Thermal Diffusivity: An Introduction
Under steady-state conditions, thermal conductivity indicates how rapidly heat moves through a substance from the hot side to the cold side, thermal diffusivity of a substance is how well a heat may be dispersed by material, taking into consideration both how rapidly the heat may be transmitted through and the speed at which its own temperature may fluctuate.
A measurement of a substance's or energy's ability to diffuse or to permit something to pass through diffusion define diffusivity.
What is Thermal Diffusivity?
The rate at which temperature spreads through a material is referred to as thermal diffusivity. Thermal conductivity and heat thermal capacity are used to compute thermal diffusivity. We use D or α (alpha) to denote thermal diffusivity. The SI unit of thermal diffusivity is m2/s.
Thermal Conductivity
It is the process by which heat is transferred from hotter to cooler regions of a body, bringing the temperature closer to equilibrium. Thermal conduction, as opposed to heat transmission through convection, results from a direct energy transfer between particles, such as molecules, atoms, and electrons, with higher and lower energies. Thermal conduction is unrelated to macroscopic displacements in the body. We use ‘k’ or ‘λ’ to represent it. Thermal resistivity is the reciprocal of thermal conductivity.
Thermal Diffusivity Formula
Thermal diffusivity is the ratio of thermal conductivity to the product of material density and specific heat capacity when the pressure is constant.
$\alpha = \dfrac{k}{{\rho {c_p}}}$
Where
k – Thermal conductivity
$\rho $- Density of the material
\[{c_p}\]- Specific heat capacity
$\rho {c_p}$- volumetric heat capacity
In other words, we can also say that thermal diffusivity is the ratio of the heat allowed to travel through the material to the heat held in the material per unit volume.
Because thermal diffusivity is a ratio between thermal conductivity and volumetric heat capacity at constant pressure, a material with a high value of thermal diffusivity doesn't always disperse heat better than a material with a low value of thermal diffusivity.
Measurement of Thermal Diffusivity
Laser Flash Method: The thermal diffusivity of several different materials is measured using the laser flash analysis or laser flash technique. A plane-parallel sample has one side heated by an energy pulse, and the time-dependent temperature increase caused by the energy input is seen on the opposite side. Energy moves toward the backside more quickly the higher the sample's thermal diffusivity.
Infrared Thermography: The science of collecting and analysing thermal data from non-contact thermal imaging sensors is known as infrared (IR) thermography. IR thermography uses the electromagnetic spectrum's infrared region to find the energy that has been released. This translates to wavelengths outside of the range of visible light.
Thermal Diffusivity of Different Materials
Interesting Facts
A heat sink is a device created to transfer heat from one piece of equipment to another. To permit the rapid transfer of heat, a heat sink must have a very high thermal diffusivity. These are used in electronic devices and computers.
Used in electric devices and machines like refrigeration systems, heating machines, machining, and other industrial purposes.
Solved Problem
1. Calculate the thermal diffusivity of the water at 25 degrees Celsius with a density of 997 kg/m3, a specific heat capacity of 4182 J/kg.K, and thermal conductivity of 0.6071 W/m.K.
Sol:
Given
k – 0.6071 W/m.K
$\rho $- 997 kg/m3
\[{c_p}\]- 4182 J/kg.K
The formula for thermal diffusivity:
$\alpha = \dfrac{k}{{\rho {c_p}}}$
$\Rightarrow \alpha = \dfrac{{0.6071}}{{997 \times 4184}}$
\[\therefore \alpha = 1455\] mm2/s
The thermal diffusivity of water is \[\alpha = 1455\] mm2/s
2. Calculate the thermal diffusivity of the Gold with a density of 19300 kg/m3, a specific heat capacity of 130 J/kg.K, and thermal conductivity of 318 W/m.K.
Sol:
Given
k – 318 W/m.K
$\rho $- 19300 kg/m3
\[{c_p}\]- 130 J/kg.K
The formula for thermal diffusivity:
$\alpha = \dfrac{k}{{\rho {c_p}}}$
$\Rightarrow \alpha = \dfrac{{318}}{{19300 \times 130}}$
\[\therefore \alpha = 126.74\] mm2/s
The thermal diffusivity of Gold is \[\alpha = 126.74\] mm2/s
Summary
In many sectors, thermal diffusivity is crucial for choosing the best materials that can transfer heat efficiently without overheating themselves. In a real-world application, it is also very useful where heat transfer takes place in computers and electronic devices. It is very important that this process happens easily otherwise creating heating problems.
FAQs on Thermal Diffusivity
1. What is thermal diffusivity and what does it represent in physics?
Thermal diffusivity, denoted by the symbol α (alpha), is a material property that measures the rate at which temperature spreads through a substance. It quantifies how quickly a material will react to a change in its thermal environment. In essence, it is the ratio of a material's ability to conduct thermal energy to its ability to store thermal energy.
2. What is the formula used to calculate thermal diffusivity?
The thermal diffusivity (α) of a material is calculated using the formula that relates thermal conductivity to its heat storage capacity. The formula is:
α = k / (ρ * cp)
Where:
- k is the thermal conductivity (in W/m·K)
- ρ (rho) is the density of the material (in kg/m³)
- cp is the specific heat capacity at constant pressure (in J/kg·K)
3. What is the primary difference between thermal conductivity and thermal diffusivity?
The key difference lies in what they measure. Thermal conductivity (k) describes how well a material transfers heat under steady conditions. A material with high conductivity allows a large amount of heat to flow through it. In contrast, thermal diffusivity (α) describes how quickly a material's temperature changes. It combines conductivity with the material's heat storage capacity to indicate the speed of temperature propagation, not just the amount of heat flow.
4. What is the SI unit for thermal diffusivity?
The standard SI unit for thermal diffusivity is square meters per second (m²/s). This unit reflects the 'diffusive' nature of heat transfer, indicating an area being affected per unit of time as temperature propagates through the material.
5. What does a high value of thermal diffusivity practically mean for a material?
A high thermal diffusivity value means that heat moves very quickly through the material, causing its temperature to equalise rapidly. Materials with high diffusivity, like metals, respond fast to temperature changes—they heat up quickly and cool down quickly. This is because the heat conducted through them is high relative to the heat they store per unit volume.
6. How does a low thermal diffusivity value affect a material's thermal behaviour?
A low thermal diffusivity value indicates that temperature changes propagate very slowly through the material. Such materials, like wood or insulation foam, act as effective thermal insulators. They take a long time to heat up and a long time to cool down because they either have low thermal conductivity, a high capacity to store heat (high density and specific heat), or both.
7. In what real-world applications is thermal diffusivity a critical property to consider?
Thermal diffusivity is crucial in applications involving transient heat transfer. For example:
- Cooking Utensils: A frying pan should have high thermal diffusivity to heat up quickly and evenly.
- Heat Sinks in Electronics: These components need high diffusivity to rapidly draw heat away from processors and prevent overheating.
- Building Insulation: Materials with low thermal diffusivity are used to slow down heat transfer, keeping buildings warm in winter and cool in summer.
- Industrial Quenching: The rate at which a metal part cools during heat treatment is governed by its thermal diffusivity.
8. Why is thermal diffusivity considered more important than thermal conductivity in situations with changing temperatures?
In dynamic or transient situations where temperatures are not constant, thermal diffusivity is more descriptive than thermal conductivity. While conductivity tells you the magnitude of heat flow, diffusivity tells you the speed of the temperature wave. For applications like a fire alarm sensor or a cooking pan, the speed of response is critical. A material with high diffusivity will signal a temperature change much faster, even if another material has higher absolute conductivity but also a much higher heat capacity.
