CHE 527 Advanced Applied Mathematical Analysis in Chemical Engineering Fall 2006
Homework 10
Due in class on Thursday, Nov. 30.
1. Consider transient heat conduction in an infinite slab which has a nonuniform initial temperature
profile:
∂T
∂t =α∂2T
∂x2
where
T=T0at x=±∞
T=T0+g(x) at t= 0
Solve for T(x, t) using Fourier transforms. Note: your solution may include unevaluated definite
integrals, but it should not include i=√−1, since T is real. What requirements must g(x) satisfy?
2. Run heat fft.m with different values of N and determine if the scaling of the computational cost is
closer to a true fast Fourier transform (i.e., Nlog2N) or a stardard Fourier transform (i.e., N2). A
few hints: (1) comment out all lines associated with plotting, (2) try running with the command: tic;
heat fft; toc to get the run time, and (3) repeat each run a few times and discard the first run, which
involves a huge overhead.
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