2019 Heat Lecture 14-15 Old Heat 01 V3
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Transport/Unit OperationsProfessor Faith A. MorrisonDepartment of Chemical EngineeringMichigan Technological UniversityCM2120—Fundamentals of ChemE 2 (Steady Unit Operations Introduction, MEB)CM3110—Transport/Unit Ops 1 (Momentum & Steady Heat Transport, Unit Operations)CM3120—Transport/Unit Ops 2 (Unsteady Heat Transport, Mass Transport, UnitOperations1 Faith A. Morrison, Michigan Tech U.First sectionof the courseis complete.Now we moveon to thesecond part.2 Faith A. Morrison, Michigan Tech U.1
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019CM3110Transport IPart II: Heat TransferIntroduction to Heat TransferProfessor Faith MorrisonDepartment of Chemical EngineeringMichigan Technological University3www.chem.mtu.edu/ fmorriso/cm310/cm310.html Faith A. Morrison, Michigan Tech U.Where do we start?Why are chemical engineersinterested in heat transfer?As before with fluid mechanics, there are engineeringquantities of interest that can only be determined once weunderstand the physics behind heat transfer.The physics of heat transfer is based on the 1st Law ofThermodynamics: Energy is Conserved.steamWhere do we start?process streamheat exchangerprocess streamcondensate4 Faith A. Morrison, Michigan Tech U.2
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Where do we start?Let’s start here:How does energy behave?1. Conduction (Brownian process)2. Convection, Forced and Free/Natural(moves with moving matter)3. Radiation (carried by electromagnetic waves)4. Byproduct of Chemical Reaction5. Byproduct of Electrical Current6. Boundary layers (thermal)7. Is a byproduct of Pressure-Volume Work(compressibility)8. Is a byproduct of Viscous Dissipation9. Simultaneous heat and mass transfer5 Faith A. Morrison, Michigan Tech U.Where do we start?How does energy behave?Often it is not possibleto isolate heat transferfrom other physics1. Conduction (Brownian process)2. Convection, Forced and Free/Natural(moves with moving matter)3. Radiation (carried by electromagnetic waves)4. Byproduct of Chemical Reaction5. Byproduct of Electrical Current6. Boundary layers (thermal)7. Is a byproduct of Pressure-Volume Work(compressibility)8. Is a byproduct of Viscous Dissipation9. Simultaneous heat and mass transferSimultaneousheat andmomentumtransfer6 Faith A. Morrison, Michigan Tech U.3
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Where do we start?How does energy behave?1. Conduction (Brownian process)2. Convection, Forced and Free/Natural(moves with moving matter)3. Radiation (carried by electromagnetic waves)4. Byproduct of Chemical Reaction5. Byproduct of Electrical Current6. Boundary layers (thermal)7. Is a byproduct of Pressure-Volume Work(compressibility)8. Is a byproduct of Viscous DissipationAdvanced9. Simultaneous heat and mass transfer7 Faith A. Morrison, Michigan Tech U.Engineering Quantities of InterestWhat do we want to determine?From (momentum) we calculated:Engineering Quantities of Interest (fluids) Average velocity Volumetric flow rate Force on a surfaceFrom (energy) we calculate:Engineering Quantities of Interest (energy) Shaft Work Total heat transferred Rate of heat transfer8 Faith A. Morrison, Michigan Tech U.4
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Engineering Quantities of InterestWhat do we want to determine?From (momentum) we calculated:Engineering Quantities of Interest (fluids) Average velocity Volumetric flow rate Force on a surfaceAnd 𝑣 & 𝜏̃ distributions, whichthrough dimensional analysis,lead to data correlations forcomplex systems, includingchemical engineering unit opsFrom (energy) we calculate:Engineering Quantities of Interest (energy) Shaft Work Total heat transferred Rate of heat transferAnd 𝑇 distributions, which (see above)9 Faith A. Morrison, Michigan Tech U.steamWhere do we start?process streamheat exchangerprocess streamcondensateWe’ve already started.Recall from last year and earlier in the semester:10 Faith A. Morrison, Michigan Tech U.5
CM3110 Morrison Lecture 14-15 (Heat 1 2)Energy quantities of interest11/7/2019Recall from CM2110Steady State Macroscopic Energy BalancesClosed system energy nitial)Open system energy balanceΔ𝐸 Δ𝐸Δ𝐻 Multiple inlets and outlets (ΔSteady stateConstant density(out-in) Review:www.chem.mtu.edu/ fmorriso/cm310/Energy Balance Notes 2008.pdf11 Faith A. Morrison, Michigan Tech U.Closed system energy balanceΔ𝐸Recall from CM2110Δ𝐸Δ𝑈𝑄𝑊(final-initial)Open system energy balanceΔ𝐸Review: Δ𝐸Δ𝐻Multiple inlets and outlets (ΔSteady stateConstant density𝑄 𝑊,(out-in) www.chem.mtu.edu/ fmorriso/cm310/Energy Balance Notes 2008.pdf12 Faith A. Morrison, Michigan Tech U.6
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance(a type of steady, open system energy balance)We’ve already started.2. There are flow problems that can be addressedwith one type of macroscopic energy balance:The Mechanical Energy BalanceSee also fluidmechanics text,chapters 1 and 9Δp 2 WΔ v gΔz F s ,onm 2 p 2 p1 Assumptions:1.2.3.4.5.6.2 v 2 v2 𝐹21 g (z 2 z1 ) F21 frictionWs ,on ,21m single-input, single outputSteady stateConstant density (incompressible fluid)Temperature approximately constantNo phase change, no chemical reactionInsignificant amounts of heat transferred13 Faith A. Morrison, Michigan Tech U.Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy BalanceFor example:2Flow in Pipes20 ft75 ft18 fttankpumpID 3.0 in50 ft1.2.3.4.5.6.Single-input, single outputSteady stateConstant density (incompressible fluid)Temperature approximately constantNo phase change, no chemical reactionInsignificant amounts of heat transferredID 2.0 in40 ftMechanical EnergyBalance14 Faith A. Morrison, Michigan Tech U.7
CM3110 Morrison Lecture 14-15 (Heat 1 2)Energy quantities of interest11/7/2019Recall from CM2110 and CM3215:Mechanical Energy BalanceFor example:CentrifugalPumpssystemWhat flow rate doesa centrifugal pumpproduce?Answer: Dependson how much work itis asked to do.pumpvalve 50%openH ( ft )Calculate with theMechanical EnergyBalance(CM2110, CM2120,CM3215)valve fullopenH d , s (V )H 2,1 (V )V ( gal / min)15 Faith A. Morrison, Michigan Tech U.Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance16 Faith A. Morrison, Michigan Tech U.8
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance(Review)The Mechanical Energy BalanceΔp 2 WΔ v gΔz F s ,on2 m p 2 p1 2 v 2 v2 𝐹21 g (z 2 z1 ) F21 frictionWs ,on ,21m Where do we get this?This is the friction due to wall drag(straight pipes) and fittings and valves.17 Faith A. Morrison, Michigan Tech U.Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance(Review)The Mechanical Energy Balance – Friction TermThe friction has been measured and published in this form:Straight pipes:Fstraight pipes L v 4f D 22Use literature plot of fas a function ofReynolds NumberFittings and Valves:Ffittings,valvesv Kf22Use literature tablesof Kf for laminar andturbulent flow18 Faith A. Morrison, Michigan Tech U.9
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance𝐹friction(Review)Friction term in Mechanical Energy Balancelength ofstraight pipeFfrictionnumber of eachtype of fitting L v 4f K fi ni D i 2Note f is a functionof velocity)(from literature; theMoody chart)(see McCabe et al., orMorrison Chapter 1, or Perry’sChem Eng Handbook)friction-losscoefficients(from literature; seeMcCabe et al.,Geankoplis, orMorrison Chapter 1)2Note that frictionoverall is directly afunction of velocity)If the velocity changes within the system (e.g.pipe diameter changes), then we need differentfriction terms for each velocity Faith A. Morrison, Michigan Tech U.Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance(Review)Data are organized in terms of two dimensionless parameters:Reynolds NumberFlowrate vz DRe densityv z average velocityD pipe diameter viscosityP0 PL pressure dropFanning Friction Factor L pipe lengthPressureDrop1 P0 PL f 42 L 1 vz D 2 Faith A. Morrison, Michigan Tech U.10
CM3110 Morrison Lecture 14-15 (Heat 1 2)Energy quantities of interest11/7/2019Recall from CM2110 and CM3215:Mechanical Energy Balance Faith A. Morrison, Michigan Tech U.Energy quantities of interestRecall from CM2110 and CM3215:Mechanical Energy Balance22 Faith A. Morrison, Michigan Tech U.11
CM3110 Morrison Lecture 14-15 (Heat 1 2)Energy quantities of interest11/7/2019Recall from CM2110 and CM3215:Open system, steady, macroscopic energybalance on mechanical systems (a.k.a.)Mechanical Energy Balance, MEB1.2.3.4.5.6.7.single-input, single-outputsteady stateconstant density (incompressible fluid)temperature approximately constantNo phase changeNo chemical reactioninsignificant amounts of heat transferred23 Faith A. Morrison, Michigan Tech U.Energy quantities of interestRecall from CM2110 and CM3215:Open system, steady, macroscopic energybalance on mechanical systems (a.k.a.)Mechanical Energy Balance, MEB1.2.3.4.5.6.7.single-input, single-outputsteady stateconstant density (incompressible fluid)temperature approximately constantNo phase changeNo chemical reactioninsignificant amounts of heat transferred ReactorsSeparatorsHeatersDryers Although ChemEscare about thesemechanicalsystems, we careequally (or more?)about:EvaporatorsCoolersUnsteady statesComplex inflow/outflow 24 Faith A. Morrison, Michigan Tech U.12
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestEngineering Quantities of InterestWhat do we want to determine?From (momentum) we calculated:Where are we?Engineering Quantities of Interest (fluids) Average velocity Volumetric flow rate Force on the wallFrom (energy) we calculate:Engineering Quantities of Interest (energy) Shaft W ork Total heat transferred Rate of heat transferEngineering Quantities of Interest (energy) Shaft Work - MEBTotal heat transferred at steady state,steady macroscopic energy balance Rate of heat transfer Temperature fields (towards datacorrelations for complex systems)25 Faith A. Morrison, Michigan Tech U.Energy quantities of interestTo determine heat transfer rates and the related performance ofchemical engineering unit operations, we need knowledge of thetemperature field and the characteristics of unsteady heat flows for idealand complex engineering units.Energy quantities of interestEngineering Quantities of InterestWhat do we want to determine?Where are we?From (momentum) we calculated:Engineering Quantities of Interest (fluids) Average velocity Volumetric flow rate Force on the wallFrom (energy) we calculate:Engineering Quantities of Interest (energy) Shaft Work Total heat transferred Rate of heat transferEngineering Quantities of Interest (energy) Shaft Work - MEBTotal heat transferred at steady state,steady macroscopic energy balance Rate of heat transfer Temperature fields (towards datacorrelations for complex systems)26 Faith A. Morrison, Michigan Tech U.13
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestEngineeringQuantities ofInterest(energy)Rate of heattransfer,conductionTotal heatflow, generalTotal heatflow, pipe𝒬𝒬𝑞𝐴𝑞𝑛 𝑞𝑘Fourier’slaw𝑘 𝑇𝑑𝑆 𝑇 𝑟𝑅𝑑𝑧𝑑𝜃27 Faith A. Morrison, Michigan Tech U.Energy quantities of interestThe Plan (Heat Transfer)1. What is the general energy balance equation wewill use? Where does it come from? 2. Apply to steady macroscopic control volumes (CM2110) 3. Apply to single-input, single-output, etc.(MEB) (CM2120, CM3215)4. Apply to microscopic control volumes5. Transport law (Fourier’s law of Heat Conduction)(Unsteady, CM3120)6. Solve for temperature fields (steady)7. Calculate engineering quantities of interest(total heat transferred; heat transfer coefficient)8. Determine (with Dimensional Analysis)correlations for complex systems involving:a.b.c.d.Forced convectionFree convectionPhase changeRadiation28 Faith A. Morrison, Michigan Tech U.14
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019DONERecall from CM2110 2.Apply to steady macroscopic control volumesClosed system energy nitial)Open system energy balanceΔ𝐸 Δ𝐸Δ𝐻Multiple inlets and outlets (ΔSteady stateConstant density (out-in) Review:www.chem.mtu.edu/ fmorriso/cm310/Energy Balance Notes 2008.pdf29 Faith A. Morrison, Michigan Tech U.Recall from CM2110 and CM3215 3.DONEApply to single-input, single-output, etc.(MEB)The Mechanical Energy BalanceΔp 2 WΔ v gΔz F s ,on2 m p 2 p1Assumptions:1.2.3.4.5.6.𝐹 2 v 2 v2 21𝐹single-input, single outputSteady stateConstant density (incompressible fluid)Temperature approximately constantNo phase change, no chemical reactionInsignificant amounts of heat transferredfrictionFriction term in Mechanical Energy Balance(Review)frictionW g (z 2 z1 ) F21 s ,on ,21m length ofstraight pipeFfrictionnumber of eachtype of fitting L v 4f K fi ni D i 2Note f is a functionof velocity)(from literature; theMoody chart)(see McCabe et al., orMorrison Chapter 1, or Perry’sChem Eng Handbook)friction-losscoefficients(from literature; seeMcCabe et al.,Geankoplis, orMorrison Chapter 1)If the velocity changes within the system (e.g.pipe diameter changes), then we need differentfriction terms for each velocity2Note that frictionoverall is directly afunction of velocity)(Where did all this comefrom? We saw in Part 1:dimensional analysis.)30 Faith A. Morrison, Michigan Tech U.15
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestThe Plan (Heat Transfer)1. What is the general energy balance equation wewill use? Where does it come from?2.3.Apply to steady macroscopic control volumesApply to single-input, single-output, etc.(MEB)DONE4.5.6.7.Apply to microscopic control volumesTransport law (Fourier’s law of Heat Conduction)(Unsteady, CM3120)Solve for temperature fields (steady)Calculate engineering quantities of interest(total heat transferred; heat transfer coefficient)8. Determine (with Dimensional Analysis)correlations for complex systems involving:a.b.c.d.Forced convectionFree convectionPhase changeRadiation31 Faith A. Morrison, Michigan Tech U.Energy quantities of interestLet’s Begin.Energy quantities of interestThe Plan (Heat Transfer)1. What is the general energy balance equation wewill use? Where does it come from?2.3.Apply to steady macroscopic control volumesApply to single-input, single-output, etc.(MEB)DONE4.5.6.7.Apply to microscopic control volumesTransport law (Fourier’s law of Heat Conduction)(Unsteady, CM3120)Solve for temperature fields (steady)Calculate engineering quantities of interest(total heat transferred; heat transfer coefficient)8. Determine (with Dimensional Analysis)correlations for complex systems involving:a.b.c.d.Forced convectionFree convectionPhase changeRadiation321. and 4. What is the general energy balanceequation for microscopic control volumes,and where does it come from? Faith A. Morrison, Michigan Tech U.16
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019What is the general energy balance equation and where does it come from?First Law ofThermodynamics:𝑑𝐸𝑑𝑡(on a body)First Law ofThermodynamics:(on a control ���𝑊,𝑪𝑽,𝑛 𝑣 𝜌𝐸 𝑑𝑆the usual convective term:net energy convected inReference for derivation: Morrison, F. A., Web Appendix D1: Microscopic EnergyBalance, Supplement to An Introduction to Fluid Mechanics (Cambridge, 2013),www.chem.mtu.edu/ fmorriso/IFM WebAppendixD2011.pdf33 Faith A. Morrison, Michigan Tech U.What is the general energy balance equation and where does it come from?First Law ofThermodynamics:(on a control volume) 𝐸 𝑡𝑛 𝑣 𝜌𝐸 𝑑𝑆𝑄,𝑊, Microscopic CV:𝜌𝑑𝐸𝑑𝑡𝑣 𝐸 𝑞𝑆Heat into CV due to conductionand reaction electrical current 𝑃𝑣 𝜏̃ 𝑣-Work by the fluid in the CVdue to pressure/volume workand viscous dissipation34 Faith A. Morrison, Michigan Tech U.17
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019What is the general energy balance equation and where does it come from?First Law ofThermodynamics:(on a control volume)𝑑𝐸𝑑𝑡𝑛 𝑣 𝜌𝐸 𝑑𝑆 𝐸 𝑡𝑊,, Microscopic CV:𝜌𝑄𝑣 𝐸 𝑞𝑆 𝑃𝑣Heat into CV due to conductionand reaction electrical current 𝜏̃ 𝑣-Work by the fluid in the CVdue to pressure/volume workand viscous dissipationIn heat-transfer unit operations, 𝑃𝑉 work andviscous dissipation are usually negligible35 Faith A. Morrison, Michigan Tech U.What is the general energy balance equation and where does it come from?First Law ofThermodynamics:(on a control volume, nowork)𝜌 𝐸 𝑡𝑣 𝐸 𝑞𝑆rate of net energy net heat net heat in, in, energy v flow out energy accumulation (convection ) conduction production conduction Fourier’s law𝑞 𝑞𝐴𝑘 𝑇e.g.chemicalreaction,electricalcurrent36 Faith A. Morrison, Michigan Tech U.18
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019What is the general energy balance equation and where does it come from?First Law ofThermodynamics:(on a control volume, nowork)𝜌 𝐸 𝑡𝑣 𝐸 𝑞𝑆rate of net energy net heat net heat in, in, energy v flow out energy accumulation (convection ) conduction production conduction Fourier’s lawNote the twodifferent 𝑞’s(watch units)𝑞 𝑞𝐴𝑘 𝑇e.g.chemicalreaction,electricalcurrent37 Faith A. Morrison, Michigan Tech U.What is the general energy balance equation and where does it come from?First Law ofThermodynamics:(on a control volume, nowork)𝜌 𝐸 𝑡𝑣 𝐸 𝑞𝑆rate of net energy net heat net heat in, in, energy v flow out energy accumulation (convection ) conduction production Other energycontributions willenter through theboundaryconditions.conduction Fourier’s law𝑞 𝑞𝐴𝑘 𝑇e.g.chemicalreaction,electricalcurrent38 Faith A. Morrison, Michigan Tech U.19
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Energy quantities of interestEnergy quantities of interestContinuing The Plan (Heat Transfer)1. What is the general energy balance equation wewill use? Where does it come from?2.3.Apply to steady macroscopic control volumesApply to single-input, single-output, etc.(MEB)DONE4.5.6.7.Apply to microscopic control volumesTransport law (Fourier’s law of Heat Conduction)(Unsteady, CM3120)Solve for temperature fields (steady)Calculate engineering quantities of interest(total heat transferred; heat transfer coefficient)8. Determine (with Dimensional Analysis)correlations for complex systems involving:a.b.c.d.Forced convectionFree convectionPhase changeRadiation395. What is the energy transport law? Faith A. Morrison, Michigan Tech U.Transport law (Fourier’s law of Heat Conduction)viscosityPart I: Momentum TransferMomentum transfer:𝜏𝜏̃momentum flux𝜇𝑑𝑣𝑑𝑥velocity gradientPart II: Heat Transferthermal conductivityHeat transfer:qxdT kAdxheat fluxtemperaturegradient40 Faith A. Morrison, Michigan Tech U.20
CM3110 Morrison Lecture 14-15 (Heat 1 2)11/7/2019Transport law (Fourier’s law of Heat Conduction)viscosityPart I: Momentum TransferMomentum transfer:𝜏𝜏̃momentum flux𝜇𝑑𝑣𝑑𝑥Newton’slaw ofviscosityvelocity gradientPart II: Heat Transferthermal conductivityHeat transfer:qxdT kAdxheat fluxFourier’s lawof heatconductiontemperaturegradient41 Faith A. Morrison, Michigan Tech U.Transport law (Fourier’s law of Heat Conduction)viscosityPart I: Momentum TransferMomentum transfer:𝜏𝜏̃How was this “law”determined?momentum flux𝜇𝑑𝑣𝑑𝑥Newton’slaw ofviscosityvelocity gradientPart II: Heat Transferthermal conductivityHeat transfer:qxdT kAdxheat fluxFourier’s lawof heatconductiontemperaturegradient42 F
CM2120—Fundamentals of ChemE 2 (Steady Unit Operations Introduction, MEB) CM3110—Transport/Unit Ops 1 (Momentum & Steady Heat Transport, Unit Operations) CM3120—Transport/Unit Ops 2 (Unsteady Heat Transport, Mass Transport, Unit Operations . (Heat 1 2) 11/7/2019 14
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2.12 Two-shells pass and two-tubes pass heat exchanger 14 2.13 Spiral tube heat exchanger 15 2.14 Compact heat exchanger (unmixed) 16 2.15 Compact heat exchanger (mixed) 16 2.16 Flat plate heat exchanger 17 2.17 Hairpin heat exchanger 18 2.18 Heat transfer of double pipe heat exchanger 19 3.1 Project Flow 25 3.2 Double pipe heat exchanger .
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heat, a heat pump can supply heat to a house even on cold winter days. In fact, air at -18 C contains about 85 percent of the heat it contained at 21 C. An air-source heat pump absorbs heat from the outdoor air in winter and rejects heat into outdoor air in summer. It is the most common type of heat pump found in Canadian homes at this time.
