# Thermal diffusivity: Definition, Formula, Units, Importance [with Pdf]

Contents

## What is thermal diffusivity in heat transfer?

The thermal diffusivity of a substance is given by the ratio of thermal conductivity (K) and the product of the density and specific heat capacity (Cp) of the material.

We can also say that thermal diffusivity is a ratio of thermal conductivity of the material to the volumetric heat capacity of the material. Here volumetric heat capacity is the product of density and specific heat.

The thermal diffusivity shows the ability of a material to conduct the heat with respect to the heat stored.

The thermal diffusivity is denoted by the symbol α.

## Thermal diffusivity equation:

Thermal diffusivity of the material is given by,

\alpha =\frac{K}{\rho\times C_{P}}

Where,
K = Thermal conductivity (W/mK)
ρ = Density of material (Kg/m^{3})
C_{p} = Specific heat capacity (J/Kg.K)

## What does thermal conductivity depend on?

As per the definition, the value of thermal diffusivity depends on the thermal conductivity, density, and specific heat capacity of the material.

The thermal diffusivity of the material is directly proportional to the thermal conductivity (K) which means that the value of α increase with the increase in thermal conductivity

The thermal diffusivity is inversely proportional to the density and specific heat. This means that the thermal diffusivity increase with a decrease in density or specific heat.

## Thermal diffusivity units:

SI unit:-

In the SI system, the unit of the thermal conductivity (K) is W/mK, the unit of density is Kg/m^{3} and the unit of specific heat is J/kg.K.

Therefore the unit of thermal diffusivity is given by,

\alpha =\frac{K}{\rho\times C_{P}} = \frac{[\text{W/m.K}]}{[\text{Kg/}m^{3}]\times [\text{J/Kg.K}]}

= m²/s

Hence the SI unit of thermal diffusivity is m²/s.

FPS unit:-

In the FPS system, the unit of the thermal conductivity is BTU/h.ft.°F, the unit of density is lb/ft³ and the unit of specific heat is BTU/lb.°F.

Therefore, the unit of thermal diffusivity is given by,

\alpha =\frac{K}{\rho\times C_{P}} = \frac{[\text{BTU/h.ft.°F}]}{[\text{lb/}ft^{3}]\times [\text{BTU/lb.°F}]}

= ft²/hr

Hence the FPS unit of thermal diffusivity is ft²/hr.

## Why is thermal diffusivity important?

Thermal diffusivity is an important term as it states, how fast heat diffuses into the material. The lower value of thermal diffusivity indicates that the material has a higher rate of thermal diffusion and hence such materials heat or cool slowly. In such cases, the specific heat and density of the material are higher or the thermal conductivity of the material is less.

While the material with a higher value of thermal diffusivity has lower heat diffusion and it can heat or cool quickly. Such material has a lower value of specific heat or the density of the material has a higher value of thermal conductivity.

Therefore in such an application where cooling or heating is required at a faster rate, in that case, the material with higher thermal diffusivity is preferred.

While in some applications, the cooling or heating of material has been done at a slower rate, hence in such application the material with lower thermal diffusivity are preferred.

## Thermal diffusivity vs conductivity:

The thermal diffusivity states the relation between heat transferred and heat stored while thermal conductivity is the ability of the material to conduct heat.

The thermal diffusivity states how fast heat diffuses into the material while the thermal conductivity indicates the rate of heat transfer per unit area and per unit temperature gradient.

The thermal diffusivity is considered only in unsteady-state cases, while the thermal conductivity is considered in both steady-state and unsteady-state cases.

FAQ’s

1. What is thermal conductivity and thermal diffusivity?

Thermal conductivity is the ability of the material to conduct the heat and thermal diffusivity is the relation between heat transferred and heat stored.

2. How do you find thermal diffusivity?

The thermal diffusivity can be found by using the following equation,
α = K/(ρ.Cp)
Where,
K = Thermal conductivity (W/mK)
ρ = Density of material (Kg/m^{3})
C_{p} = Specific heat capacity (J/Kg.K)

3. How is thermal diffusivity used?

Thermal diffusivity is used in transient or unsteady-state heat conduction analysis.

4. Is high thermal diffusivity good?

The high thermal diffusivity indicates the lower value for volumetric heat capacity (ρ.Cp) so that the material can heat or cool quickly. Therefore the higher value of thermal diffusivity is good for the applications where faster heating or cooling is required.

5. What is thermal resistance and thermal diffusivity?

Thermal resistance is the resistance offered by a material to the heat conduction while thermal diffusivity is the ratio of thermal conductivity and volumetric heat capacity. Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people.