# Thermal Diffusivity Calculator

Table of contents

What is thermal diffusivity?How to calculate thermal diffusivityExample: Using the thermal diffusivity calculatorThermal diffusivity of substancesThermographic damage detectionFAQsThe thermal diffusivity calculator will assist you in estimating the **rate of heat transfer from one point to another** for different substances. The thermal diffusivity parameter is a **function of thermal conductivity, specific heat, and fluid density.**

Thermal diffusivity is the parameter that explains the **penetration of heat in a substance** and is used to **characterize the unsteady flow of heat** and estimate the **temperature field** to understand the cooling process in a substance. You can use it to determine the **Prandtl number** used for several heat transfer processes.

This parameter is also used in modern non-destructive techniques (NDT) like thermography or **thermographic damage detection** in **composite structures**. This method is crucial for monitoring the health of different aircraft structures. The article further explains what thermal diffusivity is and the calculation of the thermal diffusivity of substances.

🙋 To dig deeper into fluid mechanics, check our Prandtl number calculator.

## What is thermal diffusivity?

* Thermal diffusivity definition —* It is the property of a substance that tells us how the heat would flow through it from one point to another. Say you heat one end of a steel plate; the heat would travel towards the cooler end. The entity's thermal diffusivity would tell us

**how fast it would go**, i.e., the

**rate of heat transfer across two points**. It is measured in the

**units**of

`area per unit time`

, i.e., $\text{mm}^2\text{/s}$ or $\text{ft}^2\text{/s}$. The **SI unit**for thermal diffusivity is $\text{m}^2\text{/s}$.

🔎 On a related topic, you may also be interested in using our thermal conductivity calculator.

Most heat-conducting solids have high thermal diffusivity; for instance, the thermal diffusivity of copper at $25 \ °\text{C}$ is $111 \text{ mm}^2\text{/s}$ whereas the value of thermal diffusivity for a carbon/carbon composite is $216.5 \text{ mm}^2\text{/s}$. This means the heat would flow **rapidly** in the carbon/carbon composite compared to copper.

The thermal diffusivity ($\alpha$) depends on **three properties** of material, i.e., **thermal conductivity $k$, specific heat capacity, $C_\mathrm{p}$, and density, $\rho$**. You can quickly convert specific heat to heat capacity with our heat capacity calculator.

Thermal conductivity and thermal diffusivity are related using the thermal diffusivity formula:

Here, the term $\rho \ C_\mathrm{p}$ is also known as **volumetric heat capacity** with units of $\text{J/m}^3\cdot\text{K}$. The volumetric heat capacity is the **heat needed to raise the temperature** of a material having unit volume by **one unit.**

You can use the **thermal diffusivity and kinematic viscosity ($\nu$)** to find the substance's **Prandtl number** ($\text{Pr}$). Mathematically, that's:

## How to calculate thermal diffusivity

Follow the steps below to use the thermal diffusivity formula:

- Fill in the
**thermal conductivity**$k$ for the material. - Enter the
**density**$\rho$ for the material. - Insert the material's
**specific heat capacity**, $C_\mathrm{p}$. - The calculator will return the
**thermal diffusivity**of the material.

💡 You can utilize the **preloaded data of common materials** from the list to directly obtain the thermal diffusivity.

## Example: Using the thermal diffusivity calculator

Find the thermal diffusivity of water considering the density as $997 \text{ kg/m}^3$, specific heat capacity as $4182 \text{ J/kg⋅K}$, and thermal conductivity, $0.607 \text{ W/m⋅K}$.

To find the thermal diffusivity:

- Fill in the
**thermal conductivity**, $k = 0.607 \text{ W/m⋅K}$. - Enter the
**density**, $\rho = 997 \text{ kg/m}^3$. - Insert the
**specific heat capacity**, $C_\mathrm{p} = 4182 \text{ J/kg⋅K}$. - Using the thermal diffusivity equation:

## Thermal diffusivity of substances

The table below has the list of thermal diffusivity of common substances:

Material | Thermal diffusivity (mm |
---|---|

Copper | 111 |

Gold | 127 |

Iron | 23 |

Air (at 300 K) | 19 |

Water | 0.14558 |

Rubber | 0.089-0.13 |

Wood (pine) | 0.082 |

Engine oil (unused, 300 K) | 0.085 |

## Thermographic damage detection

The process of thermographic damage detection is used to **monitor the health of structures**. This method is part of several non-destructive testing techniques used to detect defects or hidden subsurface damage in the structure. By non-destructive means, the testing does not interfere with the structure's structural integrity. Examples of other such techniques include ultrasound and X-ray testing.

During thermographic damage detection, flash lamps heat one side of the structure, and an infrared camera is set up on the other side to monitor the temperature progression. This method works by tracking the heat flow for any anomaly in the temperature field to locate defects or damage. Diffusivity is one of the parameters used to estimate the heat flow across the thickness of the sample.

### How do I define thermal diffusivity?

Thermal diffusivity is defined as the **rate of heat transfer in material** from one point to another. In other words, it is the ratio of thermal conductivity and volumetric heat capacity.

### What are the units of thermal diffusivity?

Thermal diffusivity is measured in the area per unit time, i.e., `meters square per second`

or `feet square per second.`

Considering, the units of thermal conductivity as `W/m⋅K`

, density being `kg/m³`

, and specific heat as `J/kg⋅K`

, we get: `(W/m K) / ((kg/m³) × (J/kg⋅K)) = m²/s`

.

### How do you calculate thermal diffusivity?

To calculate thermal diffusivity of a material:

**Multiply**the**density**of material by its**specific heat capacity**.**Divide**the**thermal conductivity**by the**product**in the previous step to obtain the thermal diffusivity.

### What is thermal diffusivity of air at 0 °C?

Thermal diffusivity of air is **18.46 mm ^{2}/s**. Considering

**density**of air as 1.2922 kg/m

^{3},

**thermal conductivity**of

`0.024 W/m⋅K`

and **specific heat**of

`1006 J/kg⋅K`

, the **thermal diffusivity**is calculated as

`α = 0.024 / (1.2922 × 1006) = 18.46 mm²/s`

.### What is thermal diffusivity of water?

Thermal diffusivity of water is **0.14558 mm ^{2}/s**. Considering

**density**of air as 997 kg/m

^{3},

**thermal conductivity**of

`0.607 W/m⋅K`

and **specific heat**of

`4182 J/kg⋅K`

, the **thermal diffusivity**is calculated as

`α = 0.607 / (4182 × 997) = 0.14558 mm²/s`

.### What are the factors affecting thermal diffusivity?

Thermal diffusivity is a function of:

**Density**;**Specific heat capacity**; and**Thermal conductivity**of the material.

The thermal diffusivity increases with an increase in thermal conductivity and decreases when the density or specific heat of the material increases.