Heat Chap08053.docx

Heat Chap08053.docx

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HeatChap08053

8-53Hotairentersasheetmetalductlocatedinabasement.Theexittemperatureofhotairandtherateofheatlossaretobedetermined.

Assumptions1Steadyflowconditionsexist.2Theinnersurfacesoftheductaresmooth.3Thethermalresistanceoftheductisnegligible.4Airisanidealgaswithconstantproperties.5Thepressureofairis1atm.

PropertiesWeexpecttheairtemperaturetodropsomewhat,andevaluatetheairpropertiesat1atmandtheestimatedbulkmeantemperatureof50C（TableA-15）,

AnalysisThesurfaceareaandtheReynoldsnumberare

whichisgreaterthan10,000.Therefore,theflowisturbulentandtheentrylengthsinthiscaseareroughly

whichismuchshorterthanthetotallengthoftheduct.Therefore,wecanassumefullydevelopedturbulentflowfortheentireduct,anddeterminetheNusseltnumberfrom

and

Themassflowrateofairis

Insteadyoperation,heattransferfromhotairtotheductmustbeequaltotheheattransferfromtheducttothesurrounding（byconvectionandradiation）,whichmustbeequaltotheenergylossofthehotairintheduct.Thatis,

AssumingtheducttobeatanaveragetemperatureofTs,thequantitiesabovecanbeexpressedas

Thisisasystemofthreeequationswiththreeunknownswhosesolutionis

Therefore,thehotairwillloseheatatarateof2622Wandexittheductat45.1C.

8-54"!

PROBLEM8-54"

"GIVEN"

T_i=60"[C]"

L=12"[m]"

side=0.20"[m]"

Vel=4"[m/s],parametertobevaried"

"epsilon=0.3parametertobevaried"

T_o=10"[C]"

h_o=10"[W/m^2-C]"

T_surr=10"[C]"

"PROPERTIES"

Fluid$='air'

C_p=CP（Fluid$,T=T_ave）*Convert（kJ/kg-C,J/kg-C）

k=Conductivity（Fluid$,T=T_ave）

Pr=Prandtl（Fluid$,T=T_ave）

rho=Density（Fluid$,T=T_ave,P=101.3）

mu=Viscosity（Fluid$,T=T_ave）

nu=mu/rho

T_ave=T_i-10"assumedaveragebulkmeantemperature"

"ANALYSIS"

A=4*side*L

A_c=side^2

p=4*side

D_h=（4*A_c）/p

Re=（Vel*D_h）/nu"Theflowisturbulent"

L_t=10*D_h"Theentrylengthismuchshorterthanthetotallengthoftheduct."

Nusselt=0.023*Re^0.8*Pr^0.3

h_i=k/D_h*Nusselt

m_dot=rho*Vel*A_c

Q_dot=Q_dot_conv_in

Q_dot_conv_in=Q_dot_conv_out+Q_dot_rad_out

Q_dot_conv_in=h_i*A*DELTAT_ln

DELTAT_ln=（T_e-T_i）/ln（（T_s-T_e）/（T_s-T_i））

Q_dot_conv_out=h_o*A*（T_s-T_o）

Q_dot_rad_out=epsilon*A*sigma*（（T_s+273）^4-（T_surr+273）^4）

sigma=5.67E-8"[W/m^2-K^4],Stefan-Boltzmannconstant"

Q_dot=m_dot*C_p*（T_i-T_e）

Vel[m/s]

Te[C]

Q[W]

1

33.85

1150

2

39.43

1810

3

42.78

2273

4

45.1

2622

5

46.83

2898

6

48.17

3122

7

49.25

3310

8

50.14

3469

9

50.89

3606

10

51.53

3726

Te[C]

Q[W]

0.1

45.82

2495

0.2

45.45

2560

0.3

45.1

2622

0.4

44.77

2680

0.5

44.46

2735

0.6

44.16

2787

0.7

43.88

2836

0.8

43.61

2883

0.9

43.36

2928

1

43.12

2970

8-55Thecomponentsofanelectronicsystemlocatedinarectangularhorizontalductarecooledbyforcedair.Theexittemperatureoftheairandthehighestcomponentsurfacetemperaturearetobedetermined.

Assumptions1Steadyflowconditionsexist.2Theinnersurfacesoftheductaresmooth.3Thethermalresistanceoftheductisnegligible.4Airisanidealgaswithconstantproperties.5Thepressureofairis1atm.

PropertiesWeassumethebulkmeantemperatureforairtobe35Csincethemeantemperatureofairattheinletwillrisesomewhatasaresultofheatgainthroughtheductwhosesurfaceisexposedtoaconstantheatflux.Thepropertiesofairat1atmandthistemperatureare（TableA-15）

Analysis（a）Themassflowrateofairandtheexittemperaturearedeterminedfrom

（b）Themeanfluidvelocityandhydraulicdiameterare

Then

whichisgreaterthan10,000.Also,thecomponentswillcauseturbulenceandthuswecanassumefullydevelopedturbulentflowintheentireduct,anddeterminetheNusseltnumberfrom

and

Thehighestcomponentsurfacetemperaturewilloccurattheexitoftheduct.Assuminguniformsurfaceheatflux,itsvalueisdeterminedfrom

8-56Thecomponentsofanelectronicsystemlocatedinacircularhorizontalductarecooledbyforcedair.Theexittemperatureoftheairandthehighestcomponentsurfacetemperaturearetobedetermined.

Assumptions1Steadyflowconditionsexist.2Theinnersurfacesoftheductaresmooth.3Thethermalresistanceoftheductisnegligible.4Airisanidealgaswithconstantproperties.5Thepressureofairis1atm.

PropertiesWeassumethebulkmeantemperatureforairtobe310Ksincethemeantemperatureofairattheinletwillrisesomewhatasaresultofheatgainthroughtheductwhosesurfaceisexposedtoaconstantheatflux.Thepropertiesofairat1atmandthistemperatureare（TableA-15）

Analysis（a）Themassflowrateofairandtheexittemperaturearedeterminedfrom

（b）Themeanfluidvelocityis

Then,

whichisgreaterthan4000.Also,thecomponentswillcauseturbulenceandthuswecanassumefullydevelopedturbulentflowintheentireduct,anddeterminetheNusseltnumberfrom

and

Thehighestcomponentsurfacetemperaturewilloccurattheexitoftheduct.Assuminguniformheatflux,itsvalueisdeterminedfrom

8-57Airentersahollow-coreprintedcircuitboard.Theexittemperatureoftheairandthehighesttemperatureontheinnersurfacearetobedetermined.

Assumptions1Steadyflowconditionsexist.2HeatgeneratedisuniformlydistributedoverthetwosurfacesofthePCB.3Airisanidealgaswithconstantproperties.4Thepressureofairis1atm.

PropertiesWeassumethebulkmeantemperatureforairtobe310Ksincethemeantemperatureofairattheinletwillrisesomewhatasaresultofheatgainthroughthehollowcorewhosesurfaceisexposedtoaconstantheatflux.Thepropertiesofairat1atmandthistemperatureare（TableA-15）

Analysis（a）Themassflowrateofairandtheexittemperaturearedeterminedfrom

（b）Themeanfluidvelocityandhydraulicdiameterare

Then,

whichislessthan2300.Therefore,theflowislaminarandthethermalentrylengthinthiscaseis

whichisshorterthanthetotallengthoftheduct.Therefore,weassumethermallydevelopingflow,anddeterminetheNusseltnumberfrom

and,

Thehighestcomponentsurfacetemperaturewilloccurattheexitoftheduct.Itsvalueisdeterminedfrom

8-58Airentersahollow-coreprintedcircuitboard.Theexittemperatureoftheairandthehighesttemperatureontheinnersurfacearetobedetermined.

Assumptions1Steadyflowconditionsexist.2HeatgeneratedisuniformlydistributedoverthetwosurfacesofthePCB.3Airisanidealgaswithconstantproperties.4Thepressureofairis1atm.

PropertiesWeassumethebulkmeantemperatureforairtobe310Ksincethemeantemperatureofairattheinletwillrisesomewhatasaresultofheatgainthroughthehollowcorewhosesurfaceisexposedtoaconstantheatflux.Thepropertiesofairat1atmandthistemperatureare（TableA-15）

Analysis（a）Themassflowrateofairandtheexittemperaturearedeterminedfrom

（b）Themeanfluidvelocityandhydraulicdiameterare

Then,

whichislessthan2300.Therefore,theflowislaminarandthethermalentrylengthinthiscaseis

whichisshorterthanthetotallengthoftheduct.Therefore,weassumethermallydevelopingflow,anddeterminetheNusseltnumberfrom

and,

Thehighestcomponentsurfacetemperaturewilloccurattheexitoftheduct.Itsvalueisdeterminedfrom

8-59EWaterisheatedbypassingitthroughthin-walledcoppertubes.Thelengthofthecoppertubethatneedstobeusedistobedetermined.

Assumptions1Steadyflowconditionsexist.2Theinnersurfacesofthetubearesmooth.3Thethermalresistanceofthetubeisnegligible.4Thetemperatureatthetubesurfaceisconstant.

PropertiesThepropertiesofwateratthebulkmeanfluidtemperatureof

are（TableA-9E）

Analysis（a）ThemassflowrateandtheReynoldsnumberare

whichisgreaterthan4000.Therefore,theflowisturbulentandtheentrylengthsinthiscaseareroughly

whichisprobablyshorterthanthetotallengthofthepipewewilldetermine.Therefore,wecanassumefullydevelopedturbulentflowintheentireduct,anddeterminetheNusseltnumberfrom

and

Thelogarithmicmeantemperaturedifferenceandthentherateofheattransferperftlengthofthetubeare

Therateofheattransferneededtoraisethetemperatureofwaterfrom54

to140

is

Thenthelengthofthecoppertubethatneedstobeusedbecomes

（b）Thefrictionfactor,thepressuredrop,andthenthepumpingpowerrequiredtoovercomethispressuredropcanbedeterminedforthecaseoffullydevelopedturbulentflowtobe

8-60Acomputeriscooledbyafanblowingairthroughitscase.Theflowrateoftheair,thefractionofthetemperatureriseofairthatisduetoheatgeneratedbythefan,andthehighestallowableinletairtemperaturearetobedetermined.

Assumptions1Steadyflowconditionsexist.2Heatfluxisuniformlydistributed.3Airisanidealgaswithconstantproperties.4Thepressureofairis1atm.

PropertiesWeassumethebulkmeantemperatureforairtobe300K.Thepropertiesofairat1atmandthistemperatureare（TableA-15）

Analysis（a）Notingthattheelectricenergyconsumedbythefanisconvertedtothermalenergy,themassflowrateofairis

（b）Thefractionoftemperatureriseofairthatisduetotheheatgeneratedbythefananditsmotoris

（c）Themeanvelocityofairis

and,

Therefore,

whichislessthan4000.Therefore,theflowislaminar.Assumingfullydevelope