- Problem Statement
- A flat plate that is 0.20 m thick has an initial temperature of 288.15 K is being cooled. After 15 minutes, the temperature is 278.15 K. After 20 minutes, the temperature is 277.38 K. What is the thermal diffusivity A of the plate?

- Relevant Equations
- dT/dt + u dT/dx = A d^(2)T/dx^(2) + Q/(pc_p)

So I started from the heat governing equation above. There is no heat generation or matter flow, so I simplified it to dT/dt = A d^(2)T/dx^(2).

Now I assume dT/dt = (278.15K-277.38K)/(1200s-900s) = 0.0025667. But then I'm stuck with the d^(2)T/dx^(2). Is the x just 0.20 m? For T I used 288.15K and 278.15K. But can I actually divide dT/dt by d^(2)T/dx^(2)? When I do it I get A = 1.02667*10^(-6), and the right answer is 1.0021*10^(-6). None of the other things I tried came that close. Any help is appreciated.

Now I assume dT/dt = (278.15K-277.38K)/(1200s-900s) = 0.0025667. But then I'm stuck with the d^(2)T/dx^(2). Is the x just 0.20 m? For T I used 288.15K and 278.15K. But can I actually divide dT/dt by d^(2)T/dx^(2)? When I do it I get A = 1.02667*10^(-6), and the right answer is 1.0021*10^(-6). None of the other things I tried came that close. Any help is appreciated.