu;rlio' in(-'a r: fesiar I c,:r-,; ilin:r fss

1(.,2'a' '\ platre r't'all 10 clir tlrick qcneLa{cr; lrr..at at tirt: r"ale of 4xl0a w/r:1;r v\,[.rerlatl tllcclric c-'rtt'rctrt is PirrisL'([ throurg,lr jt,'t'J-re convective hbal tlansfcr'tiotti[:i.1",,, lrc.t\r,rrt.rr tlr,,rt,irll .rucl Ilrcl arinl_rir:nt air is lj() W/rp:l<,. L)ci_gr.rrriuc:(i) I'.c srrr'[ar:c t.r.p.r'aIrirrr (ii) rr*r r'axirn'n-r t.r1r1rer.atr'.r.] irr r.Jr,r in,ar.Assutne ttic arlrbicLlt air' [ernpcratulc to bc 2u (,C

^nc[ the t,t:r.'ral

(\)lr(lLrctivity ol tht: rvall nr.rter:iaj to b-c .15 W/nrl(.

:,":l"terlr1rer:atur:ec1istr'ibriWTirrrt,itlrirrstr1atecit'lpr'A 40 x 210 crn slab 5 mnr trrick at .i thilo,:ur ternper-atur.e or Z.s(),)C strr:{cre,nrirIras iis l;ttrlai:c Icntpet'tttttrc lowerc'cl lo 30 uc. Fintl lhc tilrlr: at *.i,i,-t-, ri,",.ilirL) {e'tpei..ture be.o',res 90 ,,C; p=9000kg/nr3, f= 0.3g k J / kg,I{z\i'at 20 "c is r'[ort'i.g al..g a i'reaterl fiat pratc at 134 ,,C a{:. r,c6i,iivnr/s. Thc platc is 2 rrr Iorrl; anrl j.5 rn lvicic. [),..tc1.r.,i,.r. ih" t,r,,rl

J {)

10

10

of3

heai

3a.

#lri

I

:

i

i

,l

,i,- lII

Ii

3c.

4a.

\\n'st''t,&

t,,-. *i,:]n.. u'.,b.q&t,

\

tranSfer: ce:efficie't at X:0.4, anLi tile lteat 1rattSJ'elt'et-1"'['t]irl]loiltr': f irr;i 4l)1:

0f tlrt: pltrtt'.

Define tlre iollclrl,ing givin$ tlreir;igrnificaLrct-: as t'egarc{$ to clottvt'lctirrel ltt'r

transfer. (i) Rey^oltls Nr:rnber (ii) N*sselt Nttrriber (iii) llra'ti lrlttt*ber I

Water elter.s a 1.5 cm clia. alci 3nr igng ttrbe rvitlr a Velocit,l' of 1 rn/s ' T'

tube urall is rnaintaiuetl at a coulitarrt ieltr|craf ttl''.' ttf 90 o(-l i-lalcr"rtirte t

ther ircat Llatisfsr C.,eIi'icicrtt;ttrcj'iiiEr Ltrlai;it'LtOttt-tt r"i i"tctttl tl'artsl.ell'er-i lt t

exit \l/ater tenrpertlLttrc is (r4 u(l

A 30 tnr k.rlrg gSlilss ptalt: is hurri), \,or:t.ically irr iLrt: ttit: al )-'/ "cl vrlritc

tenrperatr.ile is rnaintainect at 77o(-l.Ciilcrrlate tl"rtl bounclal'y li'iyel il-rir:J<n'

at tl.rc tr.ailin14 cc{gc oI thcr plaie. ll tLrt: sinrilat: Plale isr lrla':r:rl irr ihe r'r'i

tunncl anct air is blown orrt:r ii a'rt a velocitl'oI lt nr/s esl'iitral"t:

boutrclarl' 1a1'sr tl'rickness at its; tlailing ccl5lt':'

Ail at I atrn irntl 20' lsfs over il tt:ltf icllu'th 3"'l() rrrn'r irrt'-i l'viclth =

nrrl fttll of \'\'att--l' velocitv ,rl ?.8 nr/s. '1.'hc Far'f ial prcsr:illlrJ t>i i'vi

presenr in tlrc li', iL91l6j ll:l- tu

'.1 ::_ ",1'l,l:_:aitr:jll]1";l]l'; *lr''(a. sr it rr;r'r'' ir

,,C, crrlctt ltrLt', thc t-'r'erPotettiolt t:ale itl r'r'rrlet"

Wr.jta a Shot'l.lottl Otl l'ilut'.r'ititl atrtI tir'lP wiSC: tlt"'tl'lellSilti()11

ln ar ctor,rblc.pilre ltctrt cxclrallgcl', 10000 l<g/hr'''.rt' ;trt oil lrar\iilr8';t lrlrtl'

hcal ol 2()'15 l/l<g.l( is trot,lod Ir'rlrtt 8()''C lo :()"(' b1'fl0t)i) l'r1/lrl oi w

Ctrtcr.irrrl irl ,15,'C. L)ctr.:lltriLrC [lrt'licAl '.::'t:lrtrl]lj('l';lt'"'t [t't ;rll rr!r)l'rll

tlansrfcr cocf f it'icnt of 300 \'!/rl2'l'''

L)eri.,c {lrc expr:ession. tgl t:[lcctivr-'rt.tlss Ior tll,,: l:ar"rlltll llo!v hL)fl1{))({'lli'r

a

t

?mrr:acliation shape factor of thc circr-tlar sltllace oI a tlrin h<-rllc;'r" r:yli

l:rc iof '10 cnr cliatnetel ancl 10 crn.lengtir is 0.17]fr' Wlrilt is tlie ciiapr:ts

l-he cur.r,et{ surface of the c\,linder itrith lespect to if-st'li'l

il t

lll

5lr

lj r:

' Code 06?022 -.S

B.E. (Seventh sern) Examination AppMay 2007. A.t.c.T,E.

Subject: [-Icat ar.rd lilaes 'l'ransfcr

biH

F

':I

i.

'fiure: Th.'cc hoursMechanical

Mux. Marks 100Min. Marks 35

Notc: Usc of [lM'I' datu antl steuur tables book is ;:enrrittecl. AII questiols curr;, equaltuolks. Attetllpt.olly two Pa:is liom each questiJn. Assume suitable data if my.

Deri.etnefotloning: At'> ''eQ pcrp tQ ; {)\^

;ffinermat con,lJctivit y

l'firrrr',',ot cilffusi:vity fi st aay stare

' concrucrion' and fipTransicirt

sti^;e co^ductio^, J F), Ac(,L{. .r0

.,. IA steanr boiler fuuracc is nrnclc of n layr:r. of fireclay 1.2.5 cm ttrlck and aIayer oI recl brick's0 cnr thick. If the wall temperahrre inside the boiler(ttrtrncc is 1100 aC anc{ that on the outsidc is 50 t€, tleterrnilr: the alrountof heat loss per scluar.e rneter of the frrrnace wall. (k1xscluy = 0.533 iV/rnK,

la.

1b.

*Sitit,-.l1l'{l I ' i:.

ii:r .

i^,

\"

@

krcrtbrick = 0.7 W/ytK) L0\(\o'\ \ \ ,.\iJrr;}{ Wllat is critical radius of insulation on small wire or pipe? Iixplain the

/ phyiicar significance and derive trre expression.for trrrr sanr€. 'G,ir; .,1.,

Aplane wall !J crlr thick generateo heat'at dre rate o!ar10r r,^,r/iiir 1u1,ur.,

nn eiectric currelrt is passer.l through it. 'r'he'conve:tive heat tranefercoefficier"rt betwee^ the wall and. the anrbrent airjis s0 w /m2lr. Deter:nine:(i) The surface te'rPeratur:e (ii) the

"ro*rror- temperi ture i. thr: wall.Assu.re the ambient air ternperature to be 20 oc e ncl the tjrermalconductivity of the wall mater.ial to be 1.b W/rnK.

Iu an experitnent to deternrine the thermal concluctivity or long solicl 2.5

:ill -.lilr-"!:lt-'-9:.iF .9Tg i'- p].usg{,iulr- {g'lros9--vill1.l$:81 p.1ririeil?f-1t..projecting into the room air at ?? oC, Afterlsteariy conditionr pr.evail tfietempelatules at the two points, 10 cnr apart are found to be 11J oc anrl gS

oC respectively. The convective heai tralsfer coelficient betwe:n,the rocl ,

surface ancl the ambient air is 2g w/mzl(. I)etermine the concl rcti'ity ofthe rod rnaterial.

10

10

I..g i^ thg.elirrccti.^ of flbwh^gl 1 rn wiclc.at-35 rn/s. Detern:i.'heat

l0

rTO

Dcrive the tcnrperature cristriblriojr{+itq$Xed rreat capaciry r^irrysis-

Aii at 20 "c flows ovcl a rectangulnr. .o,.rr*ir.,"r, with top surface 7s0 rnrn

tlansler frorn the top sur..face maintained at O0 "C.

| ;, ..o

I

l,t.3 b. 'water at 25 oC flows through the tube of 50 rnm diameter. Determine the

Ilow rate that will result the lteynolds number of 1600, 'Ihe tube Is

provided witl'r a nichronre-heating element on its surface and receives the

constaut heat (lux oi 800 W/m u(:tho tube, Determinc thc nvcrngu lrcat

transfer coefficient between the water and th€ tube wnll, assunre fi.rlly

.,h,:vr:ioPqtl r:rtntlll,ionu, Alntl r.lctr:urt1ln,. tlrtt leirgth of tlfe tubo fpf ttro bulk'^ temperatule o"[ water to rise fronr.25,oC t<j 50 oC.

3 c. Calculate the coeflicient of hcot traus(el by'frca convcctlort betwccn tho

horizontal wire ancl air at 25 oC. The surface oI wire is nt 95 oC ancl its

c{iameter is 2.5 rnm. Also finct itd rnnxiururn admissible current intensity if

10

the resistance of the wire is 6 ohm/rn.t

4 a. Dry saturated steam at a pressure ot 2,45 bal condenses on the surface of a

vertir:al tdbo of height 1 m. I'he tube surface is kept at7!7 oC. Estimate the

thickness of the condensate filur ancl the local heat transfer coefficient at a

distance 0.2nifrorn the upper end of the tube. l0

'10

('l

ir

10

-'{c_

-. . !

l;)

iill

tlll

ii,rf

tI:iri

-'ttu

ft

iI

1l

I

iI!.

f\i,&

F

If

II

I

t

I

I

ffi:r.1il] $l,g{.yllS_t yitll a vel6g{$,pf z.g rn/s. The partial prebsure cif wa'tUiii'i.'l

l)resctlt irr the air is .0068 bar. If the tcrnperatrrre of tlre water surfa,ce,is 15

10

- il- ,./

ti} fr'o*ive the e.xpression for LMTD in the case of parallel flora, hcar

C !," , { exchangers, State the assumptions made. l0

a;$,Vind' equivalent emissivitl.fol the radiant heat exchange berween infinitet Lrb " ,t'" 'ro,-,g cdncenb.ic.yrir-,.re*ff) [c.Cli*kt,n , r0

\t .,

{*i'..r" /

A counter flow heat exch;rnger is employec{ to cool 0.55 kg/s (Cp = Z.eS

^/ \t'" kl/kg'c) oftil fronr 115 oC to 40 oC bi, use of water. The ir.rlet and outlet

. temperatures r:f cooling water are 15 uc and z5 oc, respectively, Theoverall heat transfer coefficient is expcctecl to.,be 145p 14r/nrz nC. UsilgNTU rnethod, calculate the foliowing:

. (i) 1'hc tnass Ilow rate of water (ii) the ef(ectivenees oI tl're heat exchi,pger;l,iii

i\'1

'lt

){D {1:E11 un , airrt 20 "c, fl"*$ffi"*tray length 320imnr anJf wic{tir -

fzf,

.C, calculate tlre evapo::ation rate of water. ,

('.{". #( o",,,,u tr," ro'o*i;; ;;;i tr *i e*?,,f;s*v

^

(i) Intensity of radiariin (ii) La,rbert,s cosini lawl M

(iii) the surface area required, l0

Nqv^'Dec'

B.E. (Seventh Sem) Ex'amination 2006

A,I,C.T'8,Subiect: lleat'and IVIass Transfer---' Mechanioal'En08''

Code'067022 M

Max. Ma*s 100

Min. Murks 35'fime:'I'hree bourc-4.r*

i..','' Ltc,')i ,,' .'

ll of b .ru.to, i, made up of-aq iqfrllVcr of flro brlok ( k - 0'85 WnrK)

covered with a rrv", "r""ir"tioo C: ;i; wAttKt' 1ry reactor operates at a temperaiurc

of a 1600K*hil'Jil,eambien1,.*f"rl*it'i;;5'K i;il;i;ttt"tttitltt"ssof fircbnck

and i'sulation, *t i"t giues mioim,lii;;;; il: AG" work out the hsat loss presurung

that the inbulating material has a rnoi*o* tumpqanry "r r+isr' r{m: calculated heat

,;, ross were on*"{tuble, wourd th, ;:;iil; ##,hJayer of insulation'be a satisfactorY

Notc: U,sc of I'IMT dobbook ie pormittod' Ali quoutiono' carry equal marks' Attempt any

two parts tom eactr'[l?ffi' h!;ttii"n 4 thcro is no choico'

solution.? t .,i_.-.

i b. (i) w5rte .th-e mathematical t{Hlt6

;,*-i#ffi;fi:T[T*H"YlY':"j?&il;"#fr 'ru *d dissipated uv ."*"rtion to* ttr" bo*6uw strrface at r = b into a medium at' zero

ternperature with -;*;;';; "o"intient r''f I 5

(ii)Definethemralconductivrty.Consideranalloy.oftwometals.whosethermalconduotivities kr and kz.

-Wiil t*, tt'"*ii"":oit^'i*ti'"itlt" alloy br: iess than ki' Ereat;r

,ir* 5, or bstween kr and ur. a= sfin

il#:H[i:.ri#f#Ti,?'1r3:iil*Ht-'Ut;l#":#'*generated *a ,*dJ" il;;;*u orzo' df-ir^rnti"io4od for ttto riut,,. Thie cobls is raid

in the ,r,uiroruorrrl;;;id u t"*pur.trli'iOttc *itrtu totur "oefficient

associated with

conveotion *o ,"ii"ii";;rtd" ,t-iiru *a,*nironcreut is npprox' 8 wmzK'

calculate *" *"Ji ;;;;t.J u"iio.i, -*o

tttu oonespondingr- incroase in heat

dissipation d* ,JL;i#b* n" -di"G f*;. t" r*uitt oattving capaoitv "t T;

;;iJii;"'sible to do so'

- I 1'148 wmK) with both of the

2. a. Consider a l'2 m slab of fo';red goncrelg ( k-:-.

surfaces muintuioli"i'z,i*ri. ;*;.itr ;,rq"_g:_*urg" it releascd at the rate of 80

W/m3. Presuming that the temperaturuYdo" not vary *iih ti^"' work out the rnan'imum

reinperarure or ,inrrrtr.t what #il;"'hi;iloi or conqete can be- porued witbout

causing the temperature to exc..a gs.i'tc;;;t.d *y *httu in thu slab' ? t0

710

$ Hi;;#i.,i$ 3\lil :s

'/'r'

l'F

0b l(>{

z-1 ; (t=c. a 5 cm thick iron plate I k = 60 W/*.

oC, +,i0 ilkg.0C, p = 7850 kg/*', and q = 1.6 xl0'5 n2ls] is initialli iit Tr = 225 0C. Sudclenly, both the surfaces are exposed at anambient temperature of 25 0C heat transf-er coefficient h : 500 Wm2.0t). ialculate thecenterlinc temperature at t-2 min. after the start of cooling. Calculate th(: temporaturo utthf,di:pth 1.0 crn from' the surlbcc aI t=2 rnin. after the start of cooling. Calculate the

l0

t0,-, -

.j energy- removed froln the plate per square meter during this time..

3 a. DcriVc thc rclationship bctwccn fluid lriction and heat transfer for lar.ninar flow overflat plate. State the assumptipns luade. 10

I f 12 m/s' the3 b. In a straight tube of 60 mm diur^eter, ryater is.flowing at a velocitl' o

tube surface temperature is maintained at 70 uC and the flowing water is heated from the

, inlet temperature of 15 0C to an outlet temperaturs of 45 0C. Cal-culate the tollowing:' (i) the heat transfer coefficient from the tube surface to water(ii) the heat transfened (iii) the length of the tube.

,. -/., - .. i;- /ryn Tr t-t* .;;fuerive-the expressiort ior LMTD in the case of counter flow heat exchangers. State

,.,i T Vfi+ usurnptions made, i l0

rate Q. 10

( '.-^/.": ; '\ /g-. r..

] l,P. o/'A cross flow heat exchanger wirh a flow aJrangement such that both fluid arefr:rnixeC and having a heat transfer area A = 8.4 mz is to heat air with w&ter. Air enters atl" a temperature of lfoC and mass flow rats of 2.0 kg/s while *uto rnirrc at a temperatureof 90 0C and mass flow rate of .25 kg/s. the o'*,eriil heat transfer coefficient is U = 250w/m2.0c. calculate the exii iemperatuies of crr and-watei;;.ii;;il;i;il;;, ir*riri

l0, SX,f

3 c. consider a square plate 0.5-m by 0"5 m with one surface insulated an.d other surfacemaintained at a uriform tefi-perature of T* = 385 K which is placed in quiescent dir at

r.,1, atmospheric pressure and T-:315 K Caloulate the average heat transfer coeffrcient forI " free convection for the following tbree orientatiors ofthe hot surface:

(i) the plate is horizontal, and the hor. surface faces up. (ir)'the plate is vertical. (iii) the

, .' 4 a,, Write short ncte$ ou (i) fllm wise coridensation (ii) Physical mechanism of boiling

-,' ;6':, .Wfo"'""1J.;..boundaryraver l;'. -/ ".

;-'-.,' ." | :..,1r

ii

.,']

t,

l'lli ti'' l[li, 'ri'r it .

' ifh:llii

wl

}L.g

. t, \ J 6s

6?

xtrI1

I

Heat Transfer Test -1 7th Sem Mech.

lhves-

28-08-09

b*L'^.n U^t) **-g-tl;'r, t{i4' a*r-/* 't e-

FN , J-

b J t-rfi u*. I L- I

'3J't, .l"u 'F-x vv'-'t lrr u-tr "uj"ir^P*v:v:"ts*-l!*-;lA4- /./;fr *^u ,{o-6, farn a aaoll

,5-{an^*.r-'? '

- r,,!j" rclni*Ki'2rr1 : 1l.€l rcf ^i"t k

_ n .il e 1r,_: 1f..", if,'1ft :, . /',, r ? ,ul ! 'y,n lq

,;;#;"AlI

I

'-i: L L ;rl tt.ytr.^r.,4 o-g{ iA.z.l: {:, ,tr;.^r.' * }n}'t- Q' t-,.".,",

-.t"*t- e*oyJi *,t i",ry4 "*,W :aga-::

I t f a t t ]* -{.Ja tu.,'|-txt-a- liz t*a&t^:-&-'* fi-aoJ- |z-*s li-L St'r'>'o-"n'-oL

}--"ri;-* .\.'-' t-Ln,o6,AL (L; t,

i ,r"n,'" +rar4L Fn,".--*k:ns,j-3. L- 1gl^-<-t- t"{".-r*

, ,!t t,Lat. duL tJ.,-ln v"s-r.{let '*tr /i,!e^-^-f"r.',.-;Aa+t e-c-r-+"d'*,':

cr+ b i"rfr'*'(: r't|*"a- { ;

t' -,.-0-t + 11\. {

Heat Transfer Test 2 Date 30"10.09 B.Tech 7 Sem.

t. ro, u flow over flat plate for a constant pressure condition the integral boundary layer equation is

s6. 0up+ [@*

: u)dy = I f .oerlve the cubic velocity profile and the boundary layer thickness., ,r.* i' - oy

iI .ta O ^.na'zr14S>-----f_-*I

i

i:

I

2. a.Define Prandtl and Nusselt Number give their physical significance./ i ii, flows over a heated flat plate at a velocity of 50 m/s. The local skin friction coefficient at a point on the plate is .004.

Estimate the local heat transfer coefficient at this point. Take p6.: 0.88 kg/m3, V= 2"266x1A-'kg/m-s" Cp : 1.001 kj,&g K,

k:0.035 WmK"

,{in straisht tube of 60 mm dia. Water is florving at a velocity of 12 m/s. The tube surface temperature is maintained at 70/ oC .and the flowing water is heated ftom the inlet temperature of l5 'C to an outlet temperature of 45 'C. Taking properties

at mean bulk temperature. Calculate (i) heat transfer coefficient from tube surface to the water (ii) heat transfened (iii)length of the tube.

/4" A counter flow double pipe heat exchanger using super heated steam is used to heat water at the rate of 10000 kg/hr. The

steam enters the heat exchanger at 180 oC and leaves at 130 "C" The inlet and outlet te^mperature of water are 30 oC and 80oC respectively" If overall heat transfer coefficient from stream to water is 814 Wm2. oC, calculate the heat transfer area

required? What would be increase in area if fluid flows were parallel?

5. The overall temperature rise ofcold fluid in across flow heat exchanger is 20 oC and overall temperature drop ofhot fluidis 30 oC. The effectiveness ofheat exchanger is 0.6. The heat exchanger area is 1 m' and overall heat transfer coefhcient is

60 Wm2" oC. Find out the rate of heat transfer. Assume both fluids unmixed.

Heat and Mass'[ransfcr'f [,S'[ 0?

l. If thc velocity tlistribution iri [amirrar bountlut'y lityer ovet'a flat platc is tr: C1 * C)21'-t-

lbrrrr using the nccessary boundary corrdition'

C3yr, clclerlttirrc its

5

2. A plate of length 750 rnrn and wiclltr 250 rrtrrr has bceir pl:rccd lorrgiluclirrilllf in it strcarlr of crtttlc oil rvhiclt

florvs wiyh a velocity of 5 m/s. If the oil has kinenratic viscosilv of lxl0-{ m'/s. 'l'lrcr, find (a) botrndary lavcr'

thiclirress at rniddle of the plate. ('la) Frictiorr tlrag orr ortc side of thc phte' l0

3. Dellle apd give the physical.signifii:irrrcc ol'l)r'nrrtltl arld Nttssclt tttttttlrct" 5

4. lu a straiglrt tube ol'(r0 nrrn diametu., rvuleI is f'lorving at a vclocitv ol'12 rtr/s. l-hc ttrbc sut l'itcc lctnllct'irturc

is maintained at 70"C and flowing watcr is hcatcd I'ronr tlre inlct tcnrperaturc l5"C to an orttlet tenrllcl'irture

of 45.C. Tal<ing physical properties of'llir(cr al ils rncrrrr bulk lcrrrpcraturc firrd thc follo$'iIg (i) hcat trarrslcr'

coefficient fronr the tube surface to the rvatcr (ii) hcnl trattsfct'rcd (iii) lengtlr ol llre trrbc' l0