FTFS Chap05 P125 - Chapter 5 The First Law of...

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Chapter 5 The First Law of Thermodynamics Pipe and duct Flow 5-125 A desktop computer is to be cooled safely by a fan in hot environments and high elevations. The air flow rate of the fan and the diameter of the casing are to be determined. Assumptions 1 Steady operation under worst conditions is considered. 2 Air is an ideal gas with constant specific heats. 3 Kinetic and potential energy changes are negligible. Properties The specific heat of air at the average temperature of T ave = (45+60)/2 = 52.5 ° C = 325.5 K is C p = 1.0065 kJ/kg. ° C (Table A-2b) Analysis The fan selected must be able to meet the cooling requirements of the computer at worst conditions. Therefore, we assume air to enter the computer at 66.63 kPa and 45 ° C, and leave at 60 ° C. We take the air space in the computer as the system, which is a control volume. The energy balance for this steady-flow system can be expressed in the rate form as && & & & & () EE E Qm hm h C T T in out in out in in p −= = += ≅≅ =− Rate of net energy transfer by heat, work, and mass system (steady) Rate of change in internal, kinetic, potential, etc. energies (since ke pe 0) 12 43 4 44 444 Δ ΔΔ Ê 0 21 0 = Then the required mass flow rate of air to absorb heat at a rate of 60 W is determined to be kg/min 0.238 = kg/s 00397 . 0 C 45) - C)(60 J/kg. (1006.5 W 60 ) ( ) ( = ° ° = = = in out p in out p T T C Q m T T C m Q & & & & The density of air entering the fan at the exit and its volume flow rate are /min m 0.341 3 = = = = = = 3 3 3 kg/m 6972 . 0 kg/min 238 . 0 kg/m 6972 . 0 273)K + /kg.K)(60 kPa.m 287 . 0 ( kPa 63 . 66 ρ m V RT P & & For an average exit velocity of 110 m/min, the diameter of the casing of the fan is determined from cm 6.3 V V V = m 063 . 0 m/min) 110 ( /min) m 341 . 0 )( 4 ( 4 4 3 2 = = = = = ππ π V D D A V c & & 5-114
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Chapter 5 The First Law of Thermodynamics 5-126 A desktop computer is to be cooled safely by a fan in hot environments and high elevations. The air flow rate of the fan and the diameter of the casing are to be determined. Assumptions 1 Steady operation under worst conditions is considered. 2 Air is an ideal gas with constant specific heats. 3 Kinetic and potential energy changes are negligible. Properties The specific heat of air at the average temperature of T ave = (45+60)/2 = 52.5 ° C is C p = 1.0065 kJ/kg. ° C (Table A-3). Analysis The fan selected must be able to meet the cooling requirements of the computer at worst conditions. Therefore, we assume air to enter the computer at 66.63 kPa and 45 ° C, and leave at 60 ° C. We take the air space in the computer as the system, which is a control volume. The energy balance for this steady-flow system can be expressed in the rate form as && & & & & () EE E Qm hm h C T T in out in out in in p −= = += ≅≅ =− Rate of net energy transfer by heat, work, and mass system (steady) Rate of change in internal, kinetic, potential, etc. energies (since ke pe 0) 12 43 4 44 444 Δ ΔΔ Ê 0 21 0 = Then the required mass flow rate of air to absorb heat at a rate of 100 W is determined to be kg/min 0.397 = kg/s 006624 . 0
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FTFS Chap05 P125 - Chapter 5 The First Law of...

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