化工传递过程原理课件：第四Examples%28I%29

1、iiViCRt N121()() iIiiIISiCCRNvNvnTransport of Chemical SpeciesFluxes of Chemical SpeciesReference velocity Molar units Mass units 0 Ni ni v Ji ji vM JiM jiM1111,0,0nnMMMMiiiiiiiiinnMMiiiiiiiiiCCCNvJvJNvJnvjvjnvjFlux relationshipsDiffusion of Chemical Species ABABAAAAMMAAABDDMCM DAReference Velocity

2、Mass units Molar units- vj- J vj-MAAABAxCDx J-Ficks law for binary mixtures of A and BOne-Dimensional Steady ProblemsExample 1: Directional Solidification of a Dilute Binary Alloy022dydCUdyCdDiii(1)(0)(0)()iiiiiiidCUKCdyDCC(1)exp()( )(1)exp()iiiiiiiiiiiiyKKPeC yCKKPeUPeD(1)exp()iSiiiiiCKCKKPe 00iSiS

3、iiCyCK CExample 2: Diffusion in a binary gas with a heterogeneous reaction y=0y=LA, BCA=CA0AmBGasCatalyticsurfacenAsnSACkRdydNdydNByAy 0AyBymNN()(1)AAyAAyBytABAAyAAytABdxNxNNC DdydxNx NmC Ddy1(/)(1)AyAAtABNdCCCmdyD ( )nAySAsnANRk C L 00AACC1 11 )1 (1)1 (1ln)1 (1000mmmxmxmxDaAAAn01(1) (0)1nAdDaxmd 10

4、00nAAsnAAABACLCyk CLDaCLDC0( ) 1(/)(1) (0)nAsnAAtAAABdCkCLCCmCCdyD Example 3: Diffusion in a dilute liquid solution with a reversible homogeneous reaction y=0y=LCA=CA0,CB=CB0ABLiquidInertsurface11111()/VABABAVBRk Ck Ck KCCRKkk 212212()0()0AASBABBSBAd CDk KCCdyd CDk KCCdy00,at 00 at AABBABCCCCydCdCyL

5、dydy222210ABASBSABASBSd Cd CDDdydydCdCDDadydy10, at ayL2ASABSBD CD Ca200 at 0ASABSBaD CD Cy00()ASBAABBSDCCCCD00ABABAAyCKCLCC22221100()()AABASBSAddk Lk LKCDDC )sinh()tanh()cosh()1 ()sinh()tanh()cosh()1 (BA 1010AAdd(1)(1)1ABABeee 0e 00/1/1/BAABABABCCDDKKDD 011ABExample 4: Transient diffusion in a soli

6、d from a surface fixed concentrationDoping of semiconductors22CCDtyI.C. C=0 , y 0, t=0B.C. C=Cs, y=0 C=0, y Transient Problems22ffDty,000,1,0fyftft/SfCC yt ffSimilarity method (combination of variables)220d fdfdDdcD22cD 00 1/22tcD t2ycDt220d fdfcdd 01;0ff 22cysDt2220d fdfsdsdsThe Error Function 202(

7、0)0()1znerfzednerferf ,12syCy tCerfDt 20211snfsednerfs 22001snnednfsedn Doping of semiconductorsA 2mm thick silicon wafer is to be doped with antimony (Sb) in order to create a p-type region. This can be done by passing a SbCl3/H2 gas mixture over the surface of the wafer at 1200 oC, which fixes the

8、 surface Sb concentration at 1023 atoms /m3. Suppose that the donor density (which is just another term for the Sb concentration) is hoped to be greater than or equal to 31022 /m3, over a depth of 1m below the surface. Determine how long the wafer should be exposed to this atmosphere in order to ach

9、ieve this. 1210.720.732ssyCCerfDtyCerfCDtyDt 0-3172264exp()383.0001.3 10 exp()8.314 1473.23.4 10/1101.38 103.820.73QDDRTmstshDExample 5: Transient diffusion in a Symmetric SlabCA*CA*2Lz=0 zCA=CA0 at t=022AAACCDtz00,AACzC*,00,AAACtCt LCz*0*AAAACCCC22zDt0,1z,00,0tt zz)()(zZtTTZDTZ 0 ZZ 0(0)0Z LZ0 )cos()sin(zBzAZ2(21)2nnL)cos(zBZnnn0 DTT)exp(DtATnn