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 95P
To determine

The surface area of the heat exchanger using both LMTD method and εNTU method.

Expert Solution & Answer
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Explanation of Solution

Given:

The number of shells is 1.

The number of passes is 8.

The mass flow rate of water is 50000lbm/h.

The inlet temperature (Tc,in) of water is 70°F.

The outlet temperature (Tc,out)  of water is 150°F.

The specific heat (cp,h) of the hot air is 0.25Btu/lbm.°F.

The inlet temperature (Th,in) of air is 600°F.

The outlet temperature (Th,out) of air is 300°F.

The heat transfer coefficient (h) on the outer surface of the tube is 30Btu/h.ft2.°F.

The possible fouling resistance on water and air side is 0.0015h.ft2.°F/Btu and 0.001h.ft2.°F/Btu respectively.

Calculation:

From Table A-3E, the specific heat (cp,c) of water at the average temperature of (150+70)°F/2=110°F is 1Btu/lbm°F.

Calculate the heat gained by water from hot air using the relation.

    Q˙=m˙ccpc(TcoutTcin)=(50000lbm/h)×(1Btu/lbm°F)×(150°F70°F)=4×106Btu/h

Calculate the mass flow rate of the hot air using the relation.

    m˙hcp,h(Th,inTh,out)=m˙ccp,c(Tc,outTc,in)m˙h=m˙ccp,c(Tc,outTc,in)cph(Th,inTh,out)m˙h=(4×106Btu/h)(0.25Btu/lbm.°F)(600°F300°F)m˙h=53333.33lbm/hr

Calculate (ΔT1).

  ΔT1=Th,inTc,out=600°F150°F=450°F

Calculate (ΔT2).

  ΔT2=Th,outTc,in=300°F70°F=230°F

Calculate the logarithmic mean temperature difference LMTD of a counter flow heat exchanger using the relation.

    LMTD=ΔT1ΔT2ln(ΔT1/ΔT2)=450°F230°Fln(450°F230°F)=327.78°F

Calculate the value of P using the relation.

    p=t2t1T1t1=300°F600°F70°F600°F=0.566

Calculate the value of R using the relation.

    R=T1T2t2t1=70°F150°F300°F600°F=0.266

Refer Figure 22-19 “Correction factor F charts for common shell-and-tube and cross-flow heat exchangers.”

Obtain the value of correction factor (F) from “one-shell passes and 4,8,12,etc. (any multiple of 4 ) tube passes” as follows:

    F=0.96

Calculate the overall heat transfer rate using the relation.

    1U=1h+Rf,water+Rf,air=130Btu/hft2°F+0.0015h.ft2.°F/Btu+0.001h.ft2.°F/BtuU=27.9Btu/hft2°F

Calculate the heat transfer rate using the relation.

    Q˙=UAsFLMTDAs=Q˙UFLMTD=(4×106Btu/h)(27.9Btu/hft2°F)(0.96)(327.78°F)=455.5ft2

Calculate the heat capacity rate of the cold fluid using the relation.

    Cc=m˙ccpc=(50000lbm/h)(1Btu/lbm.°F)=50000Btu/h.°F

Calculate the heat capacity rate of the hot fluid using the relation.

    Ch=m˙hcph=(53333.33lbm/h)(0.25Btu/lbm.°F)=13333.33Btu/h.°F

Calculate the capacity rate ration using the relation.

    c=CminCmax=(13333.33Btu/h.°F)(50000Btu/h.°F)=0.266

Calculate the effectiveness of the heat exchanger using the relation.

    ε=Q˙Q˙max=Ch(ThinThout)Cmin(ThinTcin)=(600°F300°F)(600°F70°F)=0.566

Calculate the NTU using the relation.

    NTU=11+c2ln(2/ε1c1+c22/ε1c+1+c2)=11+0.2662ln(2/0.56610.2661+0.26622/0.56610.266+1+0.2662)=11.034ln(1.2333.034)=0.952

Calculate the surface area of the heat exchanger using the relation.

    NTU=UAsCminAs=NTU×CminU=(0.952)(13333.33Btu/h.°F)27.9Btu/h.ft2.°F=454.95ft2

Thus, the surface area of the heat exchanger using both LMTD method and ε,NTU method is 455.5ft2 and 454.95ft2 respectively.

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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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