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053107-132a-clab 9

# 053107-132a-clab 9 - CHEMICAL ENGINEERING 132A Professor...

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C HEMICAL E NGINEERING 132A Professor Todd Squires Spring Quarter, 2007 Computer Lab Assignment 9 Remember: <<Graphics‘Animation‘ 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: <<NumericalMath‘BesselZeros‘ BesselJZeros[0,n] BesselJ[n,r] Today we’re 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 β ( a β J 0 ( βr ) + b β Y 0 ( βr )] e - β 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. We’ll consider diffusion out of a cylinder of radius 1. We must first use the boundary conditions to decide what the a β and b β s are. First – if you plot Y 0 ( 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 β s.

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053107-132a-clab 9 - CHEMICAL ENGINEERING 132A Professor...

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