ME300HW6Solution

# ME300HW6Solution - Corrected October 2011 Problem 12.51 As...

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1 Corrected October, 2011 Problem 12.51 As seen in Fig. P12.51, moist air at 30 o C, 2 bar, and 50% relative humidity enters a heat exchanger operating at steady state with a mass flow rate of 600 kg/h and is cooled at essentially constant pressure to 20 o C. Ignoring kinetic and potential energy effects, determine the rate of heat transfer from the moist air stream, in kJ/h. 1 3 T 2 = 20 o C p 2 = 2 atm T 1 = 30 o C p 1 = 2 bar ϕ 1 =50% h kg 600 m Fig. P12.51 Solution: Known: Moist air at known conditions enters a heat exchanger operating at steady state and is cooled. Find: Determine the rate of heat transfer. Schematic and Known Data: Refer to Fig. P12.51 and below. T v 30 o C Dew point temperature p v 20 o C Engineering Model: (1) The control volume shown in the accompanying figure operates at steady state with 0 cv W and negligible effects of kinetic and potential energy.

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2 (2) Moist air acts as an ideal gas, with each component adhering to the Dalton model. (3) Pressure remains constant through the cooling process. Analysis: The first step is to determine whether condensation occurs. As long as there is no condensation the mole fraction of the water vapor, y v , remains constant. Thus, as cooling occurs at fixed mixture pressure (assumption 3), the partial pressure of the water vapor remains constant until a saturated mixture would be attained: p y p v v . The onset of condensation in this case corresponds, therefore, to the dew point temperature. Using given data  C 4 . 18 bar 2123 . 0 bar 04246 . 0 50 . 0 C 30 o dp o g 1 v T p p Accordingly, condensation does not take place. At steady state, mass rate balances result in air: a a2 a1 m m m water: v v2 v1 m m m therefore, a v m m The total mass flow rate is the sum: 1 a a v m m m m , where kg(air) (vapor) kg 00667 . 0
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