- #1
gothloli
- 39
- 0
Homework Statement
I performed an experiment where we have to find the thermal diffusivity of rubber. This is done using the phase difference of the axial and external temperatures of the rubber. The teacher's guide says to use the Kelvin functions, plot them against x. Where x = r(√(2pi/TD)) Where T is the period of the immersion, and D is the diffusivity. From the plot find the diffusivity, I'm not sure how I'm to do this from the plot.
Homework Equations
Bessel function: J(x) = 1 - [itex]\frac{x^{2}}{4}[/itex] + [itex]\frac{x^{4}}{64}[/itex] - [itex]\frac{x^{6}}{2304}[/itex]
Ber(x) = 1 - [itex]\frac{x^{4}}{64}[/itex]
Bei(x) = [itex]\frac{x^{2}}{4}[/itex] - [itex]\frac{x^{6}}{2304}[/itex]
tan([itex]\Phi[/itex]) = bei(x)/ber(x)
The Attempt at a Solution
The data I have is that of the phase difference between the axial and the external temperature graphs. From this I calcualate the x values by setting cos([itex]\Phi[/itex]) = Ber(x)
and sin([itex]\Phi[/itex]) = Bei(x). Then I plot those in terms of x. But I'm not sure if this is the way to go or how I can get diffusivity from the graph. Thanks all.