Thermodynamics HW Solutions 693

Thermodynamics HW Solutions 693 - . 1 Pr Re ) / ( 065 . 66...

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Chapter 8 Internal Forced Convection 01 . 7 Pr C; J/kg. 4182 /s m 10 004 . 1 / C W/m. 598 . 0 kg/m 998 2 6 - 3 = ° = × = ρ μ = υ ° = = ρ p C k Analysis ( a ) The mass flow rate of water is kg/s 00998 . 0 ) /s m 10 )(0.01 kg/m 998 ( 3 -3 3 = × = = V m ρ The temperature rise of water as it flows through the micro channels is C 1.2 ° = ° = = Δ ⎯→ Δ = ) C J/kg 4182 )( kg/s 00998 . 0 ( J/s 50 p p C m Q T T C m Q (b) The Reynolds number is 1 . 569 /s m 10 004 . 1 m) 10 57 . 8 m/s)( (6.667 Re m 10 571 . 8 ) m 10 3 . 0 + m 10 05 . 0 ( 2 ) m 10 3 . 0 )( m 10 05 . 0 ( 4 4 m/s 667 . 6 100 ) m 10 3 . 0 )( m 10 05 . 0 ( /s m 10 01 . 0 2 6 5 5 3 3 3 3 3 3 3 3 = × × = υ = × = × × × × = = = × × × × = = h m c h c m D V P A D A V V which is less than 2300. Therefore, the flow is laminar, and the thermal entry length in this case is m 0.0171 = m) 10 571 . 8 )( 01 . 7 )( 1 . 569 ( 05 . 0 Pr Re 05 . 0 5 × = = h t D L which is longer than the total length of the channels. Therefore, we can assume thermally developing flow, and determine the Nusselt number from (actually, the relation below is for circular tubes) [] 224 . 5 ) 01 . 7 )( 1 . 569 ( m 01 . 0 m 10 571 . 8 04 . 0 1 ) 01 . 7 )( 1 . 569 ( m 01 . 0 m 10 571 . 8 065 . 0 66 . 3 Pr Re ) / ( 04
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Unformatted text preview: . 1 Pr Re ) / ( 065 . 66 . 3 3 / 2 5 5 3 / 2 = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ × + = + + = = − − L D L D k hD Nu and C . W/m 445 , 36 ) 224 . 5 ( m 10 571 . 8 C W/m. 598 . 2 5 ° = × ° = = − Nu D k h h Then the average surface temperature of the base of the micro channels is determined to be C 22.6 ° = × ° + ° ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + = − = × = × × + = = − − − ) m 10 7 )( C . W/m 445 , 36 ( W ) 100 / 50 ( C 2 2 . 21 20 ) ( m 10 7 01 . 10 ) 05 . 3 . ( 2 2 6 2 , , , , 2 6 3 s ave m ave s ave m ave s s s hA Q T T T T hA Q pL A & & 8-55...
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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