Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 17, Problem 111P

(a)

To determine

The average surface temperature of the pipe disregarding the flanges.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Length of the pipe is 3 m.

Thickness of the pipe is 0.4 cm.

Thermal conductivity of the pipe is 52W/mK.

Outer diameter of the pipes is 10 cm.

Thickness of the flanges is 1 cm.

Outer diameter of the flange is 20 cm.

Temperature of steam is 200°C.

The heat transfer coefficient of the inside is 180W/m2K.

Temperature of ambient air is 12°C.

The heat transfer coefficient of the outside is 25W/m2K.

Calculation:

The total thermal resistance is,

  Rtotal=Ri+Rcond+Ro=1hiAi+ln(r2/r1)2πkL+1hoAo=1(180W/m2K)(π×0.092 m×6 m)+ln(5/4.6)2π(52W/mK)(6 m)+1(25W/m2K)(π×0.1 m×6 m)=0.02447°C/W

The rate of heat transfer is,

  Q˙=T1T2Rtotal=(20012)°C0.02447°C/W=7684 W

Calculate the surface temperature of the pipe.

  Q˙=T2T2Ro7684 W=(T212)°C1(25W/m2K)(π×0.1 m×6 m)T2=175°C

Thus, the average surface temperature of the pipe disregarding the flanges is 175°C.

(b)

To determine

The efficiency of the fin and the rate of heat transfer from the flanges.

(b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the value of r2cr1.

  r2cr1=r2+t2r1=0.1+0.0220.05=2.2

Calculate the value of ε.

  ε=Lc3/2hkAp=(L+t2)3/2hkt=(0.05 m+0.022 m)3/225W/m2K(52W/mK)(0.02 m)=0.29

Obtain the efficiency of the fin from Figure 17 – 44 corresponding to the above values as ηfin=0.93

Thus, the efficiency of the fin is 0.93.

Calculate the heat transfer rate from the flanges.

  Q˙finned=ηfinQ˙max=ηfinhAfin(TbT)=ηfinh[2π(r22r12)+2πr2t](TbT)=(0.93)(25W/m2K)2π[(0.1m)2(0.05m)2+(0.1 m)(0.02 m)](17512)K=226W

Thus, the heat transfer rate from the flanges is 226W.

(c)

To determine

The length of the pipe equivalent to the flanges for heat transfer purpose.

(c)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

The heat transfer rate per unit length of the pipe is,

  7684 W6 m=1271 W/m

The equivalent length of the pipe is,

  Leqv=226 W1281W/m=0.176 m=17.6 cm

Thus, the length of the pipe equivalent to the flanges for heat transfer purpose is 17.6 cm.

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Chapter 17 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

Ch. 17 - Consider a surface of area A at which the...Ch. 17 - How does the thermal resistance network associated...Ch. 17 - Consider steady one-dimensional heat transfer...Ch. 17 - Consider a window glass consisting of two...Ch. 17 - Prob. 15PCh. 17 - Prob. 16PCh. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - Prob. 19PCh. 17 - Consider a power transistor that dissipates 0.2 W...Ch. 17 - A 1.0 m × 1.5 m double-pane window consists of two...Ch. 17 - Consider a 1.2-m-high and 2-m-wide glass window...Ch. 17 - Prob. 23PCh. 17 - Prob. 24PCh. 17 - Prob. 26PCh. 17 - Prob. 27PCh. 17 - Prob. 28PCh. 17 - Prob. 29PCh. 17 - Prob. 30PCh. 17 - A 2-m × 1.5-m section of wall of an industrial...Ch. 17 - The wall of a refrigerator is constructed of...Ch. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - What is thermal contact resistance? How is it...Ch. 17 - Will the thermal contact resistance be greater for...Ch. 17 - Explain how the thermal contact resistance can be...Ch. 17 - A wall consists of two layers of insulation...Ch. 17 - A plate consists of two thin metal layers pressed...Ch. 17 - Consider two surfaces pressed against each other....Ch. 17 - Prob. 43PCh. 17 - Prob. 44PCh. 17 - Prob. 45PCh. 17 - Prob. 46PCh. 17 - Prob. 47PCh. 17 - Prob. 48PCh. 17 - Prob. 49PCh. 17 - Prob. 50PCh. 17 - Prob. 51PCh. 17 - Prob. 52PCh. 17 - Prob. 53PCh. 17 - When plotting the thermal resistance network...Ch. 17 - Prob. 55PCh. 17 - Prob. 56PCh. 17 - Prob. 57PCh. 17 - A typical section of a building wall is shown in...Ch. 17 - Prob. 59PCh. 17 - Prob. 61PCh. 17 - Prob. 62PCh. 17 - Prob. 63PCh. 17 - In an experiment to measure convection heat...Ch. 17 - What is an infinitely long cylinder? When is it...Ch. 17 - Can the thermal resistance concept be used for a...Ch. 17 - Consider a short cylinder whose top and bottom...Ch. 17 - Prob. 68PCh. 17 - 50-m-long section of a steam pipe whose outer...Ch. 17 - Superheated steam at an average temperature 200°C...Ch. 17 - Steam exiting the turbine of a steam power plant...Ch. 17 - Repeat Prob. 17–72E, assuming that a 0.01-in-thick...Ch. 17 - A 2.2-mm-diameter and 10-m-long electric wire is...Ch. 17 - Prob. 76PCh. 17 - Chilled water enters a thin-shelled 5-cm-diameter,...Ch. 17 - Steam at 450°F is flowing through a steel pipe (k...Ch. 17 - Prob. 79PCh. 17 - Prob. 80PCh. 17 - An 8-m-internal-diameter spherical tank made of...Ch. 17 - What is the critical radius of insulation? How is...Ch. 17 - Consider an insulated pipe exposed to the...Ch. 17 - A pipe is insulated to reduce the heat loss from...Ch. 17 - Prob. 86PCh. 17 - Prob. 87PCh. 17 - A 0.083-in-diameter electrical wire at 90°F is...Ch. 17 - Prob. 89PCh. 17 - Prob. 90PCh. 17 - Prob. 92PCh. 17 - What is the reason for the widespread use of fins...Ch. 17 - What is the difference between the fin...Ch. 17 - The fins attached to a surface are determined to...Ch. 17 - Explain how the fins enhance heat transfer from a...Ch. 17 - How does the overall effectiveness of a finned...Ch. 17 - Hot water is to be cooled as it flows through the...Ch. 17 - Consider two finned surfaces that are identical...Ch. 17 - The heat transfer surface area of a fin is equal...Ch. 17 - Prob. 101PCh. 17 - Prob. 102PCh. 17 - Two plate fins of constant rectangular cross...Ch. 17 - Two finned surfaces are identical, except that the...Ch. 17 - A 4-mm-diameter and 10-cm-long aluminum fin (k =...Ch. 17 - Consider a very long rectangular fin attached to a...Ch. 17 - Consider a stainless steel spoon (k = 8.7...Ch. 17 - A DC motor delivers mechanical power to a rotating...Ch. 17 - A plane wall with surface temperature of 350°C is...Ch. 17 - Prob. 111PCh. 17 - Steam in a heating system flows through tubes...Ch. 17 - Prob. 113PCh. 17 - A hot surface at 100°C is to be cooled by...Ch. 17 - Prob. 116PCh. 17 - A 40-W power transistor is to be cooled by...Ch. 17 - Prob. 118PCh. 17 - Prob. 119RQCh. 17 - Cold conditioned air at 12°C is flowing inside a...Ch. 17 - Prob. 121RQCh. 17 - Prob. 122RQCh. 17 - Prob. 123RQCh. 17 - Prob. 124RQCh. 17 - Prob. 125RQCh. 17 - Prob. 126RQCh. 17 - Prob. 127RQCh. 17 - Prob. 128RQCh. 17 - Prob. 129RQCh. 17 - Prob. 130RQCh. 17 - Prob. 131RQ
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