Explanation Given information: Diameter of the fin is 10 mm , length of the fin is 50 mm , surface temperature of the wall is 350 ° C ,thermal conductivity of the fin material is 240 W / m ⋅ K , ambient air temperature is 25 ° C and heat transfer coefficient of air is 250 W / m 2 ⋅ K . Write the expression for the cross sectional area of the fin. A c s = π 4 d 2 ...... (I) Here cross sectional area of the fin is A c s diameter of the fin is d . Write the expression for the perimeter of the circular fin. p = π d ...... (II) Here perimeter of the fin is p diameter of the fin is d . Write the expression for value m . m = h p k A c s ...... (III) Here heat transfer coefficient of the air is h , perimeter of fin is p , thermal conductivityof the fin is k and cross sectional area of the fin is A c s . Write the expression for m L . m L = h p k A c s L ...... (IV) Here length of the fin is L . Write the expression for h p k A c s . γ = h p k A c s ...... (V) Write the expression for the heat transfer rate of infinitely long fin. Q · inf , f i n = γ ⋅ ( T b − T ∞ ) ...... (VI) Here heat transfer rate of infinitely long fin is Q inf , f i n , heat transfer coefficient of the air is h , perimeter of fin is p , thermal conductivity of the fin is k cross sectional area of the fin is A c s ,base temperature of fin is T b and ambient temperature is T ∞ . Write the expression for the temperature distribution or temperature variation for the infinitely long fin. T ( x ) − T ∞ T b − T ∞ = e − m x ...... (VII) Here temperature at a distance of x is T ( x ) , ambient temperature is T ∞ ,and base temperature of the fin is T b . Write the expression for the heat transfer rate of adiabatic tip fin. Q · a d i a b t i c , f i n = γ ⋅ ( T b − T ∞ ) tanh ( m L ) ...... (VIII) Here heat transfer rate of adiabatic finis Q a d i a b a t i c , f i n , length of the fin is L . Write the expression for the temperature distribution or temperature variation for the adiabatic tip fin. T ( x ) − T ∞ T b − T ∞ = cosh [ m ( L − x ) ] cosh ( m L ) ...... (IX) Here temperature at a distance of x is T ( x ) , ambient temperature is T ∞ , wall or base temperature is T b and length of the fin is L . Write the expression for the loss of heat when tip temperature of fin is 250 ° C . Q · s p e c i f i c t e m p = γ ⋅ ( T b − T ∞ ) cosh ( m L ) − [ ( T L − T ∞ ) ( T b − T ∞ ) ] sinh ( m L ) ...... (X) Here heat transfer rate of specified temperature fin is Q · s p e c i f i c t e m p . Write the expression for the temperature distribution or temperature variation for the specified fin temperature. T ( x ) − T ∞ T b − T ∞ = [ ( T L − T ∞ ) ( T b − T ∞ ) ] sinh ( m x ) + sinh [ m ( L − x ) ] sinh ( m L ) ...... (XI) Here specified temperature is T L . Write the expression for the rate of heat transfer by the fin when fin loosing heat by the convection. Q · c o n v . = γ ⋅ ( T b − T ∞ ) sinh ( m L ) + ( h m k ) cosh ( m L ) cosh ( m L ) + ( h m k ) sinh ( m L ) ...... (XII) Here rate of heat transfer of fin loosing heat by convection is Q · c o n v . , thermal conductivity of the fin is k and length of the fin is L . Write the expression for the temperature distribution or temperature variation along thefin loosing heat by convection. T ( x ) − T ∞ T b − T ∞ = cosh [ m ( L − x ) ] + ( h m k ) sinh [ m ( L − x ) ] cosh ( m L ) + ( h m k ) sinh ( m L ) To determine (b) The heat transfer rate of adiabatic tip fin. To determine (c) The heat transfer rate of fin when tip temperature is 250 ° C . To determine (d) The heat transfer rate of the fin loosing heat by convection.

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 185P

To determine

(a)

The heat transfer rate of infinitely long fin.

To determine

(b)

The heat transfer rate of adiabatic tip fin.

To determine

(c)

The heat transfer rate of fin when tip temperature is 250 °C.

To determine

(d)

The heat transfer rate of the fin loosing heat by convection.

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Chapter 3, Problem 184P

Chapter 3, Problem 186P

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? 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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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