Heat Chap03064Word下载.docx

Heat Chap03064Word下载.docx

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.Theoutersurfaceofthetankisblackandthusitsemissivityis=1.

Analysis（a）Theinnerandtheoutersurfaceareasofsphereare

WeassumetheoutersurfacetemperatureT2tobe5°

Caftercomparingconvectionheattransfercoefficientsattheinnerandtheoutersurfacesofthetank.Withthisassumption,theradiationheattransfercoefficientcanbedeterminedfrom

Theindividualthermalresistancesare

Thenthesteadyrateofheattransfertotheicedwaterbecomes

（b）Thetotalamountofheattransferduringa24-hourperiodandtheamountoficethatwillmeltduringthisperiodare

Check:

Theoutersurfacetemperatureofthetankis

whichisveryclosetotheassumedtemperatureof5Cfortheoutersurfacetemperatureusedintheevaluationoftheradiationheattransfercoefficient.Therefore,thereisnoneedtorepeatthecalculations.

3-68Asteampipecoveredwith3-cmthickglasswoolinsulationissubjectedtoconvectiononitssurfaces.Therateofheattransferperunitlengthandthetemperaturedropsacrossthepipeandtheinsulationaretobedetermined.

Assumptions1Heattransferissteadysincethereisnoindicationofanychangewithtime.2Heattransferisone-dimensionalsincethereisthermalsymmetryaboutthecenterlineandnovariationintheaxialdirection.3Thermalconductivitiesareconstant.4Thethermalcontactresistanceattheinterfaceisnegligible.

PropertiesThethermalconductivitiesaregiventobek=15W/m°

Cforsteelandk=0.038W/m°

Cforglasswoolinsulation

AnalysisTheinnerandtheoutersurfaceareasoftheinsulatedpipeperunitlengthare

Thenthesteadyrateofheatlossfromthesteamperm.pipelengthbecomes

Thetemperaturedropsacrossthepipeandtheinsulationare

3-69

"

GIVEN"

T_infinity_1=320"

[C]"

T_infinity_2=5"

k_steel=15"

[W/m-C]"

D_i=0.05"

[m]"

D_o=0.055"

r_1=D_i/2

r_2=D_o/2

t_ins=3[cm],parametertobevaried"

k_ins=0.038"

h_o=15"

[W/m^2-C]"

h_i=80"

L=1"

ANALYSIS"

A_i=pi*D_i*L

A_o=pi*（D_o+2*t_ins*Convert（cm,m））*L

R_conv_i=1/（h_i*A_i）

R_pipe=ln（r_2/r_1）/（2*pi*k_steel*L）

R_ins=ln（r_3/r_2）/（2*pi*k_ins*L）

r_3=r_2+t_ins*Convert（cm,m）"

t_insisincm"

R_conv_o=1/（h_o*A_o）

R_total=R_conv_i+R_pipe+R_ins+R_conv_o

Q_dot=（T_infinity_1-T_infinity_2）/R_total

DELTAT_pipe=Q_dot*R_pipe

DELTAT_ins=Q_dot*R_ins

Tins[cm]

Q[W]

Tins[C]

1

189.5

246.1

2

121.5

278.1

3

93.91

290.1

4

78.78

296.3

5

69.13

300

6

62.38

302.4

7

57.37

304.1

8

53.49

305.4

9

50.37

306.4

10

47.81

307.2

3-70A50-mlongsectionofasteampipepassesthroughanopenspaceat15C.Therateofheatlossfromthesteampipe,theannualcostofthisheatloss,andthethicknessoffiberglassinsulationneededtosave90percentoftheheatlostaretobedetermined.

Assumptions1Heattransferissteadysincethereisnoindicationofanychangewithtime.2Heattransferisone-dimensionalsincethereisthermalsymmetryaboutthecenterlineandnovariationintheaxialdirection.3Thermalconductivityisconstant.4Thethermalcontactresistanceattheinterfaceisnegligible.5Thepipetemperatureremainsconstantatabout150Cwithorwithoutinsulation.6Thecombinedheattransfercoefficientontheoutersurfaceremainsconstantevenafterthepipeisinsulated.

PropertiesThethermalconductivityoffiberglassinsulationisgiventobek=0.035W/m°

C.

Analysis（a）Therateofheatlossfromthesteampipeis

（b）Theamountofheatlossper