k2/k1?2 and both insulating materials have the same thickness 30mm. If the temperature

difference between pipe wall and outer surface of insulating material is constant, which insulating material should be packed inside to enable less heat loss?

solution：

k1（lower thermal conductivity）

the insulating material with a lower thermal conductivity placed outside, rate of heat loss Q???t?Ri??tb1b2?k2Am1k1Am2 Am2?i2?L(r3?r2) r3lnr2and Am1?2?L(r2?r1), thickness of two layers are equal b1=b2=b, and k2/k1?2 r2lnr1?t?k1b?t11?2Am1Am2

Q?bb?2k1Am1k1Am2contrarily, place the material with lower thermal conductivity inside, heat loss Q???tb1b2?k1Am1k2Am2??tbb?k1Am12k1Am2?k1?t 1b1?Am12Am21Am1?2Am2?AQ??1 for m1?1

Am1QAm21?2Am2so with less heat loss obtained as the material with lower thermal conductivity is placed inside

4.7. Air at the normal pressure passes through the pipe (di 20 mm) and is heated from 20C to 100

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C. What is the film heat transfer coefficient hi between the air and pipe wall if the average

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velocity of air is 10 m/s? The properties of air at 60 C are as follows:

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Air: density ?=1.06 kg/m3, viscosity μ= 0.02 cp, conductivity k=0.0289 W/(m?C), and heat

capacity cp =1 kJ/(kg?K). Solution:

Re?du??cp??0.02?10?1.06?10600 ?30.02?101000?0.02?10?3Pr???0.692

k0.0289hi?0.023?47.6

4.8. Methyl alcohol flowing in the inner pipe of a double-pipe exchanger is cooled with water flowing in the jacket. The inner pipe is made from 25-mm Schedule 40 steel pipe. The thermal

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conductivity of steel is 45 W/(m·C). The individual coefficients and fouling factors are given in

k0.0289Re0.8Pr0.4?0.023?106000.8?0.6920.4?0.03324?1660.5?0.863di0.02the following Table. What is the overall coefficient, based on the outside area of the inner pipe?

TABLE Data for Problem 8

Coefficient/ W/(m2·°C)

Alcohol coefficient hi 1020 Water coefficient ho 1700 Inside fouling factor hdi 5680 Outside fouling factor hdo 2840 Solution:

From equation (4.3-37)

Uo?1

dodobdo11????dihdidihikdmhohdofrom appendix 3, the wall thickness is 3.25mm and outside diameter is 33.5mm for nominal diameter 25mm Schedule 40 standard steel pipe

dm?33.5?27?30.25mm 2Uo?133.533.50.0032533.511????27?568027?10204530.25170028401 ?2.184?10?4?1.216?10?3?7.998?10?5?5.882?10?4?3.521?10?4?407.4W/m2oC

4.9. Benzene with mass flow 1800kg?h-1flows through the annulus of double pipe exchanger. Its temperature changes from 20oC to 80 oC. The dimension of inner tube is ?19×2.5mm, and the dimension of outer tube is Φ38×3mm. What is individual heat transfer coefficient of benzene?

Solution:

Outside diameter of inner tube do =19mm, inside diameter of outer tube Di=32mm The equivalent diameter of annular space of double tube de is

?de?44(Di2?do2)?(Di?do)?Di?do?32?19?13mm

from equation

k?deu???h?0.023??de????0.8?cp????k?? 1 ??0.4tm?80?20?50oC 2the properties of benzene: μ=0.45×10-3Pas，cp=1.81kJ/kg.℃，k=0.138W/m℃，ρ= 850kg/m3 at average temperature of 50℃ and

average velocity of benzene flowing through the annular space of double tube is calculated as follow

m???4(Di2?do2)u

u?4m4?1800??1.13m/s

??(Di2?do2)3600???8500.0322?0.0192??Substituting the variables into equation 1 gives

kh?0.023de?deu?????????0.8?cp????k????0.40.138?0.013?1.13?850?＝0.023??0.013?0.45?10?3?

?1.81?103?0.45?10?3?????0.138???0.244?277480.8?5.90.4＝1780W/(m2·?C)0.80.4

4.10. Air at 2 atm and 20oC flows through in the pipe of tubular exchanger at 60m3?h-1, and is heated to 80C.The dimension of pipe is ?57×3.5mm and its length is 3m long. What is individual heat transfer coefficient of air side? Solution:

Temperature of air at inlet and outlet t1=20 oC, t2=80 oC. average temperature

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tm?t1?t220?80??50 oC 22from App.7, viscosity of air at 50 oC μ=0.019×10-3Pas, and

density at 2atm, on assuming that a air follows ideal law,

??PM2?29??2.188kg/m3 RT0.08206?(50?273)from App. 11, thermal conductivity of air

k?0.0242?0.0318?0.028W/mK

2from App.13 specific heat of air cp=1KJ/kgK The velocity of air flowing through tube

u?4V4?60??8.49m/s ?d23600?3.14?0.052du?Re??cp??0.05?8.49?2.188?48884.5 ?30.019?101?103?0.019?10?3Pr???0.68

k0.028h?

kNuk0.028?48884.5?0.8?0.68?0.4?62.3W/m2K ?0.023Re0.8Pr0.4?0.023dd0.054.12. A hot fluid with a mass flow rate 2250 kg/h passes through a ?25x2.5 mm tube. The physical properties of fluid are as follows:

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k=0.5 w/(m ?C), cp =4 kJ/(kg?K), viscosity 10-3 N?s/m , density 1000 kg/m Find:

(1) Heat transfer film coefficient hi , in W/(m2?K).