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: 9781260439991

Author: CENGEL

Publisher: 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...-CONNECTPLUS

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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? 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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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