Heat Chap13095.docx

Heat Chap13095.docx

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HeatChap13095

13-95Coldwaterisheatedbyhotwaterinaheatexchanger.Thenetrateofheattransferandtheheattransfersurfaceareaoftheheatexchangeraretobedetermined.

Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.5Thethicknessofthetubeisnegligible.

PropertiesThespecificheatsofthecoldandhotwateraregiventobe4.18and4.19kJ/kg.C,respectively.

AnalysisTheheatcapacityratesofthehotandcoldfluidsare

Therefore,

and

Thenthemaximumheattransferratebecomes

Theactualrateofheattransferis

Thentheeffectivenessofthisheatexchangerbecomes

TheNTUofthisheatexchangerisdeterminedusingtherelationinTable13-5tobe

Thenthesurfaceareaoftheheatexchangerisdeterminedfrom

13-96"!

PROBLEM13-96"

"GIVEN"

T_cw_in=15"[C]"

T_cw_out=45"[C]"

m_dot_cw=0.25"[kg/s]"

C_p_cw=4.18"[kJ/kg-C]"

T_hw_in=100"[C],parametertobevaried"

m_dot_hw=3"[kg/s]"

C_p_hw=4.19"[kJ/kg-C]"

"U=0.95[kW/m^2-C],parametertobevaried"

"ANALYSIS"

"WithEES,itiseasiertosolvethisproblemusingLMTDmethodthanNTUmethod.Below,weuseLMTDmethod.Bothmethodsgivethesameresults."

DELTAT_1=T_hw_in-T_cw_out

DELTAT_2=T_hw_out-T_cw_in

DELTAT_lm=（DELTAT_1-DELTAT_2）/ln（DELTAT_1/DELTAT_2）

Q_dot=U*A*DELTAT_lm

Q_dot=m_dot_hw*C_p_hw*（T_hw_in-T_hw_out）

Q_dot=m_dot_cw*C_p_cw*（T_cw_out-T_cw_in）

Thw,in[C]

Q[kW]

A[m2]

60

31.35

1.25

65

31.35

1.038

70

31.35

0.8903

75

31.35

0.7807

80

31.35

0.6957

85

31.35

0.6279

90

31.35

0.5723

95

31.35

0.5259

100

31.35

0.4865

105

31.35

0.4527

110

31.35

0.4234

115

31.35

0.3976

120

31.35

0.3748

U[kW/m2-C]

Q[kW]

A[m2]

0.75

31.35

0.6163

0.8

31.35

0.5778

0.85

31.35

0.5438

0.9

31.35

0.5136

0.95

31.35

0.4865

1

31.35

0.4622

1.05

31.35

0.4402

1.1

31.35

0.4202

1.15

31.35

0.4019

1.2

31.35

0.3852

1.25

31.35

0.3698

13-97Glycerinisheatedbyethyleneglycolinaheatexchanger.Massflowratesandinlettemperaturesaregiven.Therateofheattransferandtheoutlettemperaturesaretobedetermined.

Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.5Thethicknessofthetubeisnegligible.

PropertiesThespecificheatsoftheglycerinandethyleneglycolaregiventobe2.4and2.5kJ/kg.C,respectively.

Analysis（a）Theheatcapacityratesofthehotandcoldfluidsare

Therefore,

and

Thenthemaximumheattransferratebecomes

TheNTUofthisheatexchangeris

EffectivenessofthisheatexchangercorrespondingtoC=0.96andNTU=2.797isdeterminedusingtheproperrelationinTable13-4

Thentheactualrateofheattransferbecomes

（b）Finally,theoutlettemperaturesofthecoldandthehotfluidstreamsaredeterminedfrom

13-98Waterisheatedbyhotairinacross-flowheatexchanger.Massflowratesandinlettemperaturesaregiven.Therateofheattransferandtheoutlettemperaturesaretobedetermined.

Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.5Thethicknessofthetubeisnegligible.

PropertiesThespecificheatsofthewaterandairaregiventobe4.18and1.01kJ/kg.C,respectively.

AnalysisThemassflowratesofthehotandthecoldfluidsare

Theheattransfersurfaceareaandtheheatcapacityratesare

Therefore,

and

TheNTUofthisheatexchangeris

Notingthatthisheatexchangerinvolvesmixedcross-flow,thefluidwith

ismixed,

unmixed,effectivenessofthisheatexchangercorrespondingtoC=0.2794andNTU=0.02967isdeterminedusingtheproperrelationinTable13-4tobe

Thentheactualrateofheattransferbecomes

Finally,theoutlettemperaturesofthecoldandthehotfluidstreamsaredeterminedfrom

13-99Ethylalcoholisheatedbywaterinashell-and-tubeheatexchanger.TheheattransfersurfaceareaoftheheatexchangeristobedeterminedusingboththeLMTDandNTUmethods.

Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.

PropertiesThespecificheatsoftheethylalcoholandwateraregiventobe2.67and4.19kJ/kg.C,respectively.

Analysis（a）Thetemperaturedifferencesbetweenthetwofluidsatthetwoendsoftheheatexchangerare

Thelogarithmicmeantemperaturedifferenceandthecorrectionfactorare

Therateofheattransferisdeterminedfrom

Thesurfaceareaofheattransferis

（b）Therateofheattransferis

Themassflowrateofthehotfluidis

Theheatcapacityratesofthehotandthecoldfluidsare

Therefore,

and

Thenthemaximumheattransferratebecomes

Theeffectivenessofthisheatexchangeris

TheNTUofthisheatexchangercorrespondingtothisemissivityandC=0.78isdeterminedfromFig.13-26dtobeNTU=1.7.Thenthesurfaceareaofheatexchangerisdeterminedtobe

Thesmalldifferencebetweenthetworesultsisduetothereadingerrorofthechart.

13-100Steamiscondensedbycoolingwaterinashell-and-tubeheatexchanger.Therateofheattransferandtherateofcondensationofsteamaretobedetermined.

Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.5Thethicknessofthetubeisnegligible.

PropertiesThespecificheatofthewaterisgiventobe4.18kJ/kg.C.Theheatofcondensationofsteamat30Cisgiventobe2430kJ/kg.

Analysis（a）Theheatcapacityrateofafluidcondensinginaheatexchangerisinfinity.Therefore,

andC=0

Thenthemaximumheattransferratebecomes

and

TheNTUofthisheatexchanger

ThentheeffectivenessofthisheatexchangercorrespondingtoC=0andNTU=6.76isdeterminedusingtheproperrelationinTable13-5

Thentheactualheattransferratebecomes

（b）Finally,therateofcondensationofthesteamisdeterminedfrom

13-101"!

PROBLEM13-101"

"GIVEN"

N_pass=8

N_tube=50

T_steam=30"[C],parametertobevaried"

h_fg_steam=2430"[kJ/kg]"

T_w_in=15"[C]"

m_dot_w=1800/Convert（kg/s,kg/h）"[kg/s]"

C_p_w=4.18"[kJ/kg-C]"

D=1.5"[cm],parametertobevaried"

L=2"[m]"

U=3"[kW/m^2-C]"

"ANALYSIS"

"WithEES,itiseasiertosolvethisproblemusingLMTDmethodthanNTUmethod.Below,weuseNTUmethod.Bothmethodsgivethesameresults."

"（a）"

C_min=m_dot_w*C_p_w

C=0"sincetheheatcapacityrateofafluidcondensingisinfinity"

Q_dot_max=C_min*（T_steam-T_w_in）

A=N_pass*N_tube*pi*D*L*Convert（cm,m）

NTU=（U*A）/C_min

epsilon=1-exp（-NTU）"fromTable13-4ofthetextwithC=0"

Q_dot=epsilon*Q_dot_max

"（b）"

Q_dot=m_dot_cond*h_fg_steam

Tsteam[C]

Q[kW]

mcond[kg/s]

20

10.45

0.0043

22.5

15.68

0.006451

25

20.9

0.008601

27.5

26.12

0.01075

30

31.35

0.0129

32.5

36.58

0.01505

35

41.8

0.0172

37.5

47.03

0.01935

40

52.25

0.0215

42.5

57.47

0.02365

45

62.7

0.0258

47.5

67.93

0.02795

50

73.15

0.0301

52.5

78.38

0.03225

55

83.6

0.0344

57.5

88.82

0.03655

60

94.05

0.0387

62.5

99.27

0.04085

65

104.5

0.043

67.5

109.7

0.04515

70

114.9

0.0473

D[cm]

Q[kW]

mcond[kg/s]

1

31.35

0.0129

1.05

31.35

0.0129

1.1

31.35

0.0129

1.15

31.35

0.0129

1.2

31.35

0.0129

1.25

31.35

0.0129

1.3

31.35

0.0129

1.35

31.35

0.0129

1.4

31.35

0.0129

1.45

31.35

0.0129

1.5

31.35

0.0129

1.55

31.35

0.0129

1.6

31.35

0.0129

1.65

31.35

0.0129

1.7

31.35

0.0129

1.75

31.35

0.0129

1.8

31.35

0.0129

1.85

31.35

0.0129

1.9

31.35

0.0129

1.95

31.35

0.0129

2

31.35

0.0129

13-102Coldwaterisheatedbyhotoilinashell-and-tubeheatexchanger.TherateofheattransferistobedeterminedusingboththeLMTDandNTUmethods.

Assumptions1Steadyoperatingconditionsexist.2Theheatexchangeriswell-insulatedsothatheatlosstothesurroundingsisnegligibleandthusheattransferfromthehotfluidisequaltotheheattransfertothecoldfluid.3Changesinthekineticandpotentialenergiesoffluidstreamsarenegligible.4Theoverallheattransfercoefficientisconstantanduniform.

PropertiesThespecificheatsofthewaterandoilaregiventobe4.18and2.2kJ/kg.C,respectively.

Analysis（a）TheLMTDmethodinthiscaseinvolvesiterations,whichinvolvesthefollowingsteps:

1）Choose

2）Calculate

from

3）