Explanation Given information: Motor uses 300 W of electric power and delivers 55 % of it as mechanical power. Assume base temperature of the shaft is equal to the surface temperature motor housing. Heat transfer from an adiabatic fin tip is expressed as: Q ˙ a d i a b a t i c f i n = h p k A c ( T b − T ∞ ) tanh a L In the above equation h - Heat transfer co-efficient p - Perimeter k - Thermal conductivity A c - Cross-sectional area T b - Base temperature T ∞ - Surrounding temperature a = h p k A c Calculation: According to energy balance, W ˙ e l e c = W ˙ m e c h + Q ˙ h + Q ˙ s Assume W ˙ e l e c , W ˙ m e c h as the electrical and mechanical power respectively. Assume Q ˙ h , Q ˙ s as heat transfer rate from the motor housing and motor shaft respectively. Motor delivers 55 % of electrical power as mechanical power. Therefore W ˙ e l e c = 0.55 W ˙ e l e c + Q ˙ h + Q ˙ s The heat transfer rate Q ˙ h from the motor housing Q ˙ h = h p k A s ( T h − T ∞ ) The heat transfer rate from the motor shaft Q ˙ s = h p k A c ( T h − T ∞ ) cosh a L − ( T L − T ∞ ) ( T h − T ∞ ) sinh a L = h k π 2 D 3 4 ( T h − T ∞ ) cosh a L − ( T L − T ∞ ) ( T h − T ∞ ) sinh a L Find the value of ‘ a L ’ a L = L h p k A c Substitute and solve a L = L h π D k ( π D 2 4 ) = L 4 h k D = ( 0

6th Edition

ISBN: 9780073398198

Author: CENGEL

Publisher: RENT MCG

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Chapter 3, Problem 135P

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Surface temperature of motor housing.

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Chapter 3, Problem 134EP

Chapter 3, Problem 136P

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Chapter 3 Solutions

HEAT+MASS TRANSFER:FUND.+APPL.

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