Assignment_3_Solutions - 1 Air is flowing in parallel to a...

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1 Air is flowing in parallel to a stationary thin flat plate over the top surface. The rate of heat transfer from the plate is to be determined. Assumptions 1 Steady operating conditions exist. 2 Properties are constant. Properties The properties of air (1 atm) at the 100°C are given in Table A-15: ρ = 0.9458 kg/m 3 , c p = 1009 J/kg·K, ν = 2.306 × 10 −5 m 2 /s, and Pr = 0.7111. Analysis The flow is over the top surface of the metal foil, hence the surface area is 2 m 1 . 0 ) m 5 . 0 )( m 2 . 0 ( = = s A For flat plate, the friction force can be determined using 2 2 V A C F s f f ρ = 2 2 V A F C s f f ρ = Using the Chilton-Colburn analogy, the convection heat transfer coefficient is determined to be: 3 / 2 Pr 2 V c h C p f ρ = 3 / 2 Pr 2 = V c C h p f ρ K W/m 38 ) 7111 . 0 )( K J/kg 1009 ( ) m/s 100 )( m 1 . 0 ( ) N 3 . 0 ( Pr 2 3 / 2 2 3 / 2 = = = p s f c V A F h The surface temperature of the metal foil is ) ( = T T h q s ɺ C 181 ° = ° + = + = C 20 K W/m 38 W/m 6100 2 2 T h q T s ɺ Discussion The temperature, at 100°C, used for evaluating the fluid properties turned out to be appropriate, since the film temperature is C 100 C 101 2 ° ° = + = T T T s f 2. Assumptions 1 Steady operating conditions exist. 2 The critical Reynolds number is Re cr = 5 × 10 5 . 3 Radiation effects are negligible 4 Heat transfer from the back side of the plate is negligible. 5 Air is an ideal gas with constant properties. 6 The local atmospheric pressure is 1 atm.
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Properties The properties of air at the film temperature of ( T s + T )/2 = (65+35)/2 = 50 ° C are (Table A-15) 7228 . 0 Pr /s m 10 798 . 1 C W/m. 02735 . 0 2 5 - = × = ° = ν k Analysis The Reynolds number is 617 , 55 /s m 10 798 . 1 m) m/s)(0.25 (4 Re 2 5 = × = = ν VL L which is less than the critical Reynolds number. Thus the flow is laminar. Using the proper relation in laminar flow for Nusselt number, heat transfer coefficient and the heat transfer rate are determined to be C . W/m 37 . 15 ) 5 . 140 ( m 25 . 0
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