《化工原理I》计算题

∴ ?i?0.023?di2

RePr0.80.4?0.023?0.42?1.1795?1040.02??0.8??11.48?0.4

αi = 2318.9[W/(m.℃)]

?do??do1?? Ko?1?????d?d??o?Wm?iidm = 0.5×(0.025 + 0.02)= 0.0225(m)

250.0025?251??Ko?1?????1424.7[W/(m.℃)]

45?22.510000??2318.9?202

?tm??t2?t1?lnT?t1130?25??80?25?ln?74.13(℃)

T?t2130?802

Ao = πdo l n = 3.14×0.025×3×90 = 21.2(m) Q供 = 1424.7×21.2×74.13 = 2239(kW) ∵ Q供 > Q需 ∴ 此换热器能完成生产任务

(2)∵ 原处理量时,Re > 10 ∴ 现处理量增加20%,Re′ > 10

4

4

??diui?????i??0.023??di????0.8?Cp?????????0.4

?i??ui???????i?ui??0.8

0.8??m2???m?2????0.8?1.2m2???m2?2

????0.8?1.20.8

αi′= 1.2×2318.9 = 2683.0[W/(m.℃)]

?do??do1??Ko?1???

???d?d??o?Wm?ii250.0025?251??Ko?1?????1593.3[W/(m.℃)]

2683?2045?22.510000??2

?Cp?t2??t1??Ko?Aom2??t1t2 ?ln??T?t1??T?t2???AoT?t1Ko1593.3?21.2ln???0.7

?m2?Cp1.2?36000/3600?4.02?103T?t2T?t1?2.0 T – t = 2(T – t′) ?T?t21

2

t2′= 77.5℃

52有一单壳程单管程列管换热器,管外用120℃饱和蒸汽加热,干空气以12m/s的流速在管内流过,管子规格为φ38×2.5mm,

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总管数为200根。已知空气进口温度为26℃,要求空气出口温度为86℃,管壁和污垢热阻可以忽略,试求: (1)该换热器的管长应为多少?

(2)若气体处理量、进口温度、管长均保持不变,而管径增大为φ54×2mm,总管数减少20%,此时的出口温度为多少?(不计出口温度变化对物性的影响,忽略热损失)。

定性温度下空气的物性数据如下:Cp = 1.005kJ/(kg.K), ρ= 1.07kg/m3 , μ= 0.0199cP, λ= 0.0287W/(m.K), Pr = 0.697。 (1)空气流量 ms?n??4d2u??200??4?0.0332?12?1.07?2.2(kg/s)

Q = msCp(t2 – t1) = 2.2×1.005×(86 - 26) = 132.7(kJ/s)

Re?diu???0.033?12?1.07?3.1859?104(湍流) ?30.0199?100.80.4??0.023?diRePr?0.023?0.0287?3.1859?1040.033??0.8?0.6970.4?50.3(W/(mK))

2

忽略蒸汽冷凝、管壁和污垢的热阻:Ki = αi

?tm?t2?t186?26??59℃

ln??T?t1??T?t2??ln??120?26??120?86??2

Q132.7?103Ai???44.7(m)

Ki?tm50.3?59l?Ai44.7??2.16(m)

n??di200?3.14?0.033(2)原管截面=200? 现管截面=200??4?0.0332?0.171(m)

2

2

?1?0.20????0.052?0.314(m)

4现管内流速 u′= (0.171/0.314)×12 = 6.54(m/s)

??Redi?u????0.05?6.54?1.074?1.7582?10

0.0199?10?30.80.4?i??0.023?di??PrRe?0.023?0.0287?1.7582?1040.05??0.8?0.6970.4?28.5(W/mK)

2

Ai′= 160×3.14×0.05×2.16 = 54.3(m) Ki′ = αi′

2

??t1??Ki?Ai?msCp?t2??t1t2 ?ln??T?t1??T?t2??

ln120?2628.5?54.3??120?t22.2?1.005?103t2′= 73.3℃

53 某套管换热器中,用温度为20℃,流量为13200 kg/h的冷却水,冷却进口温度为100℃的醋酸,两流体逆流流动。换

热器刚投入使用时,冷却水出口温度为45℃,醋酸出口温度为40℃。运转一段时间后,冷热流体流量不变,进口温度不变,而冷却水的出口温度降至38℃,试求总传热系数下降的百分率。冷热流体的比热可视为常数,热损失可以忽略不计。 已知:m2=13200kg/h

t1=20℃ t2=45℃ T1=100℃ T2=40℃ t2’=38℃ 42

求:

k?k'?? k?(100?45)?(40?20)?35℃

(100?45)ln(40?20)解: ?tm 由Q=m2Cp2 ( t2-t1 ) = m1Cp1(T1-T2)

m2Cp2m1Cp1?T1?T260??2.4

t2?t125过一段时间后:

由热平衡方程 Q’=m2Cp2(t2’-t1) = m1Cp1( T1-T2’)

T1?T2'm2Cp2?t2'?t1m1Cp1

100?T2'm2Cp2 ??2.4

38?20m1Cp1 100 - T2’ = 18?2.4 解得 T2’ = 56.8℃ ?tm'?(100?38)?(56.8?20)62?36.8??48.3℃

100?3862lnln56.8?2036.8 由 Q = m2Cp2 ( t2-t1 ) = kA?tm Q’ = m2Cp2 ( t2’-t1 ) = k’A?tm’

Q'k'?tm't2'?t138?20????0.72 Qk?tmt2?t145?20?tk'35?0.72?m?0.72??0.522 k?tm'48.3

k?k'k'?100%?(1?)?100%?(1?0.522)?100%?47.8% kk

54柴油与原油在由A、B两套管组成的换热系统中进行热量交换,流程如图,原油在两套管中等量分配。已知原油及柴油的

进出口温度分别为t1 = 40℃,t2 = 100℃,T1 = 170℃,T2 = 50℃,且两流体均不发生相变化,两流体的比热为恒量。若A、B两台换热器传热面积及传热系数相等,且热损失可忽略不计。 1. 试比较两台换热器的传热单元数NTU及传热效率ε的大小; 2. 试求出口温度ta、tb、T及两换热器传热能力之比QA/QB。

柴油m1Cp1 T1 A ta 原油m2Cp2 t2 T t1

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tb

B T2

解:(1)RTol?m1Cp1m2Cp2?t2?t1100?40??0.5

T1?T2170?50∴ m1Cp1 < m2Cp2

RA?m1Cp10.5m2Cp2 RB?m1Cp10.5m2Cp2 ∴ RA = RB

RA?ta?t1t?t?RB?b1T1?TT?T2

NTUA?T?TKA?1m1Cp1?tmA NTUB?T?T2KA?m1Cp1?tmB

∴ NTUA = NTUB

?A?1?exp?NTUA?1?RA??1?exp?NTUB?1?RB?? ?B?

RA?exp?NTUA?1?RA??RB?exp?NTUB?1?RB??∴ εA = εB (10分) (2) ?A?T1?TT1?t1 ?B?T?T2T?t1

170?TT?50 T – 80T + 300 = 0 ?170?40T?402

∴ T = 76℃

RA?2m1Cp1m2Cp22m1Cp1m2Cp2?ta?t1?1

T1?Ttb?t1?1

T?T2ta = T1 – T + t1 = 170 – 76 + 40 = 134(℃)

RB??tb = T – T2 + t1 = 76 – 50 + 40 = 66(℃)

QA = m1Cp1(T1 - T)= 94 m1Cp1 QB = m1Cp1(T – T2)= 26 m1Cp1 ∴

QA94??3.6 (10分) QB2655在一单管程单壳程的列管换热器中用常压饱和水蒸气加热管内的原料气。水蒸气走壳程,冷凝水不过冷。原料气进、出口温度分别为t1 = 40℃,t2 = 80℃,流量为2200kg/h,在定性温度下的比热为2.8kJ/(kg.℃),密度为1.3 kg/m3,管内流

?速为15m/s,此时管内给热系数i=100W/(m2.℃)。换热管规格为Ф25×2.5mm。传热控制热阻可视为在管内侧,热损失忽

略不计。

1. 试求该换热器的管子根数及管长;

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