PTE 512: PROCESS TECHNOLOGY
Course Lecturer
Engr. Dr. Jeffrey O. Oseh
SchoolofEngineeringandEngineeringTechnology
DepartmentofPetroleumEngineering
Elective 3 credit units
Pre-requisite: PET 310 (Heat and Mass Transfer)
COURSE OUTLINES
1.Heattransfer:conduction,convection,and
radiation
2.HeatExchangers
3.Distillation
4.Particlesfallsinliquidcyclones
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Introduction to heat transfer
Inthiscourse,theprocessoftransferofheat
between bodiesby(conduction,convection,and
radiation)willbediscussed.Differentprocesses
associatedwiththetransferofheatbyconduction,
convection,andradiationwillalsobediscussed.
Further,theperformance ofheatexchangers,
distillationunits,andthefallingofparticlesinliquid
cycloneswillbehighlighted.
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What is heat transfer?
Heat:isthetransferofflowduetotemperaturedifferencebetween
twoobjects.
Heattransferisafundamentalpartofthermalengineering.Itisthe
scienceoftherulesgoverningthetransferofheatbetweensystemsof
differenttemperatures.itdealswiththegeneration,use,conversion,and
exchangeofthermalenergybetweenphysicalsystems.Itcanbe
definedasthemovement ofenergyfromone
substance(warmer)toanother(colder).
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3 ways energy (heat) is transferred
Figure 1
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3 ways energy (heat) is transferred
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Thermal Energy Transfer
Thermalenergytransferisheatmovingfromawarmerobjecttoacoolerobject.Heatwillcontinueto
moveuntilbothsubstancesareatthesametemperature.Themorekineticenergyofanobject,themore
itsthermalenergy.Thefastertheparticlesaremoving,thehottertheobjectbecomes.Thegreaterthe
differenceintemperaturebetweenthesubstances,thefastertheheatwilltransfer.
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Cold Hot
HEAT CONDUCTION
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•Heatistransferredfromoneparticleofmatterto
anotherinanobjectwithoutthemovement oftheobject.
Itisthetransferofheatfromonebody(warmer)tootherbody
(colder)bymeansofphysicalcontact.
•CONDUCTION = DIRECT CONTACT
•Direct collision of molecules
Cold Hot
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Example of Conduction
Conduction: Requires
material (medium) to
transfer heat.
Medium = Metal
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•Thinkofametalspoonormetalhandleinapotofwater
beingheated.
•Thefast-movingparticlesofthefirecollidewiththe
slow-movingparticlesofthecoolpot.
•Becauseofthesecollisions,theslowerparticlesmove
fasterandheatistransferred.
•Thentheparticlesofthepotcollidewiththeparticlesin
thewater,whichcollidewiththeparticlesatoneendof
thespoon.
•Astheparticlesmovefaster,themetalspoongetshotter.
Thisprocessofconductionisrepeatedallalongthe
metaluntiltheentirespoonishot.
•Medium=metalspoonorhandleofthe
pot
•Apieceofcheesemeltsasheatistransferredfromthe
meattothecheese(Directcontact).
Example of Conduction
HEAT CONVECTION
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Heattransferbyconvection isthe
transferofheatthroughthefluid(liquids
andgases)movementofcurrents.
Heatistransferredbycurrentswithin
thefluidorgas.Thesefluidcurrents
developedduetotemperaturedifference
{withinafluid,(liquid/gas)orbetweena
fluidandasolid}ortheuseofa
pump/fan.
•Convectionmovesinacircularpattern.
•Convection:Requiresmedium to
transferenergy.
Cool air
Warm air
HEAT CONVECTION
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Warmfluids(air)
rises,cool,sink,
andarewarmed
again.
•The radiator
warmstheroom
bywarming the
airaround it.
Then,thewarm
airtransfersheat
totherestofthe
room through
convection.
HEAT CONVECTION
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•Asairabove
the road
warms up,it
risesanditis
replaced by
cooler air,
forming a
convection
current.
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EXAMPLES OF RADIATION
1.Fire
2.Heat Lamps
3.Sun
•Automobile:Radiatorandenginecoolant
•Electronics:Coolingofmotherboard/CPU byfan
•Pharmaceutical:Freezedryingofvaccines
•Metallurgical:Heating/coolingduringsteelmanufacture
•Chemical:Condensation,boiling,distillationofchemicals
•Home:Refrigerator,AC,heater,dryer,stove,microwave
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HEAT TRANSFER IN VARIOUS INDUSTRIES
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RECAP OF HEAT TRANSFER
3 Ways Energy (Heat) is Transferred
*Transferred in
rays or waves
*Energy from the
Sun warms the
Earth
Mode: Radiation
*Transfer ofheat
(energy) that
happens when
moleculesbumpinto
eachother
*Objects must be
touching
“Conduction is
touching”
Mode:Conduction
*Transferofheatby
theflowofmaterial
*Inwarm air,the
molecules move
apart,soitisless
denseandrises
*Incoolerair,the
molecules move
closertogether,so
itismoredense
andsinks.
Mode:Convection
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RECAP OF HEAT TRANSFER
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CONDUCTION HEAT TRANSFER
Basics of Conduction
•Conductioninvolvesthetranslationofvibrationofmoleculesalonga
temperature gradientastheyacquirethermalenergy(mainlyanalyzed
withinsolids;however,ittakesplaceinliquidsandgasesalso).
–Actualmovement ofparticlesdoesnotoccur
•Goodconductorsofelectricityaregenerallygoodconductorsofheat
•Thermalconductivity(k)isusedtoquantifytheabilityofamaterialto
conductheat
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TEMPERATURE DIFFERENCE ACROSSASLAB
Figure1One–dimensionalheattransfer
byconduction
Slab: Q=kA(∆T/∆x)
∆T = T
1–T
2
ForthesamevalueofQ(example:useofaheateron
onesideofaslab),
For insulators (low k), “T
1–T
2” is large
For good conductors (high k), “T
1–T
2” is small
Forthesamevalueof“T
1–T
2”(example:fixedinside
temperatureofroomandoutsideairtemperature),
For insulators (low k), Q is small
For good conductors (high k), Q is large
Note:∆??????andAareassumedtobethesameinallofthe
abovesituations.
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TEMPERATURE DIFFERENCE ACROSSASLABdx
dT
kq
x'' TEMPERATURE DIFFERENCE ACROSSASLAB
The–vesignisaconsequence of
thefactthatheatistransferredin
thedirectionofdecreasingtemp.
Applying Fourier'slawofheat
conduction permits determining
temperature distributionwithina
body.
Heat conduction isnormally
transferredfromawarmerbodytoa
coolerbody.L
T
k
L
TT
kq
x
21
''
????????????
????????????
=
??????
2−??????
1
�
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HEATCONDUCTION ACROSSACYLINDER ANDASPHERE
r
i = r
1and r
o = r
2
Figure2Steady,one‐dimensionalheat
conductioninacylindricallayer
•Steadystateheattransferthroughpipesisinthenormaldirectiontothe
wallsurface
•Nosignificantheattransferoccursinotherdirections.
•Therefore,theheattransfercanbemodeledassteady‐stateand1-D.
•Thetemp.ofthepipewilldependonlyontheradialdirection,T=T(r),
asshowninFigure2.
•Since,thereisnoheatgenerationinthelayerandthermalconductivityisconstant,
theFourierlawbecomes:
�
∗
�??????�
=−�??????
�??????
��
1
Area of a cylinder ??????=2????????????�
Area at one end of the cylinder (outside) is ??????
2=(2????????????
2�)
Area at one end of the cylinder (inside) is ??????
1= (2????????????
1�)
??????
�=??????
2−??????
1, or ??????
�−??????
??????
????????????=??????
1−??????
2or ??????
??????−??????
�
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Since, there is no heat generation in the layer and thermal conductivity is constant, the Fourier
law becomes:
�
∗
�??????�
=−�??????
�??????
��
Replace the area A with ??????=�??????��
�
∗
�??????�
=−�(�??????��)
�??????
��
2
Note �
∗
�??????�
=�
∗
�
Where �
∗
??????
is constant which may be separated and solved as follows by integration
�
∗
�
න
�
�
��
��
�
=−�??????��න
??????
�
??????�
�??????=�??????��න
??????
�
??????�
�??????
�
∗
�
��
�
�
�
�
=�??????��??????
�−??????
�
Rearrangement of the equation yields:
�
∗
�
=�
∗
�??????�
=�??????��
??????
�−??????
�
��
�
�
�
�
3
�
∗
�??????�
=
??????�−??????�
�
�??????�
4
Where,
�
�??????�=
��(����)
�??????��
is the conduction resistance of a cylinder 5
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HEATCONDUCTION ACROSSACYLINDER ANDASPHERE
For A sphere:
•Followingtheanalysisabove,theconductionresistanceforthesphericallayercanbe
found:
�
∗
��ℎ
=
??????1−??????2
�
????????????ℎ
�
��ℎ=
�2−�1
4??????�
1�
2??????
Where area of a sphere is A = 4πr
2
�
��ℎis the conduction resistance of a sphere
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BasicsofConvection
•Itinvolvestransferofheatby
movement ofmoleculesoffluid
(liquid or gas) due to
Temperaturesdifferenceswithina
fluidorbetweenafluidandasolid
object.
•Energyexchange between a
surfaceandanadjacentfluid.
OR
–Anexternalagencysuchasa
pumporafan
HEAT CONVECTION
Categories of Convection
•Free(ornatural)convection
–Doesnotinvolveanyexternalagencyincausingflow
–Heattransferbetweenbottomofvesselandfluidin
it.
•Fluid comes into contact with hot solid
• Fluid temperature near solid increases
• Fluid density near solid decreases
• This results in a buoyancy force that causes flow
• Rate of heat transfer (Q & h) depends on
–Temperature difference between fluid and surface
of solid
–Coolingofhumanbody
–Coolingofradiatorfluidincarengineduringidling
–ℎ
�??????�−���??????�:5-25W/m2K;ℎ
??????����−���??????�:20-100W/m2K
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BasicsofConvection
•Itinvolvestransferofheatby
movement ofmoleculesoffluid
(liquid or gas) due to
Temperaturesdifferenceswithina
fluidorbetweenafluidandasolid
object.
•Energyexchange between a
surfaceandanadjacentfluid.
OR
–Anexternalagencysuchasa
pumporafan
HEAT CONVECTION
CategoriesofConvection
•Forcedconvection
Fluidisforcedtomovebyanexternalforce(pump/fan)
•Rateofheattransfer(Q&h)dependson
–Dimensionsandsurfacecharacteristics(smoothness)
ofsolid
•‘h’doesNOTdependon
–Temperature differencebetweenfluidandsurfaceof
solid
•‘h’stronglydependsonReynoldsnumber
–Whenallsystemandproductparameters arekept
constant,it
isflowrate(aprocessparameter)thatstronglyaffects
‘h’
–Externalagencysuchasfan/pumpcausesflow
–Coolingofradiatorfluidincarengineduringmotion
–Ice-creamfreezer(Blastair)
–Stirringapotofsoup
–Heattransferredfromcomputers(fan)
–ℎ
�??????�−���??????�:10-200W/m2K;ℎ
�??????�−���??????�:50-10,000W/m2K
–ℎ
��??????�??????�????????????����������������??????�:3,000-100,000W/m2K
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Newton’s Law of Cooling for Convection
Rateofheattransferbyconvection(forheatingorcooling)isgivenbyNewton’slawofcoolingasfollows:
Q = h A (Ts -T∞)
Q:Energytransferredperunittime(W).
h:Convectiveheattransfercoefficient(W/m²K).Itdependsonconditionsintheboundarylayer,influencedby:
Surfacegeometry
Natureoffluidmotion
Arrangement ofthefluidthermodynamic andtransportproperties
A:Surfaceareaavailableforheattransfer(m²)
∆??????=Ts–T∞:Temperaturedifference(K)
Ts:Surfacetemperatureofsolidobject(K)
T∞:Freestream(orbulkfluid)temperatureoffluid(K).
�
∗
??????
�
2
=
�
??????
istheconvectiveheatflux.Thus,Newtonlawofcoolingoccurswhentheconvectiveheatflux�
∗
is
proportionaltothedifferencebetweenthesurfaceandbulkfluidtemperatureTsandT∞,respectively.