Short Answer:

Thermal diffusivity is a property of a material that shows how quickly heat spreads through it. It represents the ability of a material to conduct heat compared to its ability to store heat. A material with high thermal diffusivity allows heat to move faster through it, while a low diffusivity means heat spreads slowly.

It is mathematically defined as the ratio of thermal conductivity to the product of density and specific heat capacity of the material. Thermal diffusivity helps engineers understand how fast a material reaches thermal equilibrium when heated or cooled.

Detailed Explanation :

Thermal Diffusivity

Thermal diffusivity is an important thermal property of materials that describes how quickly a temperature change occurs within a material when it is subjected to a change in heat. It measures the rate at which heat diffuses or spreads through a material. In simple words, it indicates how fast heat is conducted compared to how much heat the material can store.

It combines three important thermal properties — thermal conductivity (k), density (ρ), and specific heat capacity (c) — into one single property that defines how a material responds to temperature changes over time.

Mathematically, thermal diffusivity (α) is expressed as:

Where:

•  = Thermal diffusivity (m²/s)
•  = Thermal conductivity (W/m·K)
•  = Density of material (kg/m³)
•  = Specific heat capacity (J/kg·K)

This equation shows that thermal diffusivity depends directly on the material’s ability to conduct heat and inversely on how much heat it can store.

Concept and Physical Meaning

To understand thermal diffusivity, imagine a metal rod and a wooden block of the same size. When both are exposed to heat on one side, the metal quickly becomes hot along its length, while the wooden block heats slowly. This happens because metal has high thermal diffusivity, meaning it transfers heat faster, while wood has low thermal diffusivity, meaning it resists quick temperature change.

Thus, thermal diffusivity determines how fast the temperature field in a body changes when heat is applied. It gives an idea about how rapidly a material can respond to a sudden temperature difference.

• High diffusivity materials (like copper and aluminum) heat up and cool down quickly because they conduct heat fast and store less heat energy.
• Low diffusivity materials (like wood, rubber, and insulation materials) heat up slowly and store more heat energy before their temperature changes significantly.

Units of Thermal Diffusivity

The SI unit of thermal diffusivity is square meters per second (m²/s).
This unit comes from the formula .

By substituting the units:

Hence, thermal diffusivity measures how many square meters of the material can be affected by heat in one second.

Factors Affecting Thermal Diffusivity

1. Thermal Conductivity (k):
   A material with high thermal conductivity will have high thermal diffusivity because it can transfer heat more effectively. Metals usually have high conductivity and thus high diffusivity.
2. Density (ρ):
   Materials with higher density can store more heat energy per unit volume, which reduces their thermal diffusivity.
3. Specific Heat Capacity (c):
   A high specific heat capacity means the material requires more energy to change its temperature, resulting in lower diffusivity.

In summary, a good thermal conductor with low density and low specific heat will have a high thermal diffusivity.

Importance of Thermal Diffusivity

Thermal diffusivity is very important in mechanical and thermal engineering because it determines how fast heat transfer occurs during transient or unsteady-state conditions. Some key uses include:

1. Material Selection:
   Engineers choose materials based on diffusivity for heat exchangers, furnace linings, and insulation. Metals with high diffusivity are preferred where fast heat transfer is required.
2. Thermal Insulation Design:
   Materials with low diffusivity are used in thermal insulation to delay heat transfer and maintain temperature differences.
3. Transient Heat Conduction Analysis:
   In processes where temperature changes with time, such as cooling of castings or heating of rods, thermal diffusivity helps calculate the temperature distribution.
4. Temperature Control Systems:
   It is used in designing temperature-sensitive equipment like electronic components, turbines, and engines, where quick heat response or slow temperature rise is needed.
5. Thermal Shock Resistance:
   Materials with low diffusivity are better at resisting thermal shocks because they do not experience rapid temperature changes throughout their volume.

Examples of Thermal Diffusivity in Materials

• Copper: Has high diffusivity because of excellent heat conduction and low specific heat.
• Aluminum: Also has high diffusivity, commonly used in heat exchangers and radiators.
• Brick and Concrete: Have moderate diffusivity; used in construction for controlled heat transfer.
• Insulating Materials (like wool, cork): Have very low diffusivity, ideal for reducing heat flow.

These examples show how diffusivity helps determine the best material for a particular thermal application.

Relation with Heat Transfer

In unsteady-state heat conduction, thermal diffusivity determines how quickly the temperature at any point in a material changes with time. It controls how fast the heat front moves through a solid when heat is suddenly applied or removed.

A high diffusivity means the temperature equalizes quickly, while a low diffusivity means the temperature changes slowly, creating thermal lag. Thus, diffusivity connects the rate of heat conduction and the rate of temperature change in a body.

Conclusion

Thermal diffusivity is a key thermal property that defines how rapidly heat spreads through a material. It links thermal conductivity, density, and specific heat into one property that shows a material’s thermal response. Materials with high thermal diffusivity heat up and cool down quickly, while those with low diffusivity resist temperature changes. Understanding thermal diffusivity is essential for designing efficient heat transfer systems, choosing insulation materials, and analyzing transient heat conduction problems in mechanical engineering.