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 130RQ

(a)

To determine

The outlet temperatures of both streams in steady operation using the LMTD method.

(a)

Expert Solution
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Explanation of Solution

Given:

The mass flow rate of steam (m) is 2700kg/h.

The specific heat of steam (c) is 2.0kJ/kgK.

The temperature of steam inlet (Th,in) is 120°C.

The mass flow rate of other steam (m) is 1800kg/h.

The specific heat of other steam (c) is 4.2kJ/kgK.

The temperature of other steam inlet (Tc,in) is 20°C.

The overall heat transfer coefficient (U) is 2.0kW/m2K.

The area of heat exchanger (A) is 0.5m2.

Calculation:

Calculate the rate of heat transfer (Q˙1) using the relation.

    Q˙1=m˙cp(Th,inTh,out)=(2700kg/h(1h3600s))(2.0kJ/kgK)((120°C+273)KTh,out)

Calculate the rate of heat transfer (Q˙2) using the relation.

    Q˙2=m˙cp(Tc,outTc,in)=(1800(kgh)(1h3600s))(4.2kJ/kgK)(Tc,out(20°C+273)K)

Calculate the Logarithmic mean temperature (ΔTm) using the relation.

  ΔTm=ΔT1ΔT2ln(ΔT1ΔT2)=(Th,inTc,in)(Th,outTc,out)ln(Th,inTc,inTh,outTc,out)=(120°C20°C)(Th,outTc,out)ln(120°C20°CTh,outTc,out)

Calculate the heat transfer rate (Q) using the relation.

    Q˙=(2.0kW/m2K)(0.5m2)(120°C20°C)(Th,outTc,out)ln(120°C20°CTh,outTc,out)=100°C(Th,outTc,out)ln(100°CTh,outTc,out)

Solve the above equation to obtain the outlet temperature of hot steam (Thout) and outlet temperature of cold steam (Tcout) as follows:

    Thout=80.3°CTcout=48.4°C

Thus, the outlet temperatures of hot steam is 80.3°C and cold steam is 48.4°C in steady operation using the LMTD method.

(b)

To determine

The outlet temperatures of both streams in steady operation using the effectiveness–NTU method.

(b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the product of mass flow rate of hot stream and specific heat (mhcph) using the relation.

    (m˙hcp)=(2700kg/h×(1h3600s))(2000J/kgK)=(1500J/sK×1kW1000J/s)=1.5kW/K

Calculate the product of mass flow rate of cold steam and specific heat (mccpc) using the relation.

    (m˙ccpc)=(1800kg/h×(1h3600s))(4200J/kgK)(2100J/sK×1kW1000J/s)=2.1kW/K

Calculate the heat capacity ratio (c) using the relation.

    c=CminCmax=1.5kW/K2.1kW/K=0.7143=

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

  NTU=UACmin=(2.0kW/m2K)(0.5m2)1.5kW/K=0.667

Calculate the effectiveness of this parallel-flow heat exchanger (ε)  using the relation.

    ε=1exp[NTU(1+c)]1+c=1exp[(0.6667)(1+0.7143)]1+0.7143=0.3973

Calculate the maximum heat transfer rate (Qmax) using the relation.

    Q=Cmin(Th,inTc,in)=(1.5kW/m2K)((120°C+273)K(20°C+273)K)=150kW

Calculate the heat transfer rate (Q) using the relation.

    Q=εQmax=(0.3973)(150kW)=59.60kW

Calculate the outlet temperature of cold steam (Tc,out) using the relation.

    Tc,out=Tc,in+QCc=(20°C+273)K+59.6kW2.1kW/K=(321.38K273)°C=48.4°C

Calculate the outlet temperature of hot steam (Th,out) using the relation.

    Th,out=Th,inQCh=(120°C+273)K59.6kW1.5kW/K=(353.3K273)°C=80.3°C

Thus, the outlet temperatures of hot steam is 80.3°C and cold steam is 48.4°C in steady operation using the NTU method.

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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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