053107-132a-clab 9

053107-132a-clab 9 - C HEMICAL E NGINEERING 132A Professor...

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Unformatted text preview: C HEMICAL E NGINEERING 132A Professor Todd Squires Spring Quarter, 2007 Computer Lab Assignment 9 Remember: <<GraphicsAnimation Animate[Plot[f[x,t],{x,0,1},PlotRange->{0,1}],{t,0,10,.5}] as = Table[a[n],{n,0,50}] a20 = a[[20]] NIntegrate[f[x],{x,0,1}] New Commands: <<NumericalMathBesselZeros BesselJZeros[0,n] BesselJ[n,r] Today were going to explore Bessel Functions a bit. As you may recall from class, the solution to the 2D axisym- metric heat/diffusion equation is c t ( r, t ) = summationdisplay ( a J ( r ) + b Y ( r )] e- 2 Dt . (1) We did not get too much into depth as to what these Bessel Functions look like or how we could use them. Today we will start. Well consider diffusion out of a cylinder of radius 1. We must first use the boundary conditions to decide what the a and b s are. First if you plot Y ( r ) you will notice that it blows up at r = 0. We do not expect an infinite concentration so we can usually discard all of the b...
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This note was uploaded on 12/29/2011 for the course CHE 132a taught by Professor Gordon,m during the Fall '08 term at UCSB.

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053107-132a-clab 9 - C HEMICAL E NGINEERING 132A Professor...

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