26)在列管换热器。用热水加热冷水，热水流量为4.5?103kg/h,温度从950C冷却到550C,冷水温度从200C升到500C,总传热系数为2.8?103W/(m2?0C).试求：①冷水流量。②两种流体做逆流时的平均温度差和所需要的换热面积。③两种流体做并流时的平均温度差和所需要的换热面积。④根据计算结果，对逆流和并流做一比较，可得到那些结论。解1）?Qh?QCWhCph?T?WCCpc?tCph?4.181kJ/kg0CCpc?4.174kJ/kg0CWC?6010kg/h2)?t?(45?35)/Ln(45/35)?39.80C由KS?tm?WhCph?TS?4.5?103?40?4.181?103/(3600?2.8?103?39.8)?1.89m23)?tm?(75?5)/Ln(75/5)?25.850C同理4)略27)有一台新的套管换热器，用水冷却油。水走内管，油与水逆流，内管为?19?3mm，外管为?32?3mm的钢管。水与油的流速分别为1.5m/s、0.8m/s,油的密度、比热、导热系数及粘度分别为860kg/m3、1.90?103J/(kg?0C)、0.15w/(m?0C)及1.8?10?3Pa?s.水的进出口温度为100C和300C,油的进口1000C,热损失忽略不计，试计算所需要的管长。若管长增加2000，其他条件不变，则油的出口温度为多少？设油的物性数据不变。若该换热器长期使用后，水侧及油侧的污垢热阻分别为3.5?10?4m2?0C/W和1.52?10?3m2?0C/W,其他条件不变，则油的出口温度又为多少？S?2.89m2
解：1）t?(30?10)/2?200C查表得水的物性数据：??998.2kg/m3CP?4.183kJ/kg?0C??0.6w/(m?0C)??1?10?3Pa?sWC????(19?6)2?10?6?1.5/4?0.199kg/sWh????(262?192)?10?6?0.8/4?0.170kg/s?无热损失故Qh?QcQh?1.9?0.170?(100?T2)Qc?4.183?0.99?(30?10)?16.648kJ/s?T2?48.460CRe?0.013?1.5?998.2/0.001?19464.9?10000
Pr?Cp??/??7.02?i?0.023?Re0.8Pr0.4/di?6249.9w/(m?0C)de?(26?19)?7mmRe?0.007?0.8?860/(1.8?10?3)?2675.6?10000111Pr?Cp??/??22.8??1?6?105/Re1.8?0.594?0?0.023?0.914?Re0.8Pr0.3/de?412.9w/(m?0C)??45w/(m?0C)dm?(19?13)Ln(19/13)?15.8mm1/K0?1/?0?bd0/?dm?d0/?idi?0.0027361/[w/(m2?0C)]K0?365.5w/(m2?0C)?tm?(70?38.46)/Ln(70/38.46)?52.670CS?Q/K?tm?16648/(365.5?52.7)?0.865m2L?S/?d?0.865/0.019??14.5m2)管长增加2000S'?1.2S?0.4296m?0.17?1.9?1000?323.0w/0CWCCPC?0.199?4.183?1000?832.4W/0CR1?WhCph/WcCpc?323.0/832.4?0.388NTU1?KS/(WhCPh)?365.5?1.2?0.865/323.0?1.175?1?1?exp[NTU1(1?R1)]/{R1?exp[NTU1(1?R1)]}?{1?exp[1.175(1?0.388)]}/{0.388?exp[1.175(1?0.388)]}?0.6323?1?(T1?T2')/(T1?t1)T2'?T1?0.6323(T1?t1)?100?0.6323(100?10)?43.10C即油的出口温度为43.10C此时冷却水温度为:'3)1/K0?0.002736?0.00035?0.00152?0.004604'K0?217.1W/(m2?0C)
't2?WhCph(100?43.1)/WcCpc?10?0.388?(100?43.1)?10?32.10C
NTU1'?K'S/(WhCph)?217.1?0.865//323.0?0.5814R1'?R1?0.388同理?1?(T1?T2')/(T1?t1)T2'?T1?0.4112(T1?t1)?100?0.4112?(100?10)?63.00C即油的出口温度为63.00C
28)在逆流换热器中，管子规格为?38?3mm，用初温为150C.的水将2.5kg/s的甲苯由 800C冷却到300C,水走管程，水侧和甲苯侧的给热系数分别为2500W/(m2?0C),900W/(m2?0C),污垢热阻忽略不计。若水的出口温度不能高于450C,试求该换热器的传热面积。解：t?(80?30)/2?550C查得甲苯的物性数据：CP?1.8kJ/kg0CQ?2.5?1.8?50?103?2.25?105J/sdm?(38?32）Ln(38/32)?35mm1/K0?1/?0?bd0/??d0/?idi?38/(2500?32)?0.003?38/(45?35)?1/900?0.001611/[W/(m2?0C)]K0?603W/(m2?0C)?tm?(35?15)/Ln(35/15)?23.60CS?225?103/(603?23.6)?15.8m229)两种流体在一列管换热器中逆流流动，热流体进出口温度为1000C，出口温度为600C冷流体从200C加热到500C,试求下列情况下的平均温差：①换热器为单壳程，四管程。②换热器为双管程，四管程。解：PR?1）?((10050?t?m?20?(60)50)/(（/100?4050?)Ln(50/40)?44.80C?2020)）??01..37533查表得：??t?0.91?tm1???t?t11m?40.80C2）查表得：??t2?0.97?tm2???t2?tm?43.50C
30)在逆流换热器中，用水冷却某液体，水的进出口温度分别为150C和 800C，液体的进出口温度分别为1500C和750C。现因生产任务要求液体进出口温度降至700C，假设水和液体的进出口温度，流量及物性均不发生变化，换热器的损失忽略不计，试问此换热器管长增为原来的多少倍才能满足生产要求？解:?Qh?QCWhCph?T?WcCpc?t则WhCph(150?75)?WcCpc(80?15)'WhCph(150?70)?WcCpc(t2?15)'t2?84.30C?tm?(70?60)Ln(70/60)?64.90C'?tm?(65.7?55)Ln(65.7/55)?60.20C又Q?KS?tm'Q'?KS'?tm75WhCph?64.9KS80WhCph?60.2KS'?S'/S?1.149即:L'/L?1.14931) 120℃饱和水蒸汽将空气从20℃加热至80℃，空气流量1.20×104kg/h。现有单程列管换热器，?25×2.5mm钢管300根，管长3m，?0 = 104W/(m2℃)，污垢及管壁热阻不计。问此换热器能否满足要求。
20?80t??502解：℃
50℃空气，? = 1.093kg/m3，Cp = 1.005kJ/(kg?℃)，? = 0.02824W/(m?℃) ? = 1.96×10-5 Pa?s ，Pr = 0.698
V120.?104u???32.4?2?nd3600?1093.??0.022?30044 m/s du?0.020?32.4?1093.Re???3.61?104?5?196.?10＞10000
∴
?i?0.023?diRe0.8Pr0.4?0.023?0.02824?3.61?1040.020??0.8?0.6980.4
?154.5W/(m2℃)
∵?0＞＞?i ∴Ki = ?i = 124.5 W/(m2℃)
120.?104Q = WcCpc?t = 3600×1.005×60 = 201 kJ/s
100?40?655.100ln40?tm = ℃
Q = KiAi?tm 即 201×103 = 124.5Ai×65.5 ∴Ai = 24.6 m2
又，Ai = n?diL 即 24.6 = 300?×0.020L ∴ L = 1.31 m＜3 m ∴ 满足要求
32）某单壳程单管程列管换热器，用1.8×105Pa饱和水蒸汽加热空气，水蒸汽走壳程，其给热系数为105 W/(m·℃)，空气走管内，进口温度20℃，要求出口温度达110℃，空气在管内流速为10m/s。管子规格为φ25×2.5mm的钢管，管数共269根。试求换热器的管长。
若将该换热器改为单壳程双管程，总管数减至254根。水蒸汽温度不变，空气的质量流量及进口温度不变，设各物性数据不变，换热器的管长亦不变，试求空气的出口温度。
解:t?(20?110)/2?650C查空气物性数据：CP?1.007kJ/kg0C??0.0294w/m0CPr?0.695??2.04?10?5Pa?s1.8?105Pa的饱和水蒸气：T?116.60C1)Re?10245.1?10000??1.045kg/m3I?2214.3KJ/kg?i?0.023?Re0.8Pr0.4/di?47.23w/m0C每根管内:WC??d2u?/4???0.022?10?1.045?0.03283kg/sQ?WCCPC?t?0.003283?1.007?103?90?0.29753kg/s??0???i?Ki??i?tm?(96.6?6.6)/Ln(96.6/6.6)?33.540CQ?KiSi?tm?Si?0.1878m2Si??diL?L?3m
2)质量流量不变u'?269?10/254/2?21.18m/s?i'?(21.18/10)0.8?47.23?86.10w/(m?0C)Ki'??i'?83.00w/(m2C)WC'??(n/2)d2u'?/4?0.8826kg/s?R?0???t?1
0'''?tm?(t2?20)/Ln96.6/(116.6?t2)Si'?n?diL?254?3.14?0.02?3?47.85m2由方程：Q?WC'CPC?t'Q?Ki'Si'?tm'解得t2?115.70C
33）一套管换热器，用热柴油加热原油，热柴油与原油进口温度分别为155℃和20℃。已知逆流操作时，柴油出口温度50℃，原油出口60℃，若采用并流操