Explanation Given information: Surface temperature is 100 ° C . The length and diameter of fins is 3 c m , 0.25 c m . The thermal conductivity of aluminum fins is 237 W / m . K . The surrounding temperature is 30 ° C . Heat transfer coefficient is 35 W / m 2 . K . The fin efficiency η f i n is defined as: η f i n = tanh m L c m L c In the above equation, h - Heat transfer co-efficient p - Perimeter k - Thermal conductivity A c - Cross-sectional area m = h p k A c The heat transfer rate Q ˙ n o f i n of the tube under no fin case: Q ˙ n o f i n = h A n o f i n ( T b − T ∞ ) The heat transfer rate Q ˙ f i n is defined as: Q ˙ f i n = η f i n h A f i n ( T b − T ∞ ) In the above equation h - Heat transfer co-efficient A f i n - Fin cross-section area η f i n - Fin efficiency T b - Base temperature T ∞ - Surrounding temperature A n o f i n - Tube cross-section area Calculation: The value of ‘ m ’ m = h p k A c = h π D k ( π D 2 / 4 ) = 4 h k D Substitute and solve m = 4 ( 35 W / m 2 . K ) ( 237 W / m . K ) ( 0.0025 m ) = 15.37 m − 1 The fin efficiency η f i n η f i n = tanh m L c m L c Substitute and solve η f i n = tanh [ ( 15.37 m − 1 ) ( 0.03 m ) ] [ ( 15.37 m − 1 ) ( 0.03 m ) ] = 0.935 The number of fins ‘ n ’ n = 1 m 2 ( 0.006 m ) ( 0.006 m ) = 27 , 777 The cross section area of fin A f i n A f i n = n ( π D L + π D 2 4 ) = 27 , 777 ( π ( 0.0025 m ) ( 0.03 m ) + π ( 0.0025 m ) 2 4 ) = 6.68 m 2 The cross-section area A u n f i n of the un-finned portion A u n f i n = 1 − n ( π D 2 4 ) = 1 − 27 , 777 ( π ( 0

6th Edition

ISBN: 9780073398198

Author: CENGEL

Publisher: RENT MCG

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Chapter 3, Problem 142P

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Rate of heat transfer and effectiveness of fins.

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Chapter 3, Problem 141P

Chapter 3, Problem 143P

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Chapter 3 Solutions

HEAT+MASS TRANSFER:FUND.+APPL.

Ch. 3 - Consider heat conduction through a wall of...Ch. 3 - Consider heat conduction through a plane wall....Ch. 3 - What does the thermal resistance of a medium...Ch. 3 - Can we defme the convection resistance for a unit...Ch. 3 - Consider steady heat transfer through the wall of...Ch. 3 - How is the combined heat transfer coefficient...Ch. 3 - Why are the convection and the radiation...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Someone comments that a microwave oven can be...Ch. 3 - Consider two cold canned drinks, one wrapped in a...

Ch. 3 - The bottom of a pan is made of a 4-mm-thick...Ch. 3 - Consider a surface of area A at which the...Ch. 3 - How does the thermal resistance network associated...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Consider a window glass consisting of two...Ch. 3 - Prob. 16P Ch. 3 - Consider a person standing in a room at 20C with...Ch. 3 - Consider an electrically heated brick house...Ch. 3 - A12-cm18-cm circuit board houses on its surface...Ch. 3 - Water is boiling in a 25-cm-diameter aluminum pan...Ch. 3 - A cylindrical resistor element on a circuit board...Ch. 3 - Prob. 22P Ch. 3 - A1.0m1.5m double-pane window consists of two...Ch. 3 - Prob. 24P Ch. 3 - Prob. 25P Ch. 3 - Prob. 26P Ch. 3 - Prob. 27P Ch. 3 - Prob. 28EP Ch. 3 - To defog the rear window of an automobile, a very...Ch. 3 - A transparent film is to be bonded onto the top...Ch. 3 - To defrost ice accumulated on the outer surface of...Ch. 3 - Prob. 32P Ch. 3 - Prob. 33P Ch. 3 - Prob. 34P Ch. 3 - Prob. 35P Ch. 3 - Heat is to be conducted along a circuit board that...Ch. 3 - Prob. 37EP Ch. 3 - Consider a house that has a 10m20-m base and a...Ch. 3 - Prob. 39EP Ch. 3 - Prob. 40P Ch. 3 - Prob. 41P Ch. 3 - Prob. 42P Ch. 3 - Prob. 43P Ch. 3 - What is thermal contact resistance? How is it...Ch. 3 - Will the thermal contact resistance be greater for...Ch. 3 - Explain how the thermal contact resistance can be...Ch. 3 - A waII consists of two layers of insulation...Ch. 3 - Prob. 48CP Ch. 3 - Consider two surfaces pressed against each other....Ch. 3 - Prob. 50P Ch. 3 - Two 5-cm-diameter, 15-cm-long aluminum bars...Ch. 3 - Prob. 52P Ch. 3 - Two identical aluminum plates with thickness of 30...Ch. 3 - A tvolayer wall is made of two metal plates, with...Ch. 3 - Prob. 55P Ch. 3 - An aluminum plate and a stainless steel plate are...Ch. 3 - Prob. 57P Ch. 3 - Prob. 58P Ch. 3 - Prob. 59P Ch. 3 - Prob. 60P Ch. 3 - Prob. 61P Ch. 3 - What are the two approaches used in the...Ch. 3 - The thermal resistance networks can also be used...Ch. 3 - When plotting the thermal resistance network...Ch. 3 - A 10-cm-thick vall is to be constructed with...Ch. 3 - Prob. 66EP Ch. 3 - Prob. 67P Ch. 3 - Prob. 68P Ch. 3 - Prob. 69P Ch. 3 - Prob. 70P Ch. 3 - Prob. 71P Ch. 3 - Prob. 72P Ch. 3 - A 12-m-long and 5-m-high wall is constructed of...Ch. 3 - Prob. 74EP Ch. 3 - Prob. 75P Ch. 3 - Prob. 76P Ch. 3 - Prob. 77P Ch. 3 - What is an infinitely long cylinder? When is it...Ch. 3 - Can the thermal resistance concept be used for a...Ch. 3 - Consider a short cylinder whose top and bottom...Ch. 3 - Prob. 81P Ch. 3 - Prob. 82P Ch. 3 - Prob. 83P Ch. 3 - Superheated steam at an average temperature 20C is...Ch. 3 - Prob. 85P Ch. 3 - Prob. 86P Ch. 3 - Prob. 87EP Ch. 3 - Prob. 88EP Ch. 3 - Prob. 89EP Ch. 3 - Prob. 90P Ch. 3 - Prob. 91P Ch. 3 - Prob. 92P Ch. 3 - Prob. 93EP Ch. 3 - Prob. 94P Ch. 3 - Prob. 95P Ch. 3 - Prob. 96P Ch. 3 - Liquid hydrogen is flowing through an insulated...Ch. 3 - Exposure to high concentrations of gaseous ammonia...Ch. 3 - A mixture of chemicals is flowing in a pipe...Ch. 3 - Ice slurry is being transported in a pipe...Ch. 3 - Prob. 101P Ch. 3 - Prob. 102P Ch. 3 - Prob. 103P Ch. 3 - What is the critical radius of insulation? How is...Ch. 3 - Prob. 105CP Ch. 3 - Prob. 106CP Ch. 3 - Prob. 107CP Ch. 3 - A pipe is insulated such that the outer radius of...Ch. 3 - A 0.083-in-diameter electrical wire at 90F is...Ch. 3 - Repeat Prob. 3-109E, assuming a thermal contact...Ch. 3 - Prob. 111P Ch. 3 - Prob. 112P Ch. 3 - Hot air is to be cooled as it is forced to flow...Ch. 3 - Prob. 114CP Ch. 3 - Prob. 115CP Ch. 3 - The fins attached to a surface are determined to...Ch. 3 - Explain how the fins enhance heat transfer from a...Ch. 3 - How does the overall effectiveness of a finned...Ch. 3 - Hot water is to be cooled as it flows through the...Ch. 3 - Consider two finned surfaces that are identical...Ch. 3 - The heat transfer surface area of a fin is equal...Ch. 3 - Does the (a) efficiency and (b) effectiveness of a...Ch. 3 - Two pin fins are identical, except that the...Ch. 3 - Two plate fins of constant rectangular cross...Ch. 3 - Two finned surfaces are identical, except that the...Ch. 3 - Obtain a relation for the fin efficiency for a fin...Ch. 3 - Prob. 127P Ch. 3 - Consider a very long rectangular fin attached to a...Ch. 3 - Prob. 129P Ch. 3 - Prob. 130P Ch. 3 - Prob. 131P Ch. 3 - Prob. 132P Ch. 3 - Prob. 133EP Ch. 3 - Prob. 134EP Ch. 3 - Prob. 135P Ch. 3 - Prob. 136P Ch. 3 - Prob. 137P Ch. 3 - Prob. 138P Ch. 3 - Prob. 139P Ch. 3 - Prob. 140P Ch. 3 - Prob. 141P Ch. 3 - Prob. 142P Ch. 3 - Prob. 143P Ch. 3 - Prob. 144P Ch. 3 - Prob. 145P Ch. 3 - Prob. 146P Ch. 3 - The human body is adaptable to extreme climatic...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Prob. 150P Ch. 3 - What is a conduction shape factor? 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What kinds of materials...Ch. 3 - Consider a house whose attic space is ventilated...Ch. 3 - Prob. 173P Ch. 3 - Prob. 174P Ch. 3 - Prob. 175P Ch. 3 - Prob. 176P Ch. 3 - Prob. 177P Ch. 3 - Prob. 178P Ch. 3 - Determine the winter R-value and the U-factor of a...Ch. 3 - The overall heat transfer coefficient (the...Ch. 3 - Prob. 181EP Ch. 3 - Determine the summer and winter R-values. in m2 ....Ch. 3 - The overall heat transfer coefficient of a wall is...Ch. 3 - Two homes are identical, except that the walls of...Ch. 3 - Prob. 185P Ch. 3 - Consider two identical people each generating 60 V...Ch. 3 - Cold conditioned air at 12C is flowing inside a...Ch. 3 - Hot water is flowing at an average velocity of 1.5...Ch. 3 - Prob. 189P Ch. 3 - Prob. 190P Ch. 3 - Prob. 191P Ch. 3 - Prob. 192P Ch. 3 - Prob. 193P Ch. 3 - Prob. 194P Ch. 3 - Prob. 195P Ch. 3 - Prob. 196P Ch. 3 - Prob. 197P Ch. 3 - A total of 10 rectangular aluminum fins...Ch. 3 - Prob. 199P Ch. 3 - A plane wall surface at 200C is to be cooled with...Ch. 3 - Prob. 201P Ch. 3 - Prob. 202P Ch. 3 - Prob. 203P Ch. 3 - Prob. 204P Ch. 3 - A 0.6-rn-diameter, 1.9-rn-long cylindrical tank...Ch. 3 - Prob. 206P Ch. 3 - Prob. 207P Ch. 3 - A thin-walled spherical tank is buried in the...Ch. 3 - Heat is lost at a rate of 275 W per m2 area of a 1...Ch. 3 - Prob. 210P Ch. 3 - Heat is generated steadily in a 3-cm-diameter...Ch. 3 - Prob. 212P Ch. 3 - Prob. 213P Ch. 3 - Prob. 214P Ch. 3 - Prob. 215P Ch. 3 - Prob. 216P Ch. 3 - Consider two walls. A and B, with the same surface...Ch. 3 - Prob. 218P Ch. 3 - A room at 20C air temperature is losing heat to...Ch. 3 - Prob. 220P Ch. 3 - A 1-cm-diameter, 30cm-long fin made of aluminum...Ch. 3 - A hot surface at 80C in air at 20C is to be cooled...Ch. 3 - A cylindrical pin fin of diameter 0.6 cm and...Ch. 3 - A 3-cm-long. 2-nuti x 2-mm rectangular...Ch. 3 - Two finned surfaces with long fins are identical,...Ch. 3 - A 20-cm-diameter hot sphere at 120C is buried in...Ch. 3 - A 25-cm-diameter, 2.4-rn-long vertical cylinder...Ch. 3 - Prob. 228P Ch. 3 - The walls of a food storage facility are made of a...Ch. 3 - The equivalent thermal resistance for the thermal...Ch. 3 - Prob. 231P Ch. 3 - Prob. 232P Ch. 3 - Prob. 233P Ch. 3 - The fin efficiency is defined as the ratio of the...Ch. 3 - Prob. 235P Ch. 3 - In the United States, building insulation is...Ch. 3 - Prob. 237P Ch. 3 - A plane brick wall (k=0.7W/m.K) and is 10 cm...Ch. 3 - The temperature in deep space is close to absolute...Ch. 3 - In the design of electronic components, it is...Ch. 3 - Using cylindrical samples of the same material,...Ch. 3 - Find out about the wall construction of the cabins...Ch. 3 - Prob. 243P Ch. 3 - A house with 200-m2 floor space is to be heated...

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