Heat Chap05084Word格式.docx

Heat Chap05084Word格式.docx

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andothergivenquantities,thenodaltemperaturesafter560/15=20timesteps（5min）aredeterminedtobe

After5min:

T0=228.9C,T1=228.4C,T2=226.8C,T3=224.0C,andT4=219.9C

（b）Thetimeneededfortransientoperationtobeestablishedisdeterminedbyincreasingthenumberoftimestepsuntilthenodaltemperaturesnolongerchange.Inthiscasesteadyoperationisestablishedin----min,andthenodaltemperaturesundersteadyconditionsaredeterminedtobe

T0=2420C,T1=2413C,T2=2391C,T3=2356C,andT4=2306C

DiscussionThesteadysolutioncanbecheckedindependentlybyobtainingthesteadyfinitedifferenceformulation,andsolvingtheresultingequationssimultaneously.

5-85"

!

PROBLEM5-85"

"

GIVEN"

L=0.08"

[m]"

k=28"

[W/m-C]"

alpha=12.5E-6"

[m^2/s]"

T_i=100"

[C]"

g_dot=1E6"

[W/m^3]"

T_infinity=20"

h=35"

[W/m^2-C]"

DELTAx=0.02"

time=300[s],parametertobevaried"

ANALYSIS"

M=L/DELTAx+1"

Numberofnodes"

DELTAt=15"

[s]"

tau=（alpha*DELTAt）/DELTAx^2

Thetechniqueistostorethetemperaturesintheparametrictableandrecoverthem（asoldtemperatures）

usingthevariableROW.ThefirstrowcontainstheinitialvaluessoSolveTablemustbeginatrow2.

UsetheDUPLICATEstatementtoreducethenumberofequationsthatneedtobetyped.Column1

containsthetime,column2thevalueofT[1],column3,thevalueofT[2],etc.,andcolumn7theRow."

Time=TableValue（Row-1,#Time）+DELTAt

Duplicatei=1,5

T_old[i]=TableValue（Row-1,#T[i]）

end

Usingtheexplicitfinitedifferenceapproach,thesixequationsforthesixunknowntemperaturesaredeterminedtobe"

T[1]=tau*（T_old[2]+T_old[2]）+（1-2*tau）*T_old[1]+tau*（g_dot*DELTAx^2）/k"

Node1,insulated"

T[2]=tau*（T_old[1]+T_old[3]）+（1-2*tau）*T_old[2]+tau*（g_dot*DELTAx^2）/k"

Node2"

T[3]=tau*（T_old[2]+T_old[4]）+（1-2*tau）*T_old[3]+tau*（g_dot*DELTAx^2）/k"

Node3"

T[4]=tau*（T_old[3]+T_old[5]）+（1-2*tau）*T_old[4]+tau*（g_dot*DELTAx^2）/k"

Node4"

T[5]=（1-2*tau-2*tau*（h*DELTAx）/k）*T_old[5]+2*tau*T_old[4]+2*tau*（h*DELTAx）/k*T_infinity+tau*（g_dot*DELTAx^2）/k"

Node4,convection"

Time[s]

T1[C]

T2[C]

T3[C]

T4[C]

T5[C]

Row

100

1

15

106.7

104.8

2

30

113.4

112.5

111.3

3

45

120.1

119.7

119

117

4

60

126.8

126.6

126.3

125.1

123.3

5

75

133.3

133.2

132.6

131.5

129.2

6

90

139.9

139.6

139.1

137.6

135.5

7

105

146.4

146.2

145.4

144

141.5

8

120

152.9

152.6

151.8

150.2

147.7

9

135

159.3

159.1

158.1

156.5

153.7

10

…

3465

1217

1213

1203

1185

1160

232

3480

1220

1216

1206

1188

1163

233

3495

1223

1209

1192

1167

234

3510

1227

1195

1170

235

3525

1230

1198

1173

236

3540

1234

1219

1201

1176

237

3555

1237

1233

1205

1179

238

3570

1240

1226

1208

1183

239

3585

1244

1229

1211

1186

240

3600

1247

1243

1214

1189

241

5-86Thepassivesolarheatingofahousethrougha