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Unformatted text preview: Chapter 14 Mass Transfer 14134 A circular pan filled with water is cooled naturally. The rate of evaporation of water, the rate of heat transfer by natural convection, and the rate of heat supply to the water needed to maintain its temperature constant are to be determined. Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable since the mass fraction of vapor in the air is low (about 2 percent for saturated air at 25 ° C). 2 The critical Reynolds number for flow over a flat plate is 500,000. 3 Radiation heat transfer is negligible. 4 Both air and water vapor are ideal gases. Properties The airwater vapor mixture is assumed to be dilute, and thus we can use dry air properties for the mixture at the average temperature of ( ) / T T s ∞ + 2 = (15+20)/2 = 17.5 ° C = 290.5 K. The properties of dry air at 290.5 K and 1 atm are, from Table A15, /s m 10 49 . 1 /s m 10 04 . 2 731 . Pr , C W/m 0251 . 2 5 2 5 × = × = = ° ⋅ = ν α k The mass diffusivity of water vapor in air at the average temperature of 290.5 K is, from Eq. 1415, ( 29 m²/s 10 37 . 2 atm 1 K 5 . 290 10 87 . 1 10 87 . 1 5 072 . 2 10 072 . 2 10 air O H 2 × = × = × = = P T D D AB The saturation pressure of water at 20 ° C is P [email protected] C kPa. ° = 2 339 . Properties of water at 15 ° C are h P fg v = = 2466 17051 kJ / kg and kPa . (Table A9). The specific heat of water at the average temperature of (15+20)/2 = 17.5 ° C is C p = 4.184 kJ/kg. ° C. The gas constants of dry air and water are R air = 0.287 kPa.m 3 /kg.K and R water = 0.4615 kPa.m 3 /kg.K (Table A1). Analysis ( a ) The air at the water surface is saturated, and thus the vapor pressure at the surface is simply the saturation pressure of water at the surface temperature (1.7051 kPa at 15 ° C). The vapor pressure of air far from the water surface is determined from P P P v T , ( . ) ( . )( . . ∞ ° = = = = ∞ φ [email protected] [email protected] C kPa) kPa 0 30 0 30 2 339 0 7017 Treating the water vapor and the air as ideal gases and noting that the total atmospheric pressure is the sum of the vapor and dry air pressures, the densities of the water vapor, dry air, and their mixture at the water air interface and far from the surface are determined to be At the surface : ρ ρ ρ ρ ρ v s v s v s a s a s a s s v s a s P R T P R T , , , , , , . ( . . ( . . ) ( . . . . . = = ⋅ ⋅ = = = ⋅ = = + = + = 17051 04615 001283 101325 17051 0287 12052 0 01283 12052 121803 kPa kPa m / kg K)(15+ 273) K kg / m kPa kPa.m / kg K)(15+ 273) K kg / m kg / m 3 3 3 3 3 and Away from the surface : ρ ρ ρ ρ ρ v v v a a a v a P R T P R T , , , , , , . ( . . ( . . ) ( . . . . . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ = = ⋅ ⋅ = = = ⋅ ⋅ = = + = + = 07017 0 4615 0 00520 101325 0 7017 0 287 11966 00052 11966 12018 kPa kPa m / kg K)(20 + 273) K kg / m kPa kPa m / kg K)(20 + 273 K) kg / m kg / m 3 3 3 3 3 Note that ρ ρ ∞ < s , and thus this corresponds to hot surface facing down. The area of the top surface of the , and thus this corresponds to hot surface facing down....
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 Spring '06
 Rajadas

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