Tuesday, Feb 14, 2017

Equilibrium temperature profile in a pipe

Laplacian in cylindrical coordinates is

∇^{2}*u* = (1)/(*r*)(∂)/(∂*r*)(*r*(∂*u*)/(∂*r*)) + (1)/(*r*^{2})(∂^{2}*u*)/(∂*θ*^{2}) + (∂^{2}*u*)/(∂*z*^{2})

Actual plots of log(*r* ⁄ *b*) ⁄ log(*a* ⁄ *b*):

From last time:

Coefficients we computed:

(From 0 to 60mph in 20 minutes!)

numpy arrays, broadcasting, outer, linspace, arange, sum, base-0 counting, [1:]

functions (def), *for* loops

pylab, plot, xlabel, ylabel

Illustration of solution: Jupyter Notebook, HTML