kill(all)$

heat : steady state conduction ,with heat generation 'general',version 1, final
peter.vlasschaert@gmail.com,02/07/2019

depends(T,r);

dependencies;

declare(n,integer);

info : T : temperature
          k:thermal conductivity (also function of r)
          r: radius
          n: integer  (0≤n≤2)
          g(r): function of heat generation.

general ode , steady state with heat generation.

p1: 1/r^n*'diff(r^n*diff(T,r),r) +g(r)/k= 0;

example : heat generation by nuclear rod.

step :needed to use 'ode2' into maxima.
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p1a:ev(p1,diff);

n values
------------

n=0 , standard,laplace equation

p1b:subst([n=0],p1a);

p1c:ode2(p1b,T,r);

n=1, cylindrical ,laplace equation, depends on 'r'

p2b:subst([n=1],p1a);

p2c:ode2(p2b,T,r);

n=2, spherical,laplace equation, depends on 'r'

p3b:subst([n=2],p1a);

p3c:ode2(p3b,T,r);

solve specific problem ; you need BC : types
============================================
1e) Dirichlet condition :  T                       = value
2e) Neuman                  : c*dT/dr             = value ('gradient')
3e) Robin                      : c1*T+c2*dT/dr = value
============================================
https://en.wikipedia.org/wiki/Boundary_value_problem
============================================
@ value 'r'

by example: r=ri , inner radius.
                      r=ro ,outer radius

Maxima : Log(x) , Math : Ln(x)