052407-132a-clab 8

052407-132a-clab 8 - 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 8 New Commands: <<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 = as[[20]] Like last week, we’re going to solve the heat equation and animate the solutions. In class, we solved the heat equation (here I am taking K and L to be 1) ∂T ∂t = ∂ 2 T ∂x 2 (1) with non-‘simple’ boundary conditions T ( x = 0 , t ) = 0 (2) T ( x = 1 , t ) = 100 (3) and initial conditions T ( x, t = 0) = 0 . (4) This involved splitting the solution into a steady bit and a transient bit, T ( x, t ) = T s ( x ) + T tr ( x, t ) . (5) The steady part T s ( x ) = 100 x (6) takes care of the non-simple boundary conditions, and the general solution for the transient part T tr is given by T tr ( x, t ) = summationdisplay β ( a β cos βx + b β sin βx ) e- β 2 t . (7) Using the boundary condition at x = 0 kills the cosine terms ( a β = 0) and the boundary condition at...
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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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052407-132a-clab 8 - C HEMICAL E NGINEERING 132A Professor...

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