传热学第四版习题答案

习题答案 1-1 q??kA?T???T?xqkA?3?10??2.5?10???625?x??3?2

??0.2??0.6?C1-7

r1?0.25m, r2?0.3m, k?7?10?3w/m?C, h?9w/m?C, T1?30C, T???20C????2????q??T?R?T1?T?R1?R2ln0.34.145?0.25R1??? C/w?32?kLL2?7?10?L? 110.0589?R2??? C/w?9??2???0.3??L?hA2Lln?r2r1?????qL?T1?T??4.145???0.0589??11.89 w/m1-12

T1?1100?273?1373KT2?425?273?698KqA??T1?T2

?84?44???5.669?10??1373?6984??1.88?105 w/m21-31 qAqAqA?h1?T1?Tw1??100??353?Tw1???Tw1?Tw2?5.669?10?44???8??T4w1?Tw2

4??h2?Tw2?T2??15??Tw2?293?qA?300w/m2Tw1?350K, Tw2?312.9K,

2-1

T1?1300C, T2?30C, k1?1.3w/m?C, k2?0.35w/m?C, ?x1?0.02m, ????????qA?1830w/m2qA?T1?T2?RqA?18301300?301830?x2k2?R?T1?T2??0.6940 m?C/w?2??

?0.021.3??x20.35?0.6940R?R1?R2??x1k1??x2?0.2375 m2-9

ro?0.017m, ri?0.015m, ho?197w/m?C, hi?1500w/m?C, Tfo?57C, Tfi?223C, k?46w/m?C???2???2?????2??223?57?11

qL??T?R?12?hiri?T?ro??ln??r??i?2?k??12?horo??1500??0.015??197??0.017????0.017?ln???0.015?46?3016.6w/m2-10

k?0.04w/m?C,T?150x?30x

???2q??kAqqx?0dTdx??kA?300x?30???kA??30??1.2A??kA?300?0.3?30???60kA??2.4A

x?0.3This solid is heating up. 2-16

ri?0.02m, ro?0.04m, Ti?100C, To?50C, k?202w/m?Cq?4?k?Ti?To?1ri?1ro?4??202??100?50?10.02?10.04?5076.8w?????

2-36

??35.3?10w/m, T??20C, h?4000w/m?CA?0.025?0.025?0.000625m, q263??2???V?35.3?106?0.000625q?qq?h?4??0.025Tw?75.16C?????L??Tw??L?22062.5L ?T???4000?4??0.025??L??Tw?20?

2-43

??200?106w/m3,k?25w/m??C,Tw?100?C,x?0.004m q??dTdx22??qk?062

T??4?10x?c1x?c2dTBoundary condition: dx?0x?0

x?0.004,T?Tw?100c1?0,c2?164T??4?10x?164 Tmax?Tx?062??164C2-68 For case 1: Tx?L?T??20C,k?380w/m?C 20??0.005??380????q?hPkA?0???0.005?2?1204??20??4.8415w

2-72

d1?0.03m, L?0.03m, T??20C, Tw?100C, k?55w/m?C,h?68w/m?C,t?0.002m??????2??From Fig 2-12

r1?0.015m, r2?r1?L?0.045m, t?0.002mLc?L?t2?0.031mr2c?r1?Lc?0.046mAm?t?r2c?r1???0.002r2cr1Lc3/2??0.031??6.2?10?5m2

?0.0460.015kAm?3.07?68??5??556.2?10????1/2?h?1/2??0.031?3/2???0.7708From the figure ??0.58q??hA?0??0.58??68??2??100?20??0.046?2?0.0152??37.49w?

2-108

k?202w/m?C,?x?0.005m, 100uin 20atm ,ΔToverall?80C

???R1?R2?Rcontact?q??xkA1??0.005202AA??2.475?10A?4?50.88?10hcA?T80R1?R2?Rc?2?2.475?10A?5?0.88?10A?4?581818A w

?Tcontact?qRc?0.88?10?4??581818A???A????51.2?C??2-117

1??2A?x??2?r??2??0.01?x??0.0005? m4??qk??A4q0.001?k4000qdT1?dT???0.001??0.01?x?dx4?dx????0.04?x?dTdx?k4000qdx???????dT?0.04?x?2?k4000qln?0.04?x?1??T21?kq?ln2?T1?T2T1?T24000ln2?kR?q?4000ln2?k3002.32?4000ln2??380??2.32C/w?

?129w3-3

d?0.25m, D?1.2m, Tw?67C, Tfar?15C, k?1.8w/?m?C????s?2?L?D?ln???r??2?L?1.2?ln??0.125???2.778L

q?ks?T?k?2.778L??TqL??2.778?k?T??2.778??1.8??52??260w/m3-33

dTdx222??hPkA?T?T???0dTdx2Tm?1?Tm?1?2Tm??x?22Tm?1?Tm?1?2Tm??x??hPkA

?Tm?T???0?hP??x?2?hP??x?2Tm??2??T???Tm?1?Tm?1??0kAkA??3-34

k?yTm?1,n?Tm,n?x?k?xTm,n?1?Tm,n2?y?k?xTm,n?1?Tm,n2?y?0?x??yTm,n?1?Tm,n?1?2Tm?1,n?4Tm,n?0

3-35

k?yTm?1,n?Tm,n2?x?k?xTm,n?1?Tm,n2?y?0?x??yTm?1,n?Tm,n?1?2Tm,n?0

3-47 ?100??700??100?400??700?T1?T2?4T4?400?T4?T3?4T1?500?T4?T3?4T2?500?T1?T2?4T3

T1?487.5,T2?362.5,T3?437.5,T4?412.53-58

??90?106w/m3,k?20w/m??C?x??y?0.01m,q?V?90?10q?q???6??0.01?2

?9000wFor node 5,6,8,9

?T2?T4?T6?T8?450?4T5?0??T3?T5?T9?100?450?4T6?0 ??T5?T7?T11?T9?450?4T8?0?T6?T8?T12?100?450?4T9?0?For node 4,7,11,12

?T1?2T5?T7?450?4T4?0??T4?2T8?T10?450?4T7?0 ??T10?2T8?T12?450?4T11?0?T11?2T9?100?450?4T12?0?For node 2,3

?2T5?T1?T3?4.1T2?452?0 ?2T?T?100?4.1T?452?023?6For node 1

2T4?T2?T2?4.1T1?452?0

For node 10

T7?T11?2T10?225?0

T1?1923.9,T2?1723.9,T3?1120.2,T4?1994.0,T5?1786.0,T6?1158.4T7?2030.2,T8?1817.7,T9?1177.3,T10?2041.3,T11?1837.4,T12?1183.0

4-4

?cpVdTdt?hA?T??T???AT??T4?4?

t?0,T?T04-6

Aluminum sphere:

m?6kg,Ti?300C, T??20C, h?58w/m?C, T?90C, ??2707kg/m43???2???3,cp?0.896kJ/kgC????R?3m?,R?0.08088mBi??V?h???A?k?e?hAhR3kt??58??0.08088??3?202?0.00774??0.1T?T?Ti?T?90?20?cpV

?0.000887t?300?20?e?58??3?t?0.08088??2707??896??et?1563s?0.434h4-17 Copper sphere

d?0.04m,Ti?220C, T??30C, h?20w/m?C, T?80C, ??8954kg/m,cp?0.383kJ/kgC,k?380w/mC???2???3??????Bi??V?h???A?k?e?hAhR3kt??20??0.02??0.000353?380???0.1T?T?Ti?T?80?30?cpV

?20??3?t?0.000874t?220?30?e?0.02??89542707??383??et?1526s?0.424h4-24

Ti?90C, T0?30C, a?11.234?10???52?m/s, k?380w/mC,x?0.075m,t?10s

??x2at??T?x0.075211.234?10??kA?5?1.1188?10e?x2qx??kAqxATi?T04at?at90?30

e?1.11882???386???11.234?10?5??10??2??111.5kw/m24-70

Ti?200C, T??30C, h?50w/m?C, ??2000kg/ma?5.4?10?7????3, c?0.96kJ/kg?C, ???m/s, k?1.04w/mC2???

For node 3 ?x?yT3p?1?T3p?t?a?tpppppppp?T6?T3T4?T3T1?T3T7?T3?a??y??y??x??x??x?x?y?y?pp????T3p?1??x?2?T4?T6??a?t??y?2?Tp1?T7p??2a?t2a?t??1??22?????x?y??p?T3?

?t?74.1sFor node 1

?c?y2??xT1p?1?T1p?tpppp??yT5p?T1pT3?T1?yT2?T1?k????x?2?x2?x?y?p???h?xT??T1p????

T1p?1a?t??x?2?Tp5?T2??2a?t??y?2T3?p?2a?t2a?t2h?t?pT???1????T122?c?y??x???y??c?y??2h?t?t?53.45sFor node 2

?c?y?xT22?2p?1?T2p?tT1?ppp??yT1p?T2p?xT4?T2?k???2?x2?y?p???x?y?p??h??T?T??2?2??2?????p???T2??T2p?12a?t2a?t??x?2??y?2T4?2h?t2h?t?????c?x??c?y??2a?t2a?t?2h?t2h?t??T?1????22?????c?x?????x?y???c?y??t?46.9sfor node 4

?c?x2??yT4p?1?T4p?tpppp??xT8p?T4pT3?T4?xT2?T4?k????y?2?y2?y?x?p???h?yT??T4p????

T4p?1a?t??y?2?Tp8?T2??2a?t??x?2T3?p?2a?t2a?t2h?t?pT???1????T422?c?x??x???y??c?x??2h?t?t?62.1s?tmax?46.9s

4-71

Aluminum rod

d?0.025m, L?0.2m, ?x?0.04m, Ti?200C, T??20C, h?50w/m?C, ???2????2707kg/m3, c?0.896kJ/?kg?C?, a?8.418?10??5m/s,2

For node 5

?c?x?d2?42T5p?1?T5p?t?kpp2?d?T4?T5??4???x?x?2pp??h?dT??T5?dhT??T5?24?????

T5p?12a?t??x?2?2h?t4h?tpT4?????cd??c?x??2a?t4h?t2h?t?p?T?1????T5???2?cd?c?x???x????t?9.043s4-73

?c?y2??xTm,n?Tm,n?tTpm,n?1p?1ppppp??yTmp?1,n?Tmp,nTm,n?1?Tm,n?yTm?1,n?Tm,n?k???x??2?x?y2?x????h?xT?Tp?m,n????Tp?1m,n2a?t??y?2?a?t??x?2?Tpm?1,n?Tpm?1,n??2a?t2a?t2h?t?p?T???1????Tm,n22?c?y?c?y?????x?y??2h?t5-6

p?20kPa, T?5C, d?0.025m, u??1.5m/s

?The properties of air

??pRgT?20?103?287??273?5?5??0.2498kg/m3

??1.7374?10Pa?s,?x?4.64Re?1/2x,??xx?4.64??u???????1/2??4.64Re?1/2x?1.7374?10?5x???4.64??1.5?0.2498???1/2?r?0.0125

x?0.1565m5-20

p?1.013?10Pa, T??90C, Tw?10C, u??60m/s,A??0.6??0.6?m

5??2Tf?Tw?T?2pRgT??90?102?50C5????1.013?10?287??273?50??6?19.6?10kg/?m?s??1.0928kg/m3

k?0.0283w/m?C,Pr?0.698???Re??u?L?1/3??1.0928??60??0.6?19.6?100.8L?6?2.01?101/365?5?10

NuL?Prh?NukL?0.0371Re?871?0.698?134.57??0.0371?2.01?106?0.8?871?2853.0??2853.00.02830.6

q?hA?T??Tw???134.57??0.6??0.6??90?10??3875.6w5-24

p?20kPa, T?20C, x?0.3m, u??30m/s,Tw?55C,u?22.5m/s

Tw?T?2pRgT?55?2020.2?10???Tf???37.5C5????287??273?37.5??6?18.92?10kg/?m?s??0.2244kg/m3

k?0.0270w/m?C,Pr?0.706???For x=30cm,

?x?4.64Re?1/2x,??xx?4.64??u???????1/2??4.64Re?1/2x?1.892?10?0.3????4.64??22.5?0.2244????5??1/2

?4.261?10?3mFor the velocity distribution

uu?y1?y?22.5??????0.752?2???30?0.558?33y3?

my?2.3776?105-62

1???T?1?T ?r??ur?r??r?a?x???T?ur?T?r???r??r?a?xr?T?r??u?T2a?xu?T2a?xr2r?C1 ?C1?0?2?T?rT?u?T4a?xr0r?Tc ( Tc is the temperature at the center of the tube)

Tb??02?r?ucpTdr2?r?ucpdrr0?Tc2?Tw?r0??r00rTdr?rdru?T8a?x0?r0r0?Tc20u?T4a?xq?hA?Tw?Tb???kAh?kr082rk20?T?rr?r0?4kr0

Nu?h2r0?85-85

Nux?khxxk?CRennx?x?u?f?Pr??C???????f?Pr??nn?x?u?hx?C??x????u?hL?Ck????hL?hL?n???u?????fPr?Ck??????n?1???fPrx???n?1??f?Pr?L???u??Ck??????0???fPr??nL

xn?1?L0hxdxLdxLCk??u????n???n?1??f?Pr?L?n1nhL5-87

Air p?1atm, T??300K, square plate x?0.75m, u??45m/s,Tw?350K

Tf?Tw?T?2pRgT??325K5???1.013?10?287??325??6?19.6?10kg/?m?s??1.086kg/m3

k?0.02814w/m?C,Pr?0.7025???Re??u?L?1/3??1.086??45??0.75?19.6?100.8L?6?1.8695?106?5?10

5NuL?PrStL??0.0371Re??871??0.70256??1/3?0.0371?1.8695?3?106?0.8?871?2649.1?NuLRePr2649.1?1.8695?10??0.7025?2/3?2.017?10StPr2/3?2.017?10??3??0.7025??3?1.5939?102?3?C2f?w?C?u?f22?1.5939?102???1.086??45??3.505N/m2

FD?A?w??0.75??3.505??1.97Nh?NukL??2649.1?0.028140.75?99.39q?hA?T??Tw???99.39??0.75??0.75??350?300??2795.5wOr

Cf?0.074Re1/5L?1742ReL?0.074?1.8695?1051/5??17421.8695?105?0.003188

For laminar portion:

Rex?x?u????1.086??45?x1.9606?10?5?5?105

x?0.20mFor the first 20cm long

NuL?0.664Reh?NuStL?kLh1/2LPr1/3?0.6645?10?58.73?51/2??0.7025?1/3?417.4??417.4??0.028140.2058.73?cu??1.086??1006??45??3?1.1945?102/3?3

?0.944?102?3StPr2/3?1.1945?10???0.7025??3?C22f?w?C?u?f22?0.944?10???1.086??45??2.076N/mFD?A?w??0.75??0.2??2.076??0.3114N6-1

From the Appendix A of Table A-4

d?0.005m,Tb1?120C, Tw?50C, Re?1000, L?0.1m, 0.2m, 0.5m,Tb?120C, ??828.96kg/mTw?50C,??870kg/m?3?3??

?4,cp?2.307kJ/kgC,k?0.135w/mC,??0.124?10?4??????m/s, a?0.710m22/s,Pr?175,??1.6195?10m/s,?42Re?du??,u?Re??d???1000??0.1240.005?10??2.48m/s

????ρuA??828.96??2.48???0.005m?4?2????0.040kg/s(1) For L=0.1m

RePrGz?1dL??1000??175?0.0050.1?8750

?0.0001143Equation (6-9)

?d?0.0668??RePr?L?1?0.04??d/L?RePr?0.1350.0052/3Nud?3.66?kd?3.66??0.0668??8750?2/31?0.04?8750??36.16

h?Nu??36.16??976.32w/m?C

?2??T?Tb2???cp?Tb2?Tb1?q?hA?Tw?b1??m2???976.32???0.005??0.1??50?Tb2?118.85Cq?106.12w???120?Tb2?3???0.04?2.307?10?Tb2?120? 2???From Equation (6-10)

Nu1/31/3?????1.86?RePr??d/L??????w?0.14d?1.86?8750?1/3?????828.96?0.124?10?870??1.6195??4?10?4??????0.14?26.57h?Nukd??26.57?0.1350.005?717.39w/m?C

?2??T?Tb2???cp?Tb2?Tb1?q?hA?Tw?b1??m2???717.39???0.005??0.1??50?Tb2?119.15Cq?78.44w???120?Tb2?3???0.04?2.307?10?Tb2?120? 2???(2) for L=0.2

RePrGz?1dL??1000??175?0.0050.2?4375

?0.0002286Nud?3.66?kd?d?0.0668??RePr?L?1?0.04??d/L?RePr?0.1350.0052/3?3.66??0.0668??4375?2/31?0.04?4375??28.64

h?Nu??28.64??773.25w/m?C

?2??T?Tb2???cp?Tb2?Tb1?q?hA?Tw?b1??m2???773.25???0.005??0.2??50?Tb2?118.19Cq?167.03w???120?Tb2?3???0.04?2.307?10?Tb2?120? 2???(3) for L=0.5m

RePrGz?1dL??1000??175?0.0050.5?1750

?0.00057Nud?3.66?kd?d?0.0668??RePr?L?1?0.04??d/L?RePr?0.1350.0052/3?3.66??0.0668??1750?2/31?0.04?1750??20.83

h?Nu??20.83??562.38w/m?C

?2??T?Tb2???cp?Tb2?Tb1?q?hA?Tw?b1??m2???562.38???0.005??0.5??50?Tb2?116.7Cq?304.5w???120?Tb2?3???0.04?2.307?10?Tb2?120? 2???6-7

??1.0kg/s , L?1.5m,?p?7kPad?0.025m,Tb1?20C, Tw?50C, m?3??

?4Tb1?20C, ??997.4kg/m,cp?4.179kJ/kgC,k?0.604w/mC,??9.8?10??????Pa.s , Pr?6.78

um?Re??mA?μ?dumρ?1.0??4??2.042m/s2??0.025??997.4??0.025??2.042??997.4??9.8?10?42?5.2?104?2300?p?ff??pStPr2/3L?umdd222mL?u?f8??7000?0.0251.52?997.4??2.042?2?0.0566

?0.007075RePr1/3Nu?StPrh?Nukd2/3??0.007075??520000??6.78?1/32??688.9??688.9?0.6040.025?16644.7w/?m?C?T?Tb2???cp?Tb2?Tb1?q?hA?Tw?b1??m2???1664420?Tb2??3.7???0.025??1.5??50????1.0?4.179?10?Tb2?20?

2????Tb2?39.14Cq?79986.1w?From the equation Nu?0.023Reh?7081.3Tb2?25.4C?0.8Pr0.4?293.1

6-18

Water Tb1?71?C, Tb2?32?C, m??0.4kg/s (1) d?0.0125m, Tw?4?C (2) d?0.025m, Tw?20?C

Tb?51.5C, ??988.1kg/m,cp?4.174kJ/kgC,k?0.648w/mC,??5.494?10?3???????4Pa.s , Pr?3.54 (1)

um?Re??mA?μ?dumρ?0.4??4??3.3m/s2??0.0125??988.1??0.0125??3.3??988.1??5.494?10?4

4?7.419?10?2300(2)

um?Re??mA?μ?dumρ?0.4??4??0.825m/s2??0.025??988.1??0.025??0.825??988.1??5.494?10?4

4?3.709?10?2300q?h1?d1L1?Tb?Tw1??h2?d2L2?Tb?Tw2?h1L1:h2L2?d2?Tb?Tw2?:d1?Tb?Tw1???0.025??51.5?20?:?0.0125L1?ud122m1??51.5?4??0.7875:0.59375????2?p1:?p2?f1?h1??um2?????h??u?2??m1:f2L2?ud222m12?f1??L1??d2??um1?????????f??L??d??u?2??2??1??m2??d2??um1??????d??u??1??m2??St??L??d??u???1??1??2??m1?St??L??d??u??2??2??1??m2?2??L1??d2??um1????????L??d??u??2??1??m2??hL???11?hL??22???0.7875??0.025????????4??10.6:1?0.593750.0125?????

6-54

Air p?1atm,T??27C, Tw?50C, u??20m/s, d?0.04m, a?0.04m Tf?NuT??Tw2?hdkf?27?502n???38.5C?df?ud?1/3?C???Prf???3?

??1.1774kg/m,cp?1.006kJ/?kgC?,k?0.02624w/?mC?,??1.8462?10??5Pa.s , Pr?0.708

(1) for d=0.04m Re?u?d???20??0.04??1.1744?1.8462?10?5??5.1?104C?0.0266,n?0.805 (from the table 6-2)Nudf?0.02665.1?10kfdf?4?0.805?0.708?1/3?146

h?NuqLd?1460.026240.04?95.79w/m?C?2???h?d?Tw?T????95.79???0.04??50?27??276.9w(2) for a=0.04m From table 6-3

C?0.102,n?0.675 (from the table 6-3)Nudf?0.1025.1?10kfdf?4?0.675?0.708?1/3?136.8h?NuqLd?136.80.026240.04?89.77w/m?C?2??

?h4a?Tw?T????89.77?4?0.04??50?27??330.35w6-67 Air

p?3.5MPa,T??38C, Tw?20C, u??9m/s, d?0.0125m, N?400 (20 rows)Sp?0.0375m, Sn?0.0375m, L?1.5mSpd?0.03750.0125T??Tw2pRgT???

?3,Snd?3C?0.488,n?0.562Tf???

?29C3?38?2026?3.5?10287?302?40.38kg/m,cp?1.006kJ/kgC,k?0.02624w/mC,??1.8462?10???????5Pa.s , Pr?0.708

umax1?uSn?S90.0375n?d?0.0375?0.0125?18m/sSnumax2?u2?.16m/s

?21/2?4???Sn???S2??d???2?p???Redumax?0125??18??40.38?max????0.1.8462?10?5?4.92?105Nu?CRenPr1/3?0.488?4.92?105?0.562?0.708?1/3?687.7h?Nuk?687.70.02624d0.0125?1443.3w/?m2??C?m???u??20?Sn??40.38??9??20??0.0375??181.71kg/sq?hA??TT?T?2??c

?w??12??m?p?T?2?T?1??1443.3??400???0.0125??1.5???38?T?2?20??2???181.71??1006T???38??2?T?2?34.94?C6-81 Water

m??0.8kg/s, T?93?C, di?0.05m, ??0.0008m??965.3kg/m3,c?p?4.028kJ/?kgC?,k?0.68w/?m?C?,??3.15?10?4Pa.s , Pr?1.95Air

T?15?C, p?1atm, u??15m/s??1.226kg/m3,c?k?0.0255w/?m?C?,??1.81?10?5p?1.005kJ/?kgC?,Pa.s , Pr?0.703

do?di?2??0.0516m

(1) in tube

u?0.8??4?m?m?A????0.05?2?965.3??0.422m/sRe?dumρμ??0.05??0.422??965.3?3.15?10?4?6.47?104?2300

Nu?0.023Re0.8Pr0.3??0.023??64700?0.8?1.95?0.3?198.3hi?Nukd?198.30.682?i0.05?2696.4w/?m?C?,

,

(2) outside the tube

Re?u?d???15??0.0516??1.226?1.81?10?5??5.24?104C?0.0266,n?0.805 (from the table 6-2)

Nudf?0.02665.24?10kfdf?4?0.805?0.703?1/3?148.8

h?Nud?148.80.02550.0516??73.51w/m?C?2??For copper , q?1hiAiqL?1hi?di?k?380w/mC??

Tf1?Tf2?r?ln?o??ri?2?kL1hoAo??1ho?do93?151ln?0.05160.05?2??3801?903.9w/m?Tf1?Tf2?r?ln?o??ri?2?k???2696.4??0.05?????73.51???0.0516?7-10

Tw?300C, T??25C, square 1m

??Tf?Tw?T?2?162.5C?435.5K

1T???0.8106kg/m,k?0.03608w/?mC?,??2.427?103??5Pa.s , ??2.994?103-5m/s, Pr?0.685,??2?0.002296 GrL?g??Tw?T??L3?2??9.8??0.002296??300?5?25??1?2?2.994?10?25?6.903?10

9GrPr?4.832?10

9From Table 7-1, C?0.021,m?Nu?C?GrPr?h?NukLm

9??0.021?4.832?100.036081??2/5?157.0?157?5.66w/m?C?2??

q?hA?Tw?T????5.66??1??300?25??1557.6w7-13

L?6m, q?1100w/m2,qconduction?95w/m, T??20C

2?For

h?10w/?m?C?2?qw?q?qconduction?1100?95?1005w/m2 h?T?qw?T?Tf?qwh?T2?100510?100.5C100.52?20?70C?343K?

??T??3???1.029kg/m,k?0.0296w/?mC?, ??2.002?10-5m/s, Pr?0.694,??21T?0.002915

Gr*?g?qwLk?24??9.8??0.002915?1005?6?42?0.0296??2.002?10?5?15?3.126?1015

GrPr?2.177?10Nu?CGrPrh?Nu?T?Tf?kL*?*?m??0.17?2.177?100.029661??15?1/4?1161?1161?5.73w/m?C?2??

qwh?T2?175.44C?T??107.7C?380.7K?k?0.0321w/mC, ??2.313?10???-5m/s, Pr?0.688,??21T?0.002627

Gr*?g?qwLk?24??9.8??0.002627??1005??6?42?0.0321??2.313?10?5?15?1.952?1015

GrPr?1.367?10Nu?CGrPrh?Nu?T?kL*?*?m??0.17?1.367?100.03216??15?1/4?1034?1034?5.53w/m?C?2??

qwh?181.7C7-27

??0.8kg/s, Tb?90?C, di?0.025m, do?0.030m,??0.0025m,Two?85?C,T??20?C,L?0.15mmTf?Two?T?23?85?202?52.5C?325.5K

???1.093kg/m,k?0.0283w/?mC?,??19.6?10Pa.s , ??17.95?10m/s, Pr?0.698,??0.003072?6-62Grd?g??Tw?T??d3?2??9.8??0.03072??85?25??0.03?3?1.795?10??525?1.64?10

5GrPr?1.14466?10

From Table 7-1, C?0.053,m?Nu?C?GrPr?h?Nukdm14

??0.053??1144660.02830.03?1/4?9.7492??9.749?9.196w/m?C??

q?hA?Tw?T????9.196???0.03??15??85?20??845w

( Or from Figure 7-6 Nu?10) For water in pipe

??1000kg/m,k?0.68w/?mC?,??3.15?103??4Pa.s , Pr?1.95

um?Re??mA?μ?dumρ?0.8??4??1.63m/s2??0.025??1000??0.025??1.63??1000??3.15?100.8?4?1.2934?105?2300?345.23

Nu?0.023Rehi?NukdiPr0.3??0.023??1293400.68?0.8?1.95?0.3?345.230.025?9390.9w/m?C?2??For steel pipe k?43w/?m?C?

q?1hiAiq?1hi?diL??Tb?T??r?ln?o??ri?2?kL1hoAo??1ho?doL90?251ln?0.05160.05?2??380??15?1?908.44w/m?Tb?T??r?ln?o??ri?2?kL??9390.9??0.025??15????9.196???0.0316??15?so the temperature of the outside wall

Two?89.88C

?If the temperature of the outside wall is Two?89.8C

?Grd?g??Tw?T??d3?2??9.8??0.03072??89.8?25??0.03?3?1.795?10??52?1.76?10

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