Experimental data fitting to heat equation - thermal conductivity calculation

Hi, I was trying to solve my problem but I don't really know how to do it. I am trying to determine the thermal conductivity coefficient based on the heat equation:

dT/dt is measured experimentally, density (rho) and heat capacity (cp) are known. I know the geometry of my system (length 3.15 cm). I assume heat distribution in one direction (x). All I want to determine from this equation is thermal conductivity coefficient (lambda) based on measured dT/dt, density, heat capacity and geometry.

Is there anyone who can help me with that?

Thanks Kamil

[dpb]

What geometry were measurements taken over?

Attach a .mat file with the data would help somebody at least take a stab at it...

[Torsten]

Where did you measure dT/dt ?

How is the change in temperature initiated (boundary conditions) ?

What is your initial temperature (initial condition) ?

[Kamil Oster]

The geometry and conditions are included in the picture below:

There are 2 temperature probes: one in the middle of the geometry (circle) and one is measuring the temperature in the left wall. The temperature is stabilised at 100oC and then 20oC is applied on the right sight and temperature gradient is measured in the middle, until the left wall shows the decrease of the temperature. However, I'm only interested in the scenario until the left wall is constant (before the temperature is decreasing).

[dpb]

There's no way to estimate the second derivative wrt x w/ only the two points.

[Torsten]

Set up your system in "pdepe". For the times you measured the temperature in the midpoint, read the solution in the midpoint from "pdepe" and adjust "alpha" until the distance between measured and simulated temperature curves for x = 3.15 cm /2 becomes minimal.