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Mass flux of water vapor in Java Embed PDF417 in Java Mass flux of water vapor

5.2 Mass flux of water vapor generate, create pdf417 none on java projects GS1 DataBar First, from the con PDF-417 2d barcode for Java tinuity equation for density of water-vapor molecules the following equation can be written, ]rv urrv cr2 rv : ]t 5:1 . The flow is assumed to be non-divergent, and rv is the water-vapor density given by rv nm. In this definition, n is the number of molecules and m is the mass of a water molecule. In addition, c is the vapor diffusivity, given more precisely as, c 2:11 10 5 T=T0 1:94 p=p00 m2 s 1 ; 5:2 .

where, T0 = 273.15 awt barcode pdf417 K and p00 = 101325 Pa. If it is assumed that u is zero so the flow is zero or stationary flow (sum of the air-flow velocity and the vapor-flow velocity) is zero, (5.

1) becomes ]rv cr2 rv : ]t 5:3 . With the steady-sta te assumption, a basic form of Fick s first law of diffusion results for the number of molecules, n, where m is a constant (similar to Rogers and Yau, 1989), r2 rv r2 nm r2 n 0: 5:4 . Assuming isotropy, PDF 417 for Java which permits the use of spherical coordinates for this problem, (5.4) becomes   1 ] ]n R2 0; 5:5 r2 n 2 R ]R ]R where R is the distance from the center of the drop. The product rule is applied to (5.

5),     R2 ] ]n 1 ] R2 ]n 2 0; R2 ]R ]R R ]R ]R which is written more precisely as   ] ]n 2 ]n 0: ]R ]R R ]R Now letting, x   ]n ; ]R. 5:6 . 5:7 . 5:8 . Vapor diffusion growth of liquid-water drops substitution of (5. 8) into (5.7) results in ]x ]R Integration of (5.

9) over R gives, ]x dR ]R Rearranging, d ln x and finally integration gives ln x 2 ln R c0 ; 5:12 2 d ln R; 5:11 2 x: R 2 5:9 . x dR: R 5:10 . where c0 is a const pdf417 2d barcode for Java ant of integration. Taking the exponential of both sides of (5.12) gives, x c00 R 2 : Now, substituting (5.

8) back into (5.13) results in ]n c00 R 2 : ]R Integrating (5.14) over dR, ]n dR c00 R 2 dR; ]R c00 c000 ; R 5:15 5:14 5:13 .

results in n R 5:16 . where c000 is anoth awt PDF417 er constant of integration. Now, the constants of integration can be determined from the boundary conditions, which are: as R approaches R1 , n approaches n1; and when R equals the drop radius, Rr , n is equal to nr. Application of these boundary conditions to (5.

16) gives n1 c00 c000 c000 ; R1 5:17 . where c00 =R1 ( c000 , so that n1 c000 . 5.2 Mass flux of water vapor Next, using the bou ndary conditions and (5.17), (5.16) is then nr Simplifying, nr Solving (5.

19) for c00 , c00 a nr From (5.17) c000 was given by c000 n1 : Thus (5.16) becomes n R Rr nr R n1 n1 : 5:22 5:21 .

c00 c000 Rr c00 n1 : Rr 5:18 . c00 n1 : Rr n1 :. 5:19 . 5:20 . Now the rate of mas swing pdf417 2d barcode s increase or decrease at the drop s surface by way of a flux of droplets toward or away from the drop can be written as dM/dt, where M is mass,   dM ]n 2 : 5:23 c4pRr m dt ]R R Rr Equation (5.22) is used to find the derivative of n with respect to R while holding R = Rr,   dM ] Rr nr n1 =R n1 ; 5:24 c4pR2 m dt ]R R Rr rearranging, ( dM ] 1 2 c4pR m Rr nr dt ]R R Now by using ]n1 0 ]R in (5.25), the following is found, dM ] 1 c4pR2 m Rr nr dt ]R R ! n1 .

R Rr ! n1 ]n1 ]R Rr R Rr ) : 5:25 . 5:26 . 5:27 . Vapor diffusion growth of liquid-water drops Taking the derivati ve gives dM c4pRr n1 dt Now we note that rv;r nr m; and rv;1 n1 m; 5:30 5:29 nr m: 5:28 . where rv,r is the v pdf417 for Java apor density at the drop s surface, and rv,1 is the uniform density. Substitution of (5.29) and (5.

30) into (5.28) gives dM c4pRr rv;1 dt rv;r ; 5:31 . which is the mass c hange owing to vapor gradients. 5.3 Heat flux during vapor diffusional growth of liquid water An analogous procedure can be followed to get a relationship dq/dt, which is the heat flux owing to temperature gradients.

Based on dq/dt, another equation for dM/dt, different from (5.31), may be written. From the continuity equation for temperature T the following equation can be written, where K is thermal diffusivity, ]T urT Kr2 T: ]t 5:32 .

Assuming again that PDF417 for Java the flow is non-divergent, and that u is zero, so the flow is zero or stationary flow (sum of the air-flow velocity and the vapor-flow velocity) is zero. Note the value for thermal conductivity k is given as k 2:43 10. 1:832 10 1:718 10. T 296:0.   1:5.  416:0 Jm T 120:0 . K 1 : 5:33 . Next, applying u = PDF-417 2d barcode for Java 0 in (5.32), ]T Kr2 T: ]t r2 T 0: 5:34 . With the steady-sta te assumption a basic Fick s law of diffusion for T results, 5:35 .
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