# What and why thermal diffusivity?

I understand the following properties:

Thermal Conductivity: It tells how well thermal energy can get transferred to a material, from a material and within the material. A material with higher thermal conductivity will allow more energy transfer to it, within it, and from it.

Specific heat: The amount of energy required to raise/drop the temperature of a unit mass by one degree Celsius. Higher the specific heat difficult it will be to increase the temperature of a material.

Thermal diffusivity clubs these two properties.

Consider water and air. Air has a higher thermal diffusivity than water? What does this physically mean.

• Can Specific heat be defined with Fahrenheit as the temperature scale? Oct 26, 2021 at 13:26
• Yes, I guess it can be. The values in degree Celsius and Kelvin won't change because of same temperature rise, but in Fahrenheit I believe it will change. Oct 26, 2021 at 13:32
• So consider water, it does not conduct heat through itself very well, but is good at moving heat from one place to another... Oct 26, 2021 at 13:34
• If water cannot conduct heat through it very well how is it able to move heat from one place to another well🤔 like a pipe, for eg. if there are restrictions in the pipe, it will not be able to move liquid well from one place to another. Wait are we going in a conversational explanation rather than you giving a direct ans? Oct 26, 2021 at 13:43
• @SolarMike Sure. Our transatlantic friends like to use BTU/lb.deg F as a unit. Oct 26, 2021 at 21:12

Both Thermal Conductivity and Specific Heat relate two different quantities, "heat" and "temperature."

The point of giving "Thermal Diffusivity" a separate name is that it eliminates the concept of "heat".

The "heat equation" $$\frac{\partial T}{\partial t} = \alpha \nabla^2 T$$ reduces two partial differential equations in two variables to one PDE in one variable, which is easier to solve. After finding the temperatures, you can recover the heat fluxes as a separate solution step.

The numerical value of $$\alpha$$ describes how fast a local perturbation in the temperature dissipates (or diffuses) into the rest of the structure. It has a very wide range (more than 10,000 : 1) for different materials.

Note that the heat equation only applies to conduction in solids. Heat transfer in fluids is often dominated by convection, which in general is much more complicated. Thinking about "common-sense" situations comparing water and air, for example, are likely to be very misleading.

Thermal diffusivity $$\alpha\$$is:

$$\alpha= \frac{k}{\rho*C_p}$$ at constant pressure.

• k is thermal conductivity (W/(m·K))

• $$c_{p}$$ is specific heat capacity (J/(kg·K))

• $$\rho$$ is density (kg/m3)

It is a property indicating how fast say a rod can transfer heat from its hot end to its cold end, conduction.

Consider water and air. Air has a higher thermal diffusivity than water? What does this physically mean.

Because the water moves the heat by convection and because of its higher specific heat when it moves from one place to the other it carries a large amount of heat.

And because of water's high density compared to air when you plug in the density in the denominator of the diffusitivity eq. you end up with lower diffusivity.

• "It is a property indicating how fast say a rod.." won't thermal conductivity give the same information that how fast heat goes from one end to another? Oct 27, 2021 at 13:42
• thermal conductivity is about how much heat is transferred, thermal diffusivity is about how fast . the relation is l = a . r . cp, where a is thermal diffusivity, r is density and cp is the specific heat capacity Oct 27, 2021 at 14:55