# Calculate the thermal diffusivity from minimal information

#### NicolasL

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.

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#### Chestermiller

Mentor
Are those temperatures the spatial average over the thickness of the plate or something else? Do they give you any idea what the surface temperatures are, or what the boundary conditions at the surface of the plate are?

"Calculate the thermal diffusivity from minimal information"

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