Package: Loose Leaf For Fundamentals Of Thermal-fluid Sciences With 1 Semester Connect Access Card
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Chapter 22, Problem 89P

(a)

To determine

The overall heat transfer coefficient of this exchanger using the LMTD method.

(a)

Expert Solution
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Explanation of Solution

Given:

The specific heat (cph)  of the oil is 0.525Btu/lbm.°F.

The inlet temperature (thin) of oil is 300°F.

The outlet temperature (thout) of the oil is 105°F.

The mass flow rate m˙h of the oil is 5lbm/s.

The specific heat (cpc) of water is 1.0Btu/lbm.°F.

The inlet temperature (tcin) of water is 70°F.

The mass flow rate m˙c of the oil is 3lbm/s.

The diameter (D)  of the tube is 5inch

The length (L)  of the tube is 200ft.

Calculation:

Calculate the rate of heat transfer using the relation

    Q˙=m˙hcph(ThinThout)=(5lbm/s)×(0.525Btu/lbm.°F)×(300°F105°F)=511.9Btu/s

Calculate the outlet temperature of the cold fluid using the relation.

    Q˙=m˙ccpc(TcinTcout)Tcout=Tcin+Q˙m˙ccpc=70°F+511.9Btu/s(3lbm/s)(1.0Btu/lbm.°F)=240.6°F

Calculate the temperature difference between the two fluids at the two ends of the heat exchanger using the relation.

    ΔT1=ThinThout=300°F240.6°F=59.4°F

    ΔT2=ThoutTcin=105°F70°F=35°F

Calculate the logarithmic mean temperature difference using the relation.

    LMTD=ΔT1ΔT2ln(ΔT1/ΔT2)=59.4°F35°Fln(59.4°F/35°F)=46.1°F

Calculate the overall heat transfer coefficient using the relation.

    Q˙=U.As.LMTDU=Q˙As.LMTD=511.9Btu/sπ(5in(1ft12in))(200ft)(46.1°F)=0.0424Btu/s.ft2.°F

Thus, the overall heat transfer coefficient of this exchanger using the LMTD method is 0.0424Btu/s.ft2.°F.

(b)

To determine

The overall heat transfer coefficient of this exchanger using the ε,NTU method.

(b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the heat capacity rates of the hot and cold fluids using the relation

    Ch=m˙hcph=(5lbm/s)×(0.525Btu/lbm.°F)=2.625Btu/s.°F

    Cc=m˙ccpc=(3lbm/s)×(1.0Btu/lbm.°F)=3.0Btu/s.°F

Here Ch=2.625Btu/s.°F is minimum.

Calculate the capacity rate ratio using the relation.

    c=CminCmax=2.625Btu/s.°F3.0Btu/s.°F=0.875

Calculate maximum heat transfer rate using the relation.

    Q˙max=Cmin(TcinTcin)Q˙max=(2.625Btu/s.°F)(300°F70°F)=603.75Btu/s

Calculate the actual rate of heat transfer using the relation.

    Q˙=Ch(TcinThout)=(2.625Btu/s.°F)(300°F105°F)=511.9Btu/s

Calculate the effectiveness of the heat exchanger using the relation.

    ε=Q˙Q˙max=511.9Btu/s603.75Btu/s=0.85

Calculate the number of transfer units (NTU) using the relation.

    NTU=1c1ln(ε1εc1)=10.8751ln(0.8510.85×0.8751)=4.28

Calculate the heat transfer surface area using the relation.

    As=πDL=π(5/12ft)(200ft)=261.8ft2

Calculate the overall heat transfer coefficient using the relation.

    NTU=UAsCminU=NTU.CminAs=(4.28)(2.635Btu/s.°F)261.8ft2=0.0429Btu/s.ft2.°F

Thus, the overall heat transfer coefficient of this exchanger using the ε,NTU method is 0.0429Btu/s.ft2.°F.

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Chapter 22 Solutions

Package: Loose Leaf For Fundamentals Of Thermal-fluid Sciences With 1 Semester Connect Access Card

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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