Solve a 1D Heat Conduction equation using pdepe

Hi,

I've been trying to solve a 1D heat conduction equation with the boundary conditions as: u(0,t) = 0 and u(L,t) = 0, with an initial condition as: u(x,0) = f(x). The only difference between a normal 1D equation and my specific conditions is that I need to plot this vertically, i.e., consider the horizontal rod of length L as a vertical rod of depth D (or L). I have manually solved the heat equation but am not sure how to impose the conditions upon the equation

Any help will be highly appreciated...

Answer 1

[Torsten]

As far as I know, pdepe does not accept periodic boundary conditions.

Maybe

http://www.mathworks.com/matlabcentral/fileexchange/45955-periodic-reaction-diffusion-pde-solver

is of interest for you.

Best wishes

Torsten.

[Subha Bose]

Many thanks Torsten for your reply and suggestion! Let me share some more details about the PDE I'm trying to solve, which could help us both... The PDE I'm trying to solve looks like this,

ρcp ∂T/∂t= ∂/∂z(λ ∂T/∂z) or,

∂T/∂t = (I/(ρcp ))^2 (∂^2 T(z,t))/∂z^2 where,

T(0,t) = Tg(t) [is the upper boundary condition and, (here, Tg is an instrument-recorded temperature)]

T(zd,t) = Td [ is the Lower boundary condition (Here Td is subsurface temperature)]

Thanks is advance for your help regarding this...

[Torsten]

So your boundary conditions are not periodic and you can use pdepe to solve it.

Or what exactly is your problem ?

Best wishes

Torsten.

[Yizhou Du]

The similar question.

For the boundry condition T(0,t) = Tg(t) [is the upper boundary condition and, (here, Tg is an instrument-recorded temperature)]

The boundary conditions Tg(t) are not periodic. How can use pdepe to solve it?

[Torsten]

By setting

pr = ur - Tg(t)

in "pdebc" where Tg(t) is a function that supplies the temperature recorded by your instrument at time t.

Best wishes

Torsten.