One end of a solid plate was placed in contact with a constant temperature heat source. Every 2 min the temperature was measured at points 5, 10, 15, 20 and 25 cm from the end in contact with the heat source. Now I need to determine the thermal conductivity based on these temperatures. I don't have information about the amount of heat.
Based on your experiment, you will determine your material's thermal diffusivity (length²/time) . To do so, you will find closed form solution for the temperature profile in thermal design books (for example, Incropera, Heat and Mass transfer). From this, you will need two additionnal data: density and specific heat. The first quantity is straightforward to obtain, the second is also simple to measure, but should not vary too much (if you know the value for a similar material, it should be very close). What is the accuracy you are aiming at ?
One dimensional unsteady heat equation. Closed form solution or even finite differences form to substitute the points. But that will give diffusivity only as Nicolas Jobert mentioned.
Nicolas Jobert this is a college work and unfortunately it was not provided what the material is (thus neither density nor specific heat). I was thinking about one-dimensional equations, but I ended up finding nothing in the literature.
@Ravi Prattipati I was thinking about it, but my teacher advised to use only equations related to the geometry of the material (flat plate) and not to try using the finite difference method.
One thing I can remember related to geometry is Conduction shape factors. You may want to look it up in conjunction with semi-infinite solid concept with constant temperature boundary condition.
Good luck !
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