HEAT TRANSFER-HEAT TRANSFER-HEAT TRANSFER .pdf

H&MT

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Introduction
GEETHA RAVICHANDRAN M.E (Chem), PMP
B.E –1993 batch in Annamalai University
M.E –1995 batch in Annamalai University
17 years experience in gas industry which includes
8 years experience in project Management, 6 years experience in
domain Management.
My hobbies: Reading, gardening.
Like to go often to clean watery, natural places
Contact : [phone]
[email protected] , [email protected]
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MME-Chemical
MME Electrical-by Darley
Agenda
1.Heat Transfer
2.Process Calculation
3.Thermodynamics
4.Reaction Kinetics
5.Fluid Mechanics and Pumps
6.Distillation
7.Economic Analysis
8.Project Management

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MME-Chemical
MME Electrical-by Darley
HEAT TRANSMISSION

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HEAT TRANSMISSION
Therearethreefundamentaltypesofheattransfer:
Conduction,convectionandradiation.
Conduction:isthetransferofheatfromonepartofbodyto
anotherpartofthesamebody,orfromonebodytoanotherin
physicalcontactwithit,withoutappreciabledisplacementof
particlesofbody.
Convection:isthetransferofheatfromonepointtoanother
withinafluid,gasorliquidbythemixingofoneportionofthe
fluidwithanother.
Innaturalconvection,themotionofthefluidisentirely
theresultofdifferencesindensityresultingfrom
temperaturedifferences.

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HEAT TRANSMISSION
Inforcedconvection,themotionisproducedby
mechanicalmeans.Whentheforcedvelocityisrelatively
low,itshouldberealizedthat‘free-convection’factors
suchasdensityandtemperaturedifferencesmayhavean
importantinfluence.
Radiation:isthetransferofheatfromonebodytoanother,
notincontactwithitbymeansofwavemotionthroughspace.

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HEAT TRANSMISSION
Conduction:Fourier’slawisthefundamentaldifferential
equationforheattransferbyconduction:
dQ/dθ=-kA(dt/dx)where
dQ/dθistherateofflowofheat.
Aistheareaatrightanglestodirectioninwhichtheheat
flows,and
dt/dxistherateofchangeoftemperaturewiththedistance
inthedirectionofflowofheat.
kisthermalconductivity
Thermalconductivityofcork,slag,wool,char-coaland
woodfibersare2.2timesthatofairandcellularformof
rubberis1.6timesofair.

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HEAT TRANSMISSION
Conductionthroughseveralbodiesinseries:
RateofHeatflow:
q1=k1A1Δt1/x1 Δt1=t2-t1
q2=k2A2Δt2/x2Δt2=t3-t2
q3=k3A3Δt3/x3Δt3=t4-t3
Overallq=∑Δt/R
Twhereas
R=x/kA,R
T=R1+R2+R3
Δt=t4-t1
q–J/sorBtu/hrandk=J/m.s.˚KorBtu/hr.ft.˚F
t1
t4
t2
t3
x1 x2
x3

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HEAT TRANSMISSION
Convection:Inthemajorityofheattransferprocessin
industrialpractice,heatisbeingtransferredfromonefluidto
anotherthroughasolidwall.HeatConvection,involvesthe
energycarriedbythefluidbythevirtueofitsvelocity.The
heattransferexpressionforheatconvectionisexpressedby
Newton’slawofcooling
q=hAdt
h-Heattransfercoefficient;dt=Ts-Tair
A–Area
Natural convection occurs when a solid surface is in contact
with a fluid of different temperature from the surface. Heat
transfer coefficient is generally expressed by dimensionless
relation between:

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HEAT TRANSMISSION
Prandtl Number : N
Pr= c
pµ / k
Nusselt Number: N
Nu= hL/k or hD/K
Reynolds number: N
Re= DG/µ = xVρ/µ = xV/ν
GrashofNumber:N
Gr=L
3
ρg
cβΔt/µ
2
RayleighNumber:N
Ra=N
GrN
Pr
ThenheattransfercoefficientcanbeexpressedbyNusselt
equation:
hL/k=C((L
3
ρg
cβΔt/µ
2
)(c
pµ/k))
n
N
Nu=C(N
GrN
Pr)
n
T
f=(T
s+T
air)/2

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HEAT TRANSMISSION
There is a simplified
formula for air, which
gives the heat transfer
coefficient for natural
convection of air over
a flat plate [1]. This
formula is of the form,
c
p=Specific heat constant pressure
g
c=Gravitational acceleration
N
Gr=Grashof number (dimensionless)
h=Heat transfer coefficient
k=Thermal conductivity of air
L=Height or length of plate
N
Nu=Nusselt number (dimensionless)
N
Pr=Prandtl number (dimensionless)
N
Ra=Rayleigh number (dimensionless)
T
a=Temperature of ambient air
T
s=Temperature of heated surface
T=Temperature difference from surface to air
β=Coefficient of thermal expansion for air
ρ=Density of air
µ=Dynamic viscosity of air
V –velocity –m/s
G-Mass Velocity –Kg/m
2
s = V ρ
ν–kinetic viscosity = µ / ρ–m
2
/s

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HEAT TRANSMISSION
OverallHeattransferCoefficient:representsthetotal
resistancetoheattransferfromonefluidtootherfluid.
Itisameasureofoverallabilityofseriesofconductiveand
convectivetotransfertheheat.
Theheattransfercoefficientisthereciprocalofthermal
insulance.Thisisusedforbuildingmaterials(R-Value).
Itcanbeestimatedbydividingthethermalconductivityof
theconvectionfluidbyalengthscale.Theheattransfer
coefficientisoftencalculatedfromtheNusseltNumber(a
dimensionlessnumber).
1/U=(1/h
i+x
w/k+1/h
0)(x
w–wallthickness)
1/U=(1/h
i+x
w/k+1/h
d+1/h
0)(ifanyscaledeposit)

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HEAT TRANSMISSION
OverallHeattransfer:
q=UAΔt
q/A-HeatFlux
HeatResistance:
R
T=R
convection+R
conduction
R
convection=1/hA=1/h
iA
i+1/h
oA
o
R
conduction=x/kA
Heat transfer coefficient Units:
1 W/(m
2
K) = 0.85984 kcal/(h m
2o
C) = 0.1761 Btu/(ft
2
h
o
F)
1 Btu/(ft
2
h
o
F) = 5.678 W/(m
2
K) = 4.882 kcal/(h m
2o
C)
1 kcal/(h m
2o
C) = 1.163 W/(m
2
K) = 0.205 Btu/(ft
2
h
o
F)

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HEAT TRANSMISSION
ForcedConvection:
Innaturalconvection,anyfluidmotioniscausedbynatural
meanssuchasthebuoyancyeffect,i.e.theriseofwarmerfluid
andfallthecoolerfluid.Whereasinforcedconvection,the
fluidisforcedtoflowoverasurfaceorinatubebyexternal
meanssuchasapumporfan.
TherateofconvectionheattransferisexpressedbyNewton’sla
wofcooling:
q=hAdt
h-Heattransfercoefficient;dt=T
∞-T
s;A-Area
Theconvectiveheattransfercoefficienthstronglydependson
thefluidpropertiesandroughnessofthesolidsurface,andthe
typeofthefluidflow(laminarorturbulent).

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HEAT TRANSMISSION
FlowOverFlatPlate:
Thefrictionandheattransfercoefficientforaflatplatecan
bedeterminedbysolvingtheconservationofmass,
momentum,andenergyequations(eitherapproximately
ornumerically).Theycanalsobemeasuredexperimentally.
ItisfoundthattheNusseltnumbercanbeexpressedas:
N
Nu= C N
Re
m
N
Pr
n
= hL/k
whereC,m,andnareconstantsandListhelengthofthe
flatplate.Thepropertiesofthefluidareusuallyevaluated
at thefilmtemperaturedefinedas:
T
f= (T
s+T
∞)/ 2

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HEAT TRANSMISSION
LaminarFlow:
Nusseltnumberover the entire isothermal plate laminar
region:
N
Nu= 0.664N
Re
1/2
N
Pr
1/3
= hL/k
Friction coefficient:
C
f= 1.328/N
Re
1/2
TurbulentFlow:
Nusseltnumberover the entire isothermal plate turbulent
region”:
N
Nu= 0.037N
Re
4/5
N
Pr
1/3
= hL/k
Friction coefficient:
C
f= 0.074/N
Re
1/5

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HEAT TRANSMISSION
TheReynoldsnumberatwhichtheflowbecomesturbulentis
calledcriticalReynoldsnumber.ForflatplatecriticalReynold
numberis5X10
5
ForLaminarflow:N
Pr≤0.6andN
Re≤5X10
5
ForTurbulentFlow:0.6≤N
Pr≥60 5X10
5
≤N
Re≥10
7

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HEAT TRANSMISSION
Typical convective heat transfer coefficients for some common fluid flow
applications:
•Free Convection -air, gases and dry vapors : 0.5 -1000 (W/(m
2
K))
•Free Convection -water and liquids: 50 -3000(W/(m
2
K))
•Forced Convection -air, gases and dry vapors:10 -1000 (W/(m
2
K))
•Forced Convection -water and liquids:50 -10000 (W/(m
2
K))
•Forced Convection -liquid metals:5000 -40000 (W/(m
2
K))
•Boiling Water : 3.000 -100.000 (W/(m
2
K))
•Condensing Water Vapor: 5.000 -100.000 (W/(m
2
K))
Units of Heat Transfer rate :
1 W = 3.41Btu/hr= 0.8598 Kcal/hr= 60 J/m = 1 J/S

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Questions

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1.What the rate of heat transfer by conductionper unit area, by
means of conduction for a furnace wall made of fire clay. Furnace
wall thickness is 6" or half a foot. Thermal conductivity of the furnace
wall clay is 0.3 W/m·K. The furnace wall temperature can be taken to
be same as furnace operating temperature which is 650
0
C and
temperature of the outer wall of the furnace is 150
0
C.
A.110 W/m
2
B.492 W/m
2
C.380 W/m
2
D.600 W/m
2
HEAT TRANSMISSION

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1.What the rate of heat transfer by conductionper unit area, by
means of conduction for a furnace wall made of fire clay. Furnace
wall thickness is 6" or half a foot. Thermal conductivity of the furnace
wall clay is 0.3 W/m·K. The furnace wall temperature can be taken to
be same as furnace operating temperature which is 650
0
C and
temperature of the outer wall of the furnace is 150
0
C.
A.110 W/m
2
B.492 W/m
2
C.380 W/m
2
D.600 W/m
2
Ans: B
HEAT TRANSMISSION

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For the given sample problem,
T
1
= 650
0
C
T
2
= 150
0
C
L = 12" = 12 ×0.0254 m = 0.3048 m
k = 0.3 W/m·K
Hence,
Heat transfer rate per unit area of the wall is
calculated as,
Q/A = k ×(T
1
-T
2
)/L
Q/A = 0.3×(650-150)/0.3048 W/m
2
= 492.13 W/m
2
HEAT TRANSMISSION

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2.Twometalshavethesamesize.Thethermalconductivityof
metalII=2timesthethermalconductivityofmetalI.Ifone
endofmetalIisheatedsoT
1
=100
o
CandoneendofmetalII
isheatedsoT
2
=25
o
C,thenwhatisthetemperaturebetween
bothmetals.
A.90
o
C
B.100
o
C
C.50
o
C
D.60
o
C
HEAT TRANSMISSION

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2.Twometalshavethesamesize.Thethermalconductivityof
metalII=2timesthethermalconductivityofmetalI.Ifone
endofmetalIisheatedsoT
1
=100
o
CandoneendofmetalII
isheatedsoT
2
=25
o
C,thenwhatisthetemperaturebetween
bothmetals.
A.90
o
C
B.100
o
C
C.50
o
C
D.60
o
C
Ans:C
HEAT TRANSMISSION

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TheheatconductivityofmetalI=k
TheheatconductivityofmetalII=2k
ThetemperatureatoneendofmetalI=100
o
C
ThetemperatureatoneendofmetalII=25
o
C
Theequationoftheheatconduction
HEAT TRANSMISSION

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3.ThefollowingfigureshowsdifferentAandBmetalrods
connectedatoneend.Thecross-sectionalareaofbothrodsis
thesame,butthelengthofAistwicethelengthofBandthe
thermalconductioncoefficientAis3timesB.Ifthefreeends
AandBaresubjectedtodifferenttemperature,the
temperatureatthejunctionis
A.90
o
C
B.86
o
C
C.70
o
C
D.76
o
C
HEAT TRANSMISSION

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3.ThefollowingfigureshowsdifferentAandBmetalrods
connectedatoneend.Thecross-sectionalareaofbothrodsis
thesame,butthelengthofAistwicethelengthofBandthe
thermalconductioncoefficientAis3timesB.Ifthefreeends
AandBaresubjectedtodifferenttemperature,the
temperatureatthejunctionis
A.90
o
C
B.86
o
C
C.70
o
C
D.76
o
C
Ans:D
HEAT TRANSMISSION

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ThethermalconductivityofmetalA=3k
ThethermalconductivityofmetalB=k
LengthofmetalA=2l
LengthofmetalB=l
ThetemperatureofoneendmetalA=100
o
C
ThetemperatureofoneendmetalB=40
o
C
HEAT TRANSMISSION

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4. Which of the following commonly used condenser tube materials
has the lowest thermal conductivity?
A.Admirability brass.
B.Stainless steel.
C.Aluminiumbrass.
D.Titanium.
HEAT TRANSMISSION

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4. Which of the following commonly used condenser tube materials
has the lowest thermal conductivity?
A.Admirability brass.
B.Stainless steel.
C.Aluminiumbrass.
D.Titanium.
Ans: B
HEAT TRANSMISSION

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5. One end of a metal rod is maintained at 100 degrees C, and the
other end is maintained at 0 degrees C by an ice-water mixture. The
rod is 60 cm long and has a cross-sectional area of 1.25 cm^2. The
heat conducted by the rod melts 8.50 g of ice in 10.0 min. Find the
thermal conductivity of the metal if 30% of heat is lost to the
surroundings.
A.o.777cal/cm.s.
o
C
B.o.91cal/cm.s.
o
C
C.1.071cal/cm.s.
o
C
D.o.381cal/cm.s.
o
C
HEAT TRANSMISSION

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5. One end of a metal rod is maintained at 100 degrees C, and the
other end is maintained at 0 degrees C by an ice-water mixture. The
rod is 60 cm long and has a cross-sectional area of 1.25 cm^2. The
heat conducted by the rod melts 8.50 g of ice in 10.0 min. Find the
thermal conductivity of the metal if 30% of heat is lost to the
surroundings.
A.o.777cal/cm.s.
o
C
B.o.91cal/cm.s.
o
C Rateofheatflow:
C.1.071cal/cm.s.
o
C Q/t=mL
f/t
D.o.381cal/cm.s.
o
C L=Latentheatoffusion=80cal/g
Q/t=((8.5*80)/0.7)/10*60=1.619cal/s
k=(1.619/(1.25(100-0)))*60=0.777
Ans:A
HEAT TRANSMISSION

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6.Transition from laminar to turbulent zone in free convection
heat transfer is governed by the critical value of
A.Grashoffnumber.
B.Grashoffnumber & Reynolds number.
C.Reynolds number.
D.Grashoffnumber & Prandtl number.
HEAT TRANSMISSION

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6.Transition from laminar to turbulent zone in free convection
heat transfer is governed by the critical value of
A.Grashoffnumber.
B.Grashoffnumber & Reynolds number.
C.Reynolds number.
D.Grashoffnumber & Prandtl number.
Ans: D
HEAT TRANSMISSION

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7. A fluid flows over a square plate surface of 1m length. The surface
temperature is 50
0
C and the air temperature is 20
0
C. The
convective heat transfer coefficient is 2000/W.m2
0
C, Then the
heat loss from the plate surface is
A.40 KW
B.100 KW
C.60 KW
D.70 KW
HEAT TRANSMISSION

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7. A fluid flows over a square plate surface of 1m length. The surface
temperature is 50
0
C and the air temperature is 20
0
C. The
convective heat transfer coefficient is 2000/W.m2
0
C, Then the
heat loss from the plate surface is
A.40 KW
B.100 KW
C.60 KW
D.70 KW
A = 1m * 1 m = 1m
2
q=2000*1 *(50-20) = 60000 W = 60 KW
Ans: C
HEAT TRANSMISSION

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8. A 22ft uninsulated steam pipeline crosses a room. The outer
diameter of pipeline is 18 inch. The outer surface temperature is
280
0
F. The heat transfer coefficient of air is 18 Btu/hr.ft
2
.
0
F.
What is the heat flow rate from pipe into room, if the room
temperature is 72
0
F
A.387 Kw
B.114 KW
C.189 KW
D.67 KW
HEAT TRANSMISSION

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8. A 22ft uninsulated steam pipeline crosses a room. The outer
diameter of pipeline is 18 inch. The outer surface temperature is
280
0
F. The heat transfer coefficient of air is 18 Btu/hr.ft
2
.
0
F.
What is the heat flow rate from pipe into room, if the room
temperature is 72
0
F
A.387 Kw
B.114 KW
C.189 KW
D.67 KW
A = 2 πr l = (2) (3.14) (0.75)(22) = 103.62 ft
2
q= 18 (103.62) (280-72) = 387953.28 Btu/hr = 113.7 KW
Ans: B
HEAT TRANSMISSION

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9. A stainless steel plate heat exchanger with area 2m
2
and 0.1mm
thickness is used for air to air heat transmission. What is the
overall heat transfer rate if inside temperature of exchange is 100
0
C and the outside temperature is 20
0
C, thermal conductivity of
stainless steel is 16 W/m
0
K and convection heat transfer
coefficient of air is 50 W/m
2
K
A.4000 W
B.2000 W
C.1000 W
D.8000 W
HEAT TRANSMISSION

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9. A stainless steel plate heat exchanger with area 2m
2
and
0.1mm thickness is used for air to air heat transmission. What is the
overall heat transfer rate if inside temperature of exchange is 100
0
C
and the outside temperature is 20
0
C, thermal conductivity of
stainless steel is 16 W/m
0
K and convection heat transfer coefficient
of air is 50 W/m
2
K
A.4000 W
B.2000 W
C.1000 W
D.8000 W
1/U = (1/50) + (0.1*10
-3
/16)+(1/50)= 0.04
U = 25 W/m
20
K
q= 25 * 2 * (100-20) = 4000 W =4 KW
Ans: A
HEAT TRANSMISSION

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10. A liquid is stored in a large diameter tank that is maintained at
190
0
F. The tank constructed of 1.5 inch thick carbon steel plate
(k=23Btu/hr-ft-
0
F). The convective heat transfer coefficients:
Inside of tank h=30 Btu/(hr-ft2-
0
F); Exterior of tank: h=10
Btu/(hr-ft2-
0
F). The cold design air temperature is -20F. For a
fouled interior tank wall (R=0.01 (hr-ft2-
0
F)/Btu), the heat loss
flux (Btu/(hr-ft2) is most nearly
A.1,140
B.1,420
C.1470
D.1510
HEAT TRANSMISSION

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10. A liquid is stored in a large diameter tank that is maintained at
190
0
F. The tank constructed of 1.5 inch thick carbon steel plate
(k=23Btu/hr-ft-
0
F). The convective heat transfer coefficients:
Inside of tank h=30 Btu/(hr-ft2-
0
F); Exterior of tank: h=10
Btu/(hr-ft2-
0
F). The cold design air temperature is -20F. For a
fouled interior tank wall (R=0.01 (hr-ft2-
0
F)/Btu), the heat loss
flux (Btu/(hr-ft2) is most nearly
A.1,140
B.1,420
C.1470
D.1510
Ans: B
HEAT TRANSMISSION

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Ans
4
3

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7. A thermopanewindow is one in which two pieces of glass are stagnant air
layer. The following data apply:
Inside and outside convection coefficients 1 Btu/(hr-ft2-F)
Thermal conductivity of glass 0. 5 Btu/(hr-ft2-F)
Thermal conductivity of air 0. 015 Btu/(hr-ft2-F)
Glass Thickness 0.25 in.
Air gap for thermopane0.25 in.
The ratio of the heat flux for a thermopaneto that for a single glass pane is:
A.0.13
B.0.59
C.0.98
D.1.7
HEAT TRANSMISSION

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7. A thermopanewindow is one in which two pieces of glass are stagnant air
layer. The following data apply:
Inside and outside convection coefficients 1 Btu/(hr-ft2-F)
Thermal conductivity of glass 0. 5 Btu/(hr-ft2-F)
Thermal conductivity of air 0. 015 Btu/(hr-ft2-F)
Glass Thickness 0.25 in.
Air gap for thermopane0.25 in.
The ratio of the heat flux for a thermopaneto that for a single glass pane is:
A.0.13
B.0.59
C.0.98
D.1.7
Ans: B
HEAT TRANSMISSION

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6

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8. An oil cooler in a high performance engine has an outside surface area
0.12 m2and a surface temperature of 65 degree Celsius. At any
intermediate time air moves over the surface of the cooler at a
temperature of 30 degree Celsius and gives rise to a surface coefficient
equal to 45.4 W/ m2K. Find out the heat transfer rate?
A.238.43 W
B.190.68 W
C.543.67 W
D.675.98 W
HEAT TRANSMISSION

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8. An oil cooler in a high performance engine has an outside surface area
0.12 m2and a surface temperature of 65 degree Celsius. At any
intermediate time air moves over the surface of the cooler at a
temperature of 30 degree Celsius and gives rise to a surface coefficient
equal to 45.4 W/ m2K. Find out the heat transfer rate?
A.238.43 W
B.190.68 W
C.543.67 W
D.675.98 W
q=45.4 * 0.12 * (65-30) = 190.68 W
Ans: B
HEAT TRANSMISSION

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9.The rate equation used to describe the mechanism of convection is called
Newton’s law of cooling. So rate of heat flow by convection doesn’t
depend on
A.Convective heat transfer coefficient
B.Surface area through which heat flows
C.Time
D.Temperature potential difference
HEAT TRANSMISSION

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9.The rate equation used to describe the mechanism of convection is called
Newton’s law of cooling. So rate of heat flow by convection doesn’t
depend on
A.Convective heat transfer coefficient
B.Surface area through which heat flows
C.Time
D.Temperature potential difference
Ans: C
HEAT TRANSMISSION

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10.A hot plate of 15 cm2area maintained at 200 degree celsiusis exposed
to still air at 30 degree Celsius temperature. When the smaller side of
the plate is held vertical, convective heat transfer rate is 15 per cent
higher than bigger side of the plate is held vertical. Find size of the plate.
The appropriate correlation for the convection coefficient is
Nu = 0.60 (Gr Pr)0.25
A.l = 5.123 cm and b = 2.928 cm
B.l = 6.123 cm and b = 3.928 cm
C.l = 7.123 cm and b = 4.928 cm
D.l = 8.123 cm and b = 5.928 cm
HEAT TRANSMISSION

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10.A hot plate of 15 cm2area maintained at 200 degree celsiusis exposed
to still air at 30 degree Celsius temperature. When the smaller side of
the plate is held vertical, convective heat transfer rate is 15 per cent
higher than bigger side of the plate is held vertical. Find size of the plate.
The appropriate correlation for the convection coefficient is
Nu = 0.60 (Gr Pr)0.25
A.l = 5.123 cm and b = 2.928 cm
B.l = 6.123 cm and b = 3.928 cm
C.l = 7.123 cm and b = 4.928 cm
D.l = 8.123 cm and b = 5.928 cm
Ans: A
HEAT TRANSMISSION

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C=0.6, m = 0.25
h
1= C((T
s–T
air)/b)
m
h
2= C((T
s–T
air)/l)
m
h
1/h
2= (l/b)
0.25
= 1.15
l=1.75b
Area = l*b=1.75b
2
= 15
b =2.928 cm
l = 5.123 cm
Ans: A
HEAT TRANSMISSION

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11. A horizontal heated plate at 200 degree Celsius and facing upwards has
been placed in still air at 20 degree Celsius. If the plate measures 1.25 m
by 1 m, make calculations for the heat loss by natural convection. The
convective film coefficient for free convection is given by the following
empirical relation, h = 3.02 (α)
0.25
W/m2K
Where α is the mean film temperature in degrees kelvin
A) 6006 W
B) 5006 W
C) 4006 W
D) 3006 W
HEAT TRANSMISSION

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11. A horizontal heated plate at 200 degree Celsius and facing upwards has
been placed in still air at 20 degree Celsius. If the plate measures 1.25 m
by 1 m, make calculations for the heat loss by natural convection. The
convective film coefficient for free convection is given by the following
empirical relation, h = 3.02 (α)
0.25
W/m2K
Where α is the mean film temperature in degrees kelvin
A) 6006 W
B) 5006 W
C) 4006 W
D) 3006 W
Ans: D
α = 273 + 200 + 20/2 = 383 K.
h = 13.36
rate of heat loss q = h A d t = 3006 W.
HEAT TRANSMISSION

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12. Lube oil is cooled in the annulus of a double-pipe exchanger from 4500P
to 3500P by crude oil flowing in the tube. The following properties of
lube oil are at the caloric temperature
Heat capacity, Cp=0.615 Btu/lbF, Viscosity µ= 3.05cP
Thermal conductivity, k= 1.55 x10-6 Btu/S in F
The value of the Prandtl number under these conditions is:
A.12.2
B.57.4
C.28.3
D.67.7
HEAT TRANSMISSION

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12. Lube oil is cooled in the annulus of a double-pipe exchanger from 4500P
to 3500P by crude oil flowing in the tube. The following properties of
lube oil are at the caloric temperature
Heat capacity, Cp=0.615 Btu/lbF, Viscosity µ= 3.05cP
Thermal conductivity, k= 1.55 x10-6 Btu/S in F
The value of the Prandtl number under these conditions is:
A.12.2
B.57.4
C.28.3
D.67.7
Ans: D
HEAT TRANSMISSION
k=1.55x10-6 Btu/S in
o
F=66960x10-6 Btu/hrft
0
F
µ=3.05cP=7.378 lb/ft-hr
C
p=0.615 Btu/lbF
N
Pr= (0.615x7.378)/(66960x10-6) = 67.76

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13. Which of the following is an example of steady state heat transfer?
A) Boilers and turbines
B) Cooling of I.C engine
C) Chilling effect of cold wind on a warm body
D) Electric bulb cools down by the surrounding atmosphere
HEAT TRANSMISSION

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13. Which of the following is an example of steady state heat transfer?
A) Boilers and turbines
B) Cooling of I.C engine
C) Chilling effect of cold wind on a warm body
D) Electric bulb cools down by the surrounding atmosphere
Ans: D
HEAT TRANSMISSION

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14. Heat transfer takes place according to which law?
A) Newton’s law of cooling
B) Second law of thermodynamics
C) Newton’s second law of motion
D) First law of thermodynamics
HEAT TRANSMISSION

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14. Heat transfer takes place according to which law?
A) Newton’s law of cooling
B) Second law of thermodynamics
C) Newton’s second law of motion
D) First law of thermodynamics
Ans: B
HEAT TRANSMISSION

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15. Heat transfer takes place in liquids and gases is essentially due to
a) Radiation
b) Conduction
c) Convection
d) Conduction as well as convection
HEAT TRANSMISSION

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15. Heat transfer takes place in liquids and gases is essentially due to
a) Radiation
b) Conduction
c) Convection
d) Conduction as well as convection
Ans: C
HEAT TRANSMISSION

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16.The appropriate rate equation for convective heat transfer between a
surface and adjacent fluid is prescribed by
A.Newton’s first law
B.Wein’s displacement law
C.Kirchhoff’s law
D.Newton’s law of cooling
HEAT TRANSMISSION

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16.The appropriate rate equation for convective heat transfer between a
surface and adjacent fluid is prescribed by
A.Newton’s first law
B.Wein’s displacement law
C.Kirchhoff’s law
D.Newton’s law of cooling
Ans: D
HEAT TRANSMISSION

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17.During a cold winter season, a person prefers to sit near a fire.
Which of the following modes of heat transfer provides him the
maximum heat?
a) Conduction from the fire
b) If it is near the fire, convection sounds good
c) Convection and radiation together
d) Radiation will provide quick warmth
HEAT TRANSMISSION

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17.During a cold winter season, a person prefers to sit near a fire.
Which of the following modes of heat transfer provides him the
maximum heat?
a) Conduction from the fire
b) If it is near the fire, convection sounds good
c) Convection and radiation together
d) Radiation will provide quick warmth
Ans: D
HEAT TRANSMISSION

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18. Heat transfer in a long, hollow cylinder which is maintained at uniform
but different temperatures on its inner and outer surfaces may be
assumed to be taking place in which direction?
A.Axial only
B.Unpredictable
C.Radial only
D.No heat transfer takes place
HEAT TRANSMISSION

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18. Heat transfer in a long, hollow cylinder which is maintained at uniform
but different temperatures on its inner and outer surfaces may be
assumed to be taking place in which direction?
A.Axial only
B.Unpredictable
C.Radial only
D.No heat transfer takes place
Ans: C
HEAT TRANSMISSION

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19.A tank is maintained at 250 F using 50-psig saturated steam. The tank
heat loss is 75,000 Btu/h and is compensated for by using a 1-in sch. 40
pipe worm heater.
The following data apply:
T steam(50psig)= 298 F
Convective heat transfer coefficients
Condensing steam h 1,200 Btu/(hr-ft2-F)
Exterior of pipe to fluid h = 40 Btu/(hr-ft2-F)
Pipe data
Thermal conductivity 26 Btu/(hr-ft-F)
Interior pipe diameter 1.049 in.
Exterior pipe diameter 1.315 in.
The length (ft) of pipe needed for the wo rmheater
A.86
B.120
C.145
D.168
HEAT TRANSMISSION

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19.A tank is maintained at 250 F using 50-psig saturated steam. The tank
heat loss is 75,000 Btu/h and is compensated for by using a 1-in sch. 40
pipe worm heater.
The following data apply:
T steam(50psig)= 298 F
Convective heat transfer coefficients
Condensing steam h 1,200 Btu/(hr-ft2-F)
Exterior of pipe to fluid h = 40 Btu/(hr-ft2-F)
Pipe data
Thermal conductivity 26 Btu/(hr-ft-F)
Interior pipe diameter 1.049 in.=0.08742ft (ri=0.0437ft)
Exterior pipe diameter 1.315 in.=0.1096ft (ro=0.0548ft)
The length (ft) of pipe needed for the worm heater
A.86
B.120
C.145
D.168
Ans: B
HEAT TRANSMISSION

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Interior pipe diameter 1.049 in.=0.08742ft (ri=0.0437ft)
Exterior pipe diameter 1.315 in.=0.1096ft (ro=0.0548ft)
1/U = (1/h
i+ x
w/k+ 1/h
0) = ((1/1200) +(0.011/26)+ ( 1/40))
1/U = 0.0263
U = 38.086
q = UA Δt=75000
A = 75000/(38.086* (298-250))
= 41.03 = 2πrl=2*3.14*0.0548*l
l= 119.7 ft
HEAT TRANSMISSION

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20.Engineoilat60°Cflowsovera5mlongflatplatewhose
temperatureis20°Cwithavelocityof2m/s.Therateofheat
transferperunitwidthoftheentireplate is:
HEAT TRANSMISSION
Thepropertiesoftheoilatthefilmtemperatureare:
ρ = 876 kg/m
3
; k=0.144 W/m K ; ν= 242 X 10
-6
m
2
/s C
p= 1950 J/kgK
A.10.82 KW
B.11.04 KW
C.9.3 KW
D.12.5 KW

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20.Engineoilat60°Cflowsovera5mlongflatplatewhose
temperatureis20°Cwithavelocityof2m/s.Therateofheat
transferperunitwidthoftheentireplate is:
HEAT TRANSMISSION
Thepropertiesoftheoilatthefilmtemperatureare:
ρ = 876 kg/m
3
; k=0.144 W/m K ; ν= 242 X 10
-6
m
2
/s C
p= 1950 J/kgK
A.10.82 KW
B.11.04 KW
C.9.3 KW
D.12.5 KW
Ans: B

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ν=µ/ρ
µ= νρ= 242 x 10
-6
* 876 = 0.212 Kg/m s
N
Pr= C
pµ / k = 0.00195 * 211992 / 0.144 = 2870.83
N
Re= xV/ν= 5 X 2 / 242 x 10
-6
= 0.0413 X 10
6
N
Nu= 0.664N
Re
1/2
N
Pr
1/3
= hL/k
h= 55.2 W/m
2
K
The Rate of heat transfer per Unit width
Q = hAΔT = 55.2*5*1*40 = 11040 W = 11.04 KW
HEAT TRANSMISSION

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21. Air at atmospheric pressure and 20 degree Celsius flows with 6 m/s
velocity through main trunk duct of air conditioning system. The duct is
rectangular in cross-section and measures 40 cm by 80 cm. Determine
heat loss per meter length of duct corresponding to unit temperature
difference. The relevant thermos-physical properties of air are, v = 15 *
10-6m2/s, α = 7.7 * 10-6m2/hr, k = 0.026 W/m degree
A) 42.768 W
B) 74.768 W
C) 58.768 W
D) 65.768 W
HEAT TRANSMISSION

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21. Air at atmospheric pressure and 20 degree Celsius flows with 6 m/s
velocity through main trunk duct of air conditioning system. The duct is
rectangular in cross-section and measures 40 cm by 80 cm. Determine
heat loss per meter length of duct corresponding to unit temperature
difference. The relevant thermos-physical properties of air are, v = 15 *
10-6m2/s, α = 7.7 * 10-6m2/hr, k = 0.026 W/m degree
A) 42.768 W
B) 74.768 W
C) 58.768 W
D) 65.768 W
Ans: B
HEAT TRANSMISSION

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V = 6m/s
ν= 15 X 10
-6
m2/s
N
Re= xV/ν= 0.8 X 6 / 15 x 10
-6
= 0.32 X 10
6
ν=µ/ρ
µ= νρ
N
Pr= C
pµ / k = C
pνρ/k α= k/ρC
p
= ν / α
= 15 X 10
-6
/ ((7.7 X 10
-6
)/60X60)=7013
N
Nu= 0.664N
Re
1/2
N
Pr
1/3
= hL/k
h= 233.65W/m
2
K
dq/dt= hA= 233.65 * 0.32 = 74.768W
HEAT TRANSMISSION