Question

Exercise 8. the temperature function in a laterally insulated rod made of copper is found (say experimentally) to be e−0.046t cos(0.2x). find the thermal diffusivity k of copper.

Answer 1

u2(x,t) = e^-k(w2^2)tcos(w2x)
= e^-0.046tcos(0.2x)
w2 = 0.2, w2^2 = 0.04

-0.046t = -k(w2^2)t
-0.046 = -k(0.2)^2
-0.046 = -k(0.04)
1.15 = k