Explanation Given information: The power dissipated by the device is 20 W , the mass of the device is 20 g , the specific heat of the device is 850 J / kg ° C , the surface area of the device is 4 cm 2 , the time for the operation is 5 min , the ambient temperature of the device is 25 ° C , the coefficient of heat transfer is 12 W / m 2 ° C , the mass of the aluminium sink is 200 g and the surface area of the aluminium sink is 80 cm 2 . Write the expression for the energy balance on the device. E i n − E o u t + E g e n e r a t i o n = Δ E d e v i c e − Q ˙ o u t Δ t + E ˙ g e n e r a t i o n Δ t = m C p ( T − T ∞ ) E ˙ g e n e r a t i o n Δ t − h A s ( T + T ∞ 2 − T ∞ ) Δ t = m C p ( T − T ∞ ) ....... (I) Here, the power dissipated from the device is E ˙ g e n e r a t i o n , the time of operation of the device is Δ t , the coefficient of the heat transfer is h , the surface area of the device is A s , the ambient temperature of the device is T ∞ , the temperature of the device after 5 min is T , the mass of the device is m and the specific heat of the device is C p . Write the expression for the energy balance on the device when the aluminium sink is attached. E ˙ g e n e r a t i o n Δ t − h ( A s + A 1 ) ( T + T ∞ 2 − T ∞ ) Δ t = ( m + m 1 ) C p ( T − T ∞ ) ....... (II) Here, the surface area of the aluminium sink is A 1 and the mass of the sink is m 1 . Calculation: Substitute 20 W for E ˙ g e n e r a t i o n , 5 min for Δ t , 12 W / m 2 ° C for h , 4 cm 2 for A s , 25 ° C for T ∞ , 20 g for m and 850 J / kg ° C for C p in Equation (I). ( 20 W × 5 min ) − ( 12 W / m 2 ° C × 4 cm 2 ) ( T − 25 ° C 2 ) × 5 min = ( 20 g × 850 J / kg ° C ) ( T − 25 ° C ) [ ( 20 W ) ( 1 J/s 1 W ) ( 5 min ) ( 60 s 1 min ) − ( 12 W / m 2 ° C ( 1 J/s 1 W ) × 4 cm 2 ( 1 m 2 10 4 cm 2 ) ) ( T − 25 ° C 2 ) × ( 5 min ) ( 60 s 1 min ) ] = [ ( 20 g ( 1 kg 1000 g ) × 850 J / kg ° C ) ( T − 25 ° C ) ] 6000 J − 0

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 4, Problem 38P

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The temperature of device at the end of 5 min operating period.

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Chapter 4, Problem 37P

Chapter 4, Problem 39CP

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Chapter 4 Solutions

Heat and Mass Transfer: Fundamentals and Applications

Ch. 4 - What is the physical significance of the Biot...Ch. 4 - What is lumped system analysis? When is it...Ch. 4 - In what medium is the lumped system analysis more...Ch. 4 - For which solid is the lumped system analysis more...Ch. 4 - For which kinds of bodies made of the same...Ch. 4 - Consider heat transfer between two identical hot...Ch. 4 - Consider heat transfer between two identical hot...Ch. 4 - Consider a hot baked potato on a plate. The...Ch. 4 - Consider a potato being baked in an oven that is...Ch. 4 - Consider two identical 4-kg pieces of roast beef....

Ch. 4 - Consider a sphere and a cylinder of equal volume...Ch. 4 - Obtain relations for the characteristic lengths of...Ch. 4 - Obtain a relation for the time required for a...Ch. 4 - A brick of 20310257mm in dimension is being burned...Ch. 4 - Prob. 15P Ch. 4 - Prob. 16P Ch. 4 - Metal plates...Ch. 4 - Prob. 18P Ch. 4 - Prob. 19P Ch. 4 - A 6-mm-thick stainless steel strip...Ch. 4 - After heat treatment, the 2-cm-thick metal plates...Ch. 4 - A long copper rod of diameter 2.0 cm is initially...Ch. 4 - Prob. 23P Ch. 4 - Steel rods...Ch. 4 - To warm up some milk for a baby, a mother pours...Ch. 4 - A person is found dead at 5 p.m. in a room whose...Ch. 4 - Prob. 27P Ch. 4 - In an experiment, the temperature of a hot gas...Ch. 4 - Prob. 29P Ch. 4 - Pulverized coal particles are used in oxy-fuel...Ch. 4 - Oxy-fuel combustion power plants use pulverized...Ch. 4 - Plasma spraying is a process used for coating a...Ch. 4 - Consider a spherical shell satellite with outer...Ch. 4 - Prob. 34P Ch. 4 - Prob. 35P Ch. 4 - Prob. 36EP Ch. 4 - Consider a sphere of diameter 5 cm, a cube of side...Ch. 4 - Prob. 38P Ch. 4 - An egg is to be cooked to a certain level of...Ch. 4 - What is an infinitely long cylinder? 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