Explanation Given information: The surface temperature is 350 ° C , the ambient temperature is 25 ° C , the thermal conductivity is 235 W / m-K , the heat transfer coefficient 154 W / m 2 -K , the length of the fin is 50 mm , the width of the fin is 100 mm and the thickness of the fin is 5 mm . Write the expression for the perimeter of the fin. p = 2 ( w + t ) ....... (I) Here, the perimeter of the fin is p , the width of the fin is w and the thickness of the fin is t . Write the expression for the cross-section area. A c s = w t ....... (II) Here, the cross-sectional area of the fin is A c s . Write the expression for the fin coefficient m . m = h p k A c s ....... (III) Here, the fin coefficient is m , the heat transfer coefficient is h , the thermal conductivity of the fin material is k . Write the expression for the fin efficiency. η = 1 m L ....... (IV) Write the expression for the heat transfer rate. Q = h p k A c s ( T o − T ∞ ) tanh ( m L ) ....... (V) Here, the heat transfer rate is Q , the T o is the base temperature and the surrounding temperature is T ∞ . Write the expression for the fin effectiveness. ε = k p h A c s ....... (VI) Here, the effectiveness of the fin is ε . Calculation: Substitute 100 mm for w and the 5 mm for t in equation (I). p = 2 ( 100 mm+5 mm ) ( 1 m 1000 mm ) = 0.21 m Substitute 100 mm for w and the 5 mm for t in equation (II) A c s = ( 100 mm ) ( 5 mm ) ( 1 m 1000 mm ) 2 = 1.05 × 10 − 4 m 2 Substitute 154 W / m 2 -K for h , 0.21 m for p , 1.05 × 10 − 4 m 2 for A c s and 235 W / m-K for k . m = ( 154 W / m 2 -K ) ( 0.21 m ) ( 235 W / m-K ) ( 1

Heat and Mass Transfer: Fundamentals and Applications

5th Edition

ISBN: 9780073398181

Author: Yunus A. Cengel Dr., Afshin J. Ghajar

Publisher: McGraw-Hill Education

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Question

Chapter 3, Problem 125P

To determine

The efficiency, heat transfer rate and effectiveness of the fin.

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Chapter 3, Problem 124P

Chapter 3, Problem 126P

Chapter 3 Solutions

Heat and Mass Transfer: Fundamentals and Applications

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 - Prob. 36P Ch. 3 - Heat is to be conducted along a circuit board that...Ch. 3 - Prob. 38EP Ch. 3 - Consider a house that has a 10m20-m base and a...Ch. 3 - Prob. 40EP Ch. 3 - Prob. 41P Ch. 3 - Prob. 42P 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. 47CP Ch. 3 - Consider two surfaces pressed against each other....Ch. 3 - Prob. 49P Ch. 3 - Two 5-cm-diameter, 15-cm-long aluminum bars...Ch. 3 - Prob. 51P Ch. 3 - Two identical aluminum plates with thickness of 30...Ch. 3 - A tvolayer wall is made of two metal plates, with...Ch. 3 - An aluminum plate and a stainless steel plate are...Ch. 3 - Prob. 55P Ch. 3 - Prob. 56P Ch. 3 - Prob. 57P 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. 62EP Ch. 3 - Prob. 63P Ch. 3 - Prob. 64P Ch. 3 - Prob. 65P Ch. 3 - Prob. 66P Ch. 3 - Prob. 67P Ch. 3 - Prob. 68P Ch. 3 - A 12-m-long and 5-m-high wall is constructed of...Ch. 3 - Prob. 70EP Ch. 3 - Prob. 71P Ch. 3 - Prob. 72P 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. 76P Ch. 3 - Prob. 77P Ch. 3 - Prob. 78P Ch. 3 - Superheated steam at an average temperature 20C is...Ch. 3 - Prob. 80EP Ch. 3 - Prob. 81EP Ch. 3 - Prob. 82P Ch. 3 - Prob. 83P Ch. 3 - Prob. 84P Ch. 3 - Prob. 85P Ch. 3 - Prob. 86EP Ch. 3 - Prob. 87P Ch. 3 - Prob. 88P 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. 93P Ch. 3 - Prob. 94P Ch. 3 - Prob. 95P Ch. 3 - What is the critical radius of insulation? How is...Ch. 3 - Prob. 97CP Ch. 3 - Prob. 98CP Ch. 3 - Prob. 99CP 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. 103P Ch. 3 - Prob. 104P Ch. 3 - Hot air is to be cooled as it is forced to flow...Ch. 3 - Prob. 106CP Ch. 3 - Prob. 107CP 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. 119P Ch. 3 - Consider a very long rectangular fin attached to a...Ch. 3 - Prob. 121P Ch. 3 - Prob. 122EP Ch. 3 - Prob. 123EP Ch. 3 - Prob. 124P Ch. 3 - Prob. 125P Ch. 3 - Prob. 126P Ch. 3 - Prob. 127P Ch. 3 - Prob. 128P Ch. 3 - Prob. 129P Ch. 3 - Prob. 130P Ch. 3 - Prob. 131P Ch. 3 - Prob. 132P Ch. 3 - Prob. 133P Ch. 3 - Prob. 134P 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. 138P Ch. 3 - What is a conduction shape factor? How is it...Ch. 3 - What is the value of conduction shape factors in...Ch. 3 - Prob. 141P Ch. 3 - A thin-walled cylindrical container is placed...Ch. 3 - Prob. 143P Ch. 3 - Prob. 144P Ch. 3 - Prob. 145P Ch. 3 - Prob. 146EP Ch. 3 - Prob. 147P Ch. 3 - Prob. 148P Ch. 3 - Prob. 149P Ch. 3 - Prob. 150P Ch. 3 - Prob. 151P Ch. 3 - Prob. 152P Ch. 3 - Consider a house with a flat roof whose outer...Ch. 3 - Prob. 154P Ch. 3 - Radioactive material, stored in a spherical vessel...Ch. 3 - What is the R-value of a wall? How does it differ...Ch. 3 - What is effective emissivity for a plane-parallel...Ch. 3 - Prob. 158CP Ch. 3 - What is a radiant barrier? What kinds of materials...Ch. 3 - Consider a house whose attic space is ventilated...Ch. 3 - Prob. 161P Ch. 3 - Prob. 162P Ch. 3 - Prob. 163P Ch. 3 - Prob. 164P Ch. 3 - Prob. 165P Ch. 3 - Prob. 166P Ch. 3 - Determine the winter R-value and the U-factor of a...Ch. 3 - The overall heat transfer coefficient (the...Ch. 3 - Prob. 169EP 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. 173P 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. 177P Ch. 3 - Prob. 178P Ch. 3 - Prob. 179P Ch. 3 - Prob. 180P Ch. 3 - Prob. 181P Ch. 3 - Prob. 182P Ch. 3 - Prob. 183P Ch. 3 - Prob. 184P Ch. 3 - Prob. 185P Ch. 3 - A total of 10 rectangular aluminum fins...Ch. 3 - Prob. 187P Ch. 3 - A plane wall surface at 200C is to be cooled with...Ch. 3 - Prob. 189P Ch. 3 - Prob. 190P Ch. 3 - Prob. 191P Ch. 3 - Prob. 192P Ch. 3 - A 0.6-rn-diameter, 1.9-rn-long cylindrical tank...Ch. 3 - Prob. 194P Ch. 3 - Prob. 195P 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. 198P Ch. 3 - Heat is generated steadily in a 3-cm-diameter...Ch. 3 - Prob. 200P Ch. 3 - Prob. 201P Ch. 3 - Prob. 202P Ch. 3 - Prob. 203P Ch. 3 - Prob. 204P Ch. 3 - Consider two walls. A and B, with the same surface...Ch. 3 - Prob. 206P Ch. 3 - A room at 20C air temperature is losing heat to...Ch. 3 - Prob. 208P 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. 216P 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. 219P Ch. 3 - Prob. 220P Ch. 3 - Prob. 221P Ch. 3 - The fin efficiency is defined as the ratio of the...Ch. 3 - Prob. 223P Ch. 3 - In the United States, building insulation is...Ch. 3 - Prob. 225P 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. 231P Ch. 3 - A house with 200-m2 floor space is to be heated...

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