Heat Transfer Fundamentals & Equipment (Supplemental Chapter 9)
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1 Heat Transfer Fundamentals & Equipment (Supplemental Chapter 9) Tpics Fundamentals f heat transfer & exchange Heat transfer acrss bundaries Cnductin Cnvectin Radiatin Cupled with internal energy changes Sensible heat effects Phase change Equipment heat exchangers Cmbines infrmatin abut fluid flw & heat transfer acrss internal bundaries Cnsideratins When d I need t knw the specifics f the heat exchange cnfiguratin? Hw is the heat transfer area related t the utlet temperatures? What is the difference between in-tank heat exchange & an external heat exchanger? 2 1
2 Heat Transfer Mdes f heat transfer Cnductin Flw f heat thrugh material with n bulk mvement f the material itself Usually thught f thrugh slid but can als be thrugh a stagnant fluid In general q kt and U kt t Integrated steady-state versin fr flat sld: Q Tht Tcld k A x thrugh a circular pipe: Q 2 kt ht Tcld L lnd Di Q DLM Tht Tcld k A D x ˆ 3 Heat Transfer Mdes f heat transfer Cnvectin Equatin f change fr internal energy includes cnvective effect t Uˆ Uˆ v q p v : v Include terms fr Cnvective transprt Cnductive energy transfer Reversible energy transfrmatin frm cmpressin effects Irreversible energy transfrmatin frm viscus effects 4 2
3 Heat Transfer Mdes f heat transfer Bundary cnditins t relate flw f heat t/frm fluid frm the heat transfer surface Cnvectin Flw f heat assciated with fluid mvement natural & frced cnvectin Q ht ht T A cld Radiatin Heat transferred via electrmagnetic radiatin Q 4 4 Tht Tcld A 2 2 T ht Tcld Tht Tcld Tht Tcld 5 Heat Exchangers Sme Basics Fcus is n the system t have heat flw frm the ht fluid(s) t the cld fluid(s) usually withut direct cntact Use bulk flw parameters t relate the heat cnductin acrss the flw barrier t the change in energy f the ht & cld fluids Accunt fr the series f resistances t heat transfer between the ht & cld fluids Heat exchangers Heat t & frm flwing fluids thrugh impermeable barrier(s) Driving frce fr heat thrugh barriers is the temperature difference between the tw fluids n ppsite sides f the barrier Relate the heat effects in the flwing fluids t the change in enthalpy Often this can be related t the difference in the inlet & utlet temperatures fr the fluids ˆ ˆ Q m Hˆ Hˆ Q m C T T ˆ fr cnstant C Q m Hˆ Hˆ Q m C T T fr cnstant Cˆ H H H in H ut H H p H H in H ut p H C C Cut Cin C C pc Cut Cin pc 6 3
4 Heat Exchangers Sme Basics Relate the heat acrss the barrier t the temperature difference acrss the barrier d Q / L dx THin TCut U T T Q UA T T h c h c AREA AVERAGED It can be shwn that fr many typical cnfiguratins the AREA AVERAGED temperature difference is the LMTD (Lg Mean Temperature Difference) TH(x) TC(x) x THut TCin where Q UA T T TH TC TH TC LM LM 0 C0 TH T ln TH T 1 C1 7 Heat Exchangers Sme Basics LMTD is a prescribed calculatin calculating the LMTD frm the prcedure is always crrect. LMTD T T T 1 ln T LMTD is apprpriate fr use as the area averaged temperature difference when temperature vs. heat released/absrbed is a straight line 1-1 c-current & cunter-current flw and Bth ht & cld sides have a cnstant heat r Only pure cmpnent phase change n ne side r the ther (n subcling r superheating) 8 4
5 Heat Exchangers Sme Basics Heat exchanger cnfiguratins C-Current vs. Cunter-Current vs. Crss-Current flws Cunter-current flw allws the utlet temperatures t apprach mre clsely t the inlet temperature f the ther fluid Crss-current flw is cmplicated & requires knwledge f the actual flw patterns Heat exchangers Industrial Heat Exchangers Industrial heat exchangers have a cmbinatin f heat transfer thrugh multiple barriers and a cmbinatin f cunter-current & c-current flw LMTD must be crrected t give the actual area-averaged temperature difference (i.e. driving frce) 9 Heat Exchanger Example 1 Given the heat exchanger cnfiguratin shwn Determine duty & unknwn temperature if cunter-current flw c-current flw These values d nt depend n the flw cnfiguratin Duty frm the cld side Q m C T T C p C C ut C in kcal/h Ht side utlet temperature t clse energy balance Q Qm HCpH THut THin THut THin mc H p H C Feed 5127 kg/h 1 kcal/kg C 20 C??? C 50 C Heat Medium 4749 kg/h 0.8 kcal/kg C 100 C 10 5
6 Heat Exchanger Example 2 Given the heat exchanger cnfiguratin shwn Determine LMTD if cunter-current flw LMTD if c-current flw Cunter-current flw LMTD C-current flw LMTD ln ln C 35.7 C Feed 5127 kg/h 1 kcal/kg C 20 C 61.9 C 50 C Heat Medium 4749 kg/h 0.8 kcal/kg C 100 C 11 Heat Exchangers Cmplicated Flw Many industrial heat exchangers have cmplicated flw paths cnsisting f multiple shell & tube passes The area-averaged temperature difference has needs t include cnfiguratin infrmatin Fr example a 1-2 (1 shell & 2 tube passes) exchanger cmbines bth cunter & ccurrent flw The fluid in the shell pass transfers heat separately t the tw tube banks Ref: GPSA Data Bk 13 th ed. 12 6
7 Heat Exchangers Cmplicated Flw 1-2 exchanger calculatins require a cnfiguratin crrectin t relate the area-averaged temperature difference t the LMTD Base the LMTD n cunter-current flw & apply crrectin t this F P R 1ln 1 RP 2 2PR 1 R 1 R 1ln 2 2 PR 1 R 1 Ref: Kern Prcess Heat Transfer McGraw-Hill 1965 Ref: GPSA Data Bk 13 th ed. 13 Heat Exchanger Example 2 Given the heat exchanger cnfiguratin shwn as a 1-2 shell & tube exchanger Determine Crrected LMTD if ht stream n the shell side Crrected LMTD if cld stream n the shell side Fr bth cases LMTD fr pure cunter-current flw LMTD ln C Feed 5127 kg/h 1 kcal/kg C 20 C 61.9 C 50 C Heat Medium 4749 kg/h 0.8 kcal/kg C 100 C 14 7
8 Heat Exchanger Example 2 Ht stream n the shell side t2 t P T t T1T R 1.27 t t P R 1ln 1 RP F PR 1 R 1 R 1ln 2 2 PR 1 R 1 CMTD F LMTD C Ref: GPSA Data Bk 13 th ed. 15 Heat Exchanger Example 2 Cld stream n the shell side t2 t P T t T1T R t t P R 1ln 1 RP F PR 1 R 1 R 1ln 2 2 PR 1 R 1 CMTD F LMTD C Ref: GPSA Data Bk 13 th ed. 16 8
9 Heat Transfer What if there is pure cmpnent phase change? If there is nly phase change then the LMTD is still the apprpriate areaaveraged temperature difference If there is superheating and/r subcling the situatin is mre cmplicated Fr a pure cmpnent nly with phase change The temperature will remain cnstant The heat released/absrbed will be related t the enthalpy f phase change at the exchanger cnditins (pressure & temperature) Q m Hˆ H H vap Since the temperature vs. heat released/absrbed curve is a straight line then the LMTD is apprpriate fr the area-averaged temperature difference 17 Heat Exchanger Example 3 This time prvide the heat by cndensing saturated 50 psig steam (4.46 bar-a C/297.7 F ΔH vap = kcal/kg) Determine duty steam flwrate & LMTD Duty frm the cld side C p C C ut C in Q m C T T kcal/h Ht side utlet temperature t clse energy balance Q QmHHvap mh Hvap kg/h Feed 5127 kg/ h 1 kcal/kg C 20 C C 50 C Heat Medium Sat Steam???? kg/h kcal/kg C 18 9
10 Heat Exchanger Example 3 LMTD? Since the steam has a cnstant temperature it des nt matter whether it is cnsider c-current r cunter-current LMTD ln C Feed 5127 kg/ h 1 kcal/kg C 20 C C 50 C Heat Medium Sat Steam???? kg/h kcal/kg C 19 Heat Transfer What if there are cils in a wellmixed tank? An ideal well-mixed tank has then same temperature at any pint in the tank it is the same as the utlet temperature frm the tank The utside f the cils will experience this single temperature Since the temperature is cnstant it will lead t the applicability f the LMTD as the area-averaged temperature difference 20 10
11 Heat Exchanger Example 4 Given the heat cil cnfiguratin in a well mixed tank Determine LMTD The utside f the cils experience a single temperature that f the utlet LMTD ln C Feed 5127 kg/ h 1 kcal/kg C 20 C 50 C Heat Medium 4749 kg/ h 0.75 kcal/kg C 100 C 61.9 C 21 Heat Transfer Sme Basics Thermal resistances are added when in series Can be cmbined int an verall heat transfer cefficient Acrss a flat plate (i.e. cnstant crss sectinal area) 1 1 L 1 U h k h i Fr radial heat transfer (e.g. thrugh the wall f a tube) must als take int accunt the change in area with respect t radius Overall heat transfer cefficient must als be related t a reference area r diameter 1 1 L 1 UA ha i i kaave ha 1 1 A L A D D D 1 ln U hi Ai k Aave h hi Di k Di h 22 11
12 Typical Film Cefficients Biprcess Engineering Principles 2 nd ed Pauline Dran Elsevier Science & Technlgy Cpyright 2012 Elsevier Inc. All rights Reserved. 23 Heat Transfer Crrelatins fr Film Cefficients Flw in tubes with n phase change hd D v C NNu NRe NPr p k k When there is a significant difference between wall & bulk fluid b hd D v Cp b NNu NRe NPr w k k w Stirred liquids heat transfer frm cil frm tank jacket b hd ND C i i p b NNu 0.9 NRe i NPr 0.9 w k k w b hd ND C i i p b NNu 0.36 NRe i NPr 0.36 w k k w
13 Heat Transfer What if we have fuling f the heat transfer surface(s)? Add fuling int the sum f thermal resistances Acrss a flat plate (i.e. cnstant crss sectinal area) 1 1 L 1 1 L Rfi Rf U h k h h k h h h i i f i f Over a radial tube 1 1 D 2D D 1 1 D 1 ln U hi Di k Di h hf i Di hf 25 Typical Fuling Cefficients Biprcess Engineering Principles 2 nd ed Pauline Dran Elsevier Science & Technlgy Cpyright 2012 Elsevier Inc. All rights Reserved
14 Heat Exchanger Design Cmbine prcess cnsideratins (flw rates temperatures prperties f fluids) with the cnfiguratin t btain the areaaveraged temperature difference (usually the LMTD) Determine the required UA Q QUAT UA LM T LM Determine the verall heat transfer cefficient & determine the required area Heat transfer area usually assciated with the bare utside area f the tubes 27 Heat Exchanger Example 5 Given a batch 35 C that is generating 15.5 kw heat t be remved by cling water (15 C heated t 25 C) The verall heat transfer cefficient is 340 W/m 2 K. Determine LMTD? Hw much heat transfer area is needed? What length f 4 cm diameter stainless steel pipe is needed t prvide this area? LMTD ln C Q UA T A 3.16 m 2 LM A 3.16 A DL L 25.1 m D 0.04 Cling Water??? kg/h 1 kcal/kg C 15 C 35 C 15.5 kw 25 C 28 14
15 Heat Exchangers What if there is phase change and sensible heat change? Superheating and/r subcling with phase change gives a cmplicated heat exchange situatin & LMTD is n lnger the applicable area-averaged temperature difference Each zne will generally have different film cefficients leading t different verall heat transfer cefficients Best t treat as sequential heat exchangers 29 Heat Exchangers What if there is phase change and sensible heat change? Bigger issue if there is superheated vapr fllwed by cndensatin Internal pinch pint will limit the ΔT driving frce May even have a crss ver design will nt wrk as intended! 30 15
16 Summary Analysis f heat exchangers builds n the understanding f the basics f heat transfer by cnductin cnvectin and/r radiatin Different cnfiguratins will lead t different areaaveraged temperature differences leading t different required heat transfer areas Typically the LMTD Stirred vessels will have a single temperature against the heat transfer area
17 Supplemental Slides Typical Tank Heating Cnfiguratins Biprcess Engineering Principles 2 nd ed Pauline Dran Elsevier Science & Technlgy Cpyright 2012 Elsevier Inc. All rights Reserved
18 Shell & Tube Heat Exchangers 35 Shell & Tube Heat Exchangers Shell side Baffles used in the shell side t minimize channeling Tube side Maniflds allw fr even distributin f fluids int the tubes & cllectin/mixing f fluids ut f the tubes Multiple tube passes make it easier t pull the tube bundle fr maintenance/cleaning and have better allwance fr thermal expansin effects Fig. 3.6 Fundamentals f Natural Gas Prcessing 2 nd ed. Kidnay Parrish & McCartney
19 Shell and Tube Heat Exchangers (Types) Ref: GPSA Data Bk 13 th ed. 37 Kettle Rebiler Shell & tube heat exchanger with the tubes submerged in biling liquid n the shell side Main resistance t heat transfer is n the tube side since biling is ccurring n the shell side Fig. 3.7 Fundamentals f Natural Gas Prcessing 2 nd ed. Kidnay Parrish & McCartney
20 Air Cled Heat Exchangers Fans either push air thrugh (frced draft) r pull air thrugh (induced draft) tube bundle Can cntrl the air flw rate either with a variable speed mtr r with luviers Fig. 3.8 Fundamentals f Natural Gas Prcessing 2 nd ed. Kidnay Parrish & McCartney Plate Frame Heat Exchangers Psitives Lw cst Cmpact high area per weight & vlume Can get very clse apprach temperatures (5 F r lwer) Can be disassembled t clean Negative cnsideratins Limited maximum allwable wrking pressure Susceptible t plugging Fig. 3.9 Fundamentals f Natural Gas Prcessing 2 nd ed. Kidnay Parrish & McCartney
21 Tank Heaters Integrated int existing equipment (i.e. tanks r vessels) Ref: GPSA Data Bk 13 th ed. 41 Air-Cled Exchangers Fundamentals Air cled exchangers cl fluids with ambient air Seasnal variatin can greatly impact perfrmance Utilize finned tube in increase heat transfer surface area
22 Air-Cled Exchangers Types Hrizntal air-cled exchangers One r mre tube sectins served by ne r mre axial flw fans An enclsing / supprting structure. Classified as frced draft r induced draft depending n the tube/fam lcatin EDB Pgs 10-2 t 10-4 Basic design cnsideratins Layut f tubes / fans EDB Fig 10-3 Typical tube and fan sizes / selectin Header design EDB Fig 10-5 Air-Cled Exchangers Types Frced Draft vs. Induced Draft Advantages: Slightly lwer hrsepwer Better maintenance accessibility Easily adaptable fr warm air recirculatin Mst cmmn in gas industry Advantages Better distributin f air Less pssibility f air recirculatin Less effect f sun rain r hail Increased capacity in the event f fan failure 22
23 Air-Cled Exchanger Thermal Design ( Temperature CMTD Figs 10-8 & 9) F ~ 1.0 fr 3+ Over/Under Passes Cling Twer Principles Evaprative cling (Psychrmetry) Dry Bulb versus Wet Bulb Temperature Cntact dry air with water Saturatin f air (vaprizatin f sme water) takes energy Air is cled belw ambient t Wet Bulb temperature Takes advantage f air belw 100% humidity Wet Bulb MUST be lwer than Dry Bulb temperature 23
24 Cling Twer Principles Evaprative cling (Psychrmetry) Wet bulb and dry bulb data fr varius lcatins arund the wrld Fig 11-3 Example: Hw cld can yu get? Air temperature: 95 F RH = 65% Temperature with cling twer? Temperature with air cler? Wet bulb=84 F 24
25 Cling Twers Mechanical Induced Draft Cling Twers Mechanical Frced Draft Twertechinc.cm 25
26 Cling Twers Wet Surface Air Cler Heat Exchanger Example S-1 Exchanger duty & ht fluid utlet temperature determined frm energy balance arund exchanger Qm ˆ ccp c Tc ut Tc in Btu/hr Q Thut Thin F mc ˆ h p h Determinatin f UA requires cnfiguratin infrmatin 1-1 cunter-current flw 1-1 c-current flw T 85.1 F T LMTD ln F LMTD ln Q Btu UA T 85.1 hr F LMTD Q Btu UA T 55.4 hr F LMTD 52 26
27 Heat Exchanger Example S exchanger T 85.1 F LMTD ln P R F 0.86 (frm chart) 2 Q UA F T 2 LMTD Btu hr F Ref: GPSA Data Bk 13 th ed. 53 Heat Exchanger Example S
28 Heat Exchanger Example S-1 Representatin f temperature prfiles with cmbined flw becmes mre cmplicated
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