# How to find thermal diffusivity

This is a question about nondimensionalization in the heat equation $$\rho c \frac{\partial u}{\partial t}= \kappa \frac{\partial^2 u}{\partial x^2}~?$$

How could one devise a nondestructive experiment to find the thermal diffusivity i.e $$\frac{\kappa}{\rho c}$$?

• In the current form it is not clear what your first question means... may be you could reformulate it. As of your second question, you could check en.wikipedia.org/wiki/Specific_heat_capacity#Measurement Commented Oct 4, 2021 at 2:35
• I'm sorry. The question isn't clear. I didn't write correctly. I changed it
– Jama
Commented Oct 4, 2021 at 2:37
• @Jama Hello and welcome to Physics.SE! Please ask only one question per post. Commented Oct 4, 2021 at 3:50
• What are your thoughts so far on how to do what you want? Commented Oct 4, 2021 at 3:56
• Well I know I can write it as $u_t=D u_{tt}$ where D is the quantity I'm looking for. But that's not helping. Now I'm thinking that the units of D are $L^2 M T^-5$ and I should equate that to $[\rho]^a[c]^b[\kappa]^c$ and solve for $a,b,c$?
– Jama
Commented Oct 4, 2021 at 4:22

I would advise simply finding the individual properties $$\rho, c, k$$, as these can all be found via steady state experiments which are much easier to set up and would have less uncertainty.