Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 22, Problem 23P
To determine

The overall heat transfer coefficient based on the inner and the outer surface of copper tube.

Expert Solution & Answer
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Explanation of Solution

Given:

The heat capacity for hot fluid (C) is 4440W/K.

The inlet temperature for hot fluid (Thi) is 150°C.

The length of tube (L) is 1.5m.

The thermal conductivity of copper (k) is 250W/mK.

The inner diameter of inner tube (Di) is 2cm.

The outer diameter of inner tube (Do) is 2.25cm.

The mass flow rate of hot fluid (m˙h) is 2kg/s.

The exit temperature of hot fluid (Te) is 50°C.

The inlet temperature for cold fluid (Tci) is 20°C.

The outlet temperature for cold fluid (Tce) is 70°C.

The outside fouling factor (Rf)o is 0.00015m2K/W.

The outside fouling factor (Rf)i is 0.0001m2K/W.

Calculation:

Refer Table A-19 “Properties of liquid”.

Obtain the following properties of liquid corresponding to the temperature of 100°C as follows:

ρ=840kg/m3

cp=2220kJ/kgK

k=0.1367W/mK

μ=0.01718×103kg/ms

Pr=279.1

Refer Table A-15 “Properties of water”.

Obtain the following properties of liquid corresponding to the average temperature of 45°C as follows:

ρ=990.1kg/m3

cp=4180kJ/kgK

k=0.637W/mK

μ=0.596×103kg/ms

Pr=3.91

Calculate the inner surface areas of the heart exchanger.

  Ai=πDiL=π(2cm(1m100cm))(1.5m)=0.0942m2

Calculate the outer surface areas of the heart exchanger.

  Ao=πDoL=π(2.25cm(1m100cm))(1.5m)=0.106m2

Calculate the volume flow rate of the oil.

  V=4m˙hρπDi2=4(2kg/s)π(840kg/m3)(2cm(1m100cm))=7.58m/s

Calculate the Reynolds number for the oil.

  Re=ρVDiμ=(840kg/m3)(7.58m/s)(2cm(1m100cm))0.01718kg/ms=7412

Calculate the mass flow rate of cooling water.

  C(ThiThe)=m˙ccpc(TceTci)(4440W/K)(150°C50°C)=m˙c(70°C20°C)m˙c=2.124kg/s

Calculate the hydraulic diameter of the annular space on the shell side.

  Dh=DoDi=6cm(1m100cm)2.25cm(1m100cm)=0.0375m

Calculate the average velocity of cooling water.

  V=4m˙ρπDh2=4(2.124kg/s)(990.1kg/m3)π(0.0375m)2=1.942m/s

Calculate the number for the flow of water.

  Re=ρVDhμ=(990.1kg/m3)(1.942m/s)(0.0375m)0.596×102kg/ms=120980

Calculate the friction factor for oil.

  f=(0.79lnRe1.64)2=(0.79ln(7412)1.64)2=0.03429

Calculate the friction factor for water.

  f=(0.79lnRe1.64)2=(0.79ln(120980)1.64)2=001728

Calculate the Nusselt number for oil.

  Nu=(f/8)(Re1000)Pr1+12.7f/8(Pr2/31)=(0.03429/8)(74121000)279.11+12.70.03429/8(279.12/31)=214.94

Calculate the inner convective heat transfer coefficient for oil.

  hi=kDNu=(0.1367W/mK)(214.94)0.02m=1469.11W/m2K

Calculate the Nusselt number for water.

  Nu=(f/8)(Re1000)Pr1+12.7f/8(Pr2/31)=(0.01728/8)(1209801000)3.911+12.70.01728/8(3.912/31)=540.52

Calculate the inner convective heat transfer coefficient for water.

  ho=kDhNu=(0.637W/mK)(540.52)0.0375m=9188.25W/m2K

Calculate the overall heat transfer coefficient.

    1UAs=1hiAi+(Rf)iAi+ln(DoDi)2πkL+(Rf)oAo+1hoAo=[1(1469.1W/m2K)(0.0942m2)+0.0015m2K/W0.0942m2+ln(2.25cm2cm)2π(25W/mK)(1.5m)+0.0001m2K/W0.106m2+1(9188.25W/m2K)(0.106m2)]=0.01083K/W

Calculate the overall heat transfer based on the inner surface.

  1UiAi=1UAs1Ui=(0.01083K/W)(0.0942m2)Ui=979.4W/m2K

Calculate the overall heat transfer based on the outer surface.

  1UoAo=1UAs1Ui=(0.01083K/W)(0.106m2)Ui=871.09W/m2K

Thus, overall heat transfer based on the outer surface is 871.09W/m2K and overall heat transfer based on the inner surface is 979.4W/m2K.

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Chapter 22 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 22 - Prob. 11PCh. 22 - Prob. 12PCh. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 15PCh. 22 - Prob. 17PCh. 22 - Prob. 18PCh. 22 - Prob. 19PCh. 22 - Water at an average temperature of 110°C and an...Ch. 22 - Prob. 21PCh. 22 - Prob. 23PCh. 22 - Prob. 24PCh. 22 - Under what conditions is the heat transfer...Ch. 22 - Consider a condenser in which steam at a specified...Ch. 22 - What is the heat capacity rate? What can you say...Ch. 22 - Under what conditions will the temperature rise of...Ch. 22 - Show that the temperature profile of two fluid...Ch. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Prob. 33PCh. 22 - Prob. 34PCh. 22 - Prob. 35PCh. 22 - Prob. 36PCh. 22 - Prob. 37PCh. 22 - Prob. 38PCh. 22 - Prob. 39PCh. 22 - A double-pipe parallel-flow heat exchanger is to...Ch. 22 - Glycerin (cp = 2400 J/kg·K) at 20°C and 0.5 kg/s...Ch. 22 - Prob. 43PCh. 22 - A single pass heat exchanger is to be designed to...Ch. 22 - Prob. 45PCh. 22 - Prob. 46PCh. 22 - Prob. 47PCh. 22 - A counter-flow heat exchanger is stated to have an...Ch. 22 - Prob. 49PCh. 22 - Prob. 51PCh. 22 - Prob. 52PCh. 22 - Prob. 54PCh. 22 - Prob. 56PCh. 22 - A performance test is being conducted on a...Ch. 22 - In an industrial facility a counter-flow...Ch. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - A shell-and-tube heat exchanger with 2-shell...Ch. 22 - A shell-and-tube heat exchanger with 2-shell...Ch. 22 - Repeat Prob. 22–64 for a mass flow rate of 3 kg/s...Ch. 22 - A shell-and-tube heat exchanger with 2-shell...Ch. 22 - A single-pass cross-flow heat exchanger is used to...Ch. 22 - Prob. 68PCh. 22 - Prob. 69PCh. 22 - Prob. 70PCh. 22 - Prob. 71PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Under what conditions can a counter-flow heat...Ch. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 77PCh. 22 - Prob. 78PCh. 22 - Prob. 79PCh. 22 - Prob. 80PCh. 22 - Prob. 81PCh. 22 - Consider an oil-to-oil double-pipe heat exchanger...Ch. 22 - Hot water enters a double-pipe counter-flow...Ch. 22 - Hot water (cph = 4188 J/kg·K) with mass flow rate...Ch. 22 - Prob. 85PCh. 22 - Cold water (cp = 4180 J/kg·K) leading to a shower...Ch. 22 - Prob. 89PCh. 22 - Prob. 90PCh. 22 - Prob. 91PCh. 22 - Prob. 92PCh. 22 - Prob. 93PCh. 22 - Prob. 94PCh. 22 - Prob. 95PCh. 22 - Air (cp = 1005 J/kg·K) enters a cross-flow heat...Ch. 22 - A cross-flow heat exchanger with both fluids...Ch. 22 - Prob. 98PCh. 22 - Prob. 99PCh. 22 - Oil in an engine is being cooled by air in a...Ch. 22 - Prob. 101PCh. 22 - Prob. 102PCh. 22 - Prob. 103PCh. 22 - Water (cp = 4180 J/kg·K) enters the...Ch. 22 - Prob. 105PCh. 22 - Prob. 106PCh. 22 - Prob. 107PCh. 22 - Prob. 109PCh. 22 - Consider the flow of saturated steam at 270.1 kPa...Ch. 22 - Prob. 111RQCh. 22 - Prob. 112RQCh. 22 - Prob. 113RQCh. 22 - A shell-and-tube heat exchanger with 1-shell pass...Ch. 22 - Prob. 115RQCh. 22 - Prob. 116RQCh. 22 - Prob. 117RQCh. 22 - Prob. 118RQCh. 22 - A shell-and-tube heat exchanger with two-shell...Ch. 22 - Saturated water vapor at 100°C condenses in the...Ch. 22 - Prob. 121RQCh. 22 - Prob. 122RQCh. 22 - Prob. 123RQCh. 22 - Prob. 124RQCh. 22 - Prob. 125RQCh. 22 - A cross-flow heat exchanger with both fluids...Ch. 22 - In a chemical plant, a certain chemical is heated...Ch. 22 - Prob. 128RQCh. 22 - Prob. 129RQCh. 22 - Prob. 130RQCh. 22 - Prob. 134DEP
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