# Calculate the thermal diffusivity from minimal information

• NicolasL
In summary, the conversation discusses simplifying the heat governing equation to dT/dt = A d^(2)T/dx^(2) and using the given temperatures and time to solve for A. The speaker is unsure if they can divide dT/dt by d^(2)T/dx^(2) and shares their calculated value of A, which is slightly off from the correct answer. They also mention the possibility of using spatial average temperatures and boundary conditions to better understand the heat transfer.
NicolasL
Homework 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.

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?

## 1. What is thermal diffusivity?

Thermal diffusivity is a measure of how quickly heat can pass through a material. It is defined as the ratio of a material's thermal conductivity to its heat capacity.

## 2. How is thermal diffusivity calculated?

Thermal diffusivity can be calculated by dividing the thermal conductivity of a material by its density and specific heat capacity. This can also be expressed as the product of thermal conductivity and the square root of the ratio of specific heat capacity to density.

## 3. What minimal information is needed to calculate thermal diffusivity?

To calculate thermal diffusivity, you will need to know the thermal conductivity, density, and specific heat capacity of the material in question. These values can typically be found in material databases or through experimental measurements.

## 4. What are the units of thermal diffusivity?

Thermal diffusivity is typically expressed in units of square meters per second (m²/s) in the SI system. In some cases, it may also be expressed in units of square centimeters per second (cm²/s).

## 5. Why is thermal diffusivity an important property to calculate?

Thermal diffusivity is an important property in understanding how heat is transferred through different materials. It is used in various fields such as engineering, geology, and materials science to design and analyze heat transfer systems and processes.

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