Solving a PDE using PDE Toolbox

This problem invoves an inner pipe with a constant wall temp, an annular space with conduction only, and an insulated outer pipe (no heat transfer)

I'm trying to solve the following Partial Differental Equation as my Governing Equation:

Initial Condition:

@ t = 0s, T = 573 K (uniformly distributed)

Boundary Conditions:

@ r = ri, T = 673 K (constant)

@ r = ro, dT/dr = 0 (insulated end)

This is my first time using pdepe, any help would be appreciated.

I'd like to be able to plot (Temperature vs time) for varying points between the inner and outer radii.

Answer 1

[Torsten]

C.ri = 0.0125;
C.ro = 0.0375;

C.alpha = 1.905*10^-5; 

C.Ti = 673;
C.T0 = 573;

r = linspace(C.ri,C.ro,50);
t = linspace(0,2000,2001);

m = 1;
eqn = @(r,t,T,dudx)heatcondPDE(r,t,T,dudx,C);
ic = @(r)heatcondPDE_IC(r,C);
bc = @(rl,Tl,rr,Tr,t)heatcondPDE_BC(rl,Tl,rr,Tr,t,C);
sol = pdepe(m,eqn,ic,bc,r,t);

T = sol(:,:,1);
plot(r,[T(1,:);T(5,:);T(10,:);T(20,:);T(30,:);T(40,:);T(80,:)])
grid on

function T0 = heatcondPDE_IC(r,C)
  if r == C.ri
    T0 = C.Ti;
  else
    T0 = C.T0;
  end
end

function [c, f, s] = heatcondPDE(r,t,T,dudx,C)
  c = 1;
  f = C.alpha *dudx;
  s = 0;
end

function [pl,ql,pr,qr] = heatcondPDE_BC(rl,Tl,rr,Tr,t,C)
  pl = Tl - C.Ti;
  ql = 0; 
  pr = 0; 
  qr = 1;
end

[Tony Stianchie]

Thank You!!!