Problema 23 Capitulo 1 - [SOLUCAO] FUNDAMENTOS DE TRANSFERENCIA DE CALOR E DE MASSA 7ed

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PROBLEM 1.23 
KNOWN: Width, input power and efficiency of a transmission. Temperature and convection 
coefficient associated with air flow over the casing. 
FIND: Surface temperature of casing. 
SCHEMATIC: 
 
 
 
ASSUMPTIONS: (1) Steady state, (2) Uniform convection coefficient and surface temperature, (3) 
Negligible radiation. 
ANALYSIS: From Newton’s law of cooling, 
 
 ( ) ( )2s s sq hA T T 6 hW T T∞ ∞= − = − 
 
where the output power is ηPi and the heat rate is 
 
 ( )i o iq P P P 1 150 hp 746 W / hp 0.07 7833Wη= − = − = × × = 
 
Hence, 
 
 ( )s 2 22
q 7833 WT T 30 C 102.5 C
6 hW 6 200 W / m K 0.3m
∞= + = ° + = °× ⋅ ×
 < 
 
COMMENTS: There will, in fact, be considerable variability of the local convection coefficient over 
the transmission case and the prescribed value represents an average over the surface.