# Thermal conductivity

Thermal conductivity is an important physical property of materials that determines their ability to conduct heat. It refers to the rate at which heat is transferred through a material under a given set of conditions. This property is crucial in many engineering and scientific applications where heat transfer plays a vital role.

## Definition of thermal conductivity

Thermal conductivity is a measure of a material’s ability to conduct heat. It is the property of a material that determines the rate at which heat is transferred through it when a temperature difference exists between its ends. In other words, it is a measure of how easily or quickly heat flows through a material when there is a temperature difference between the two sides of the material. Thermal conductivity is expressed in units of watts per meter kelvin (W/mK) and is typically denoted by the symbol ‘k’. Materials with high thermal conductivity conduct heat very easily, while those with low thermal conductivity conduct heat more slowly. Some examples of materials with high thermal conductivity are metals like copper and aluminum, while materials like plastics and wood have relatively low thermal conductivity. The thermal conductivity of a material depends on various factors, such as its chemical composition, density, and temperature. The SI unit of thermal conductivity is watts per meter-kelvin (W/mK). It is a material-specific property, meaning that it depends on the composition and structure of the material. Some materials are good conductors of heat, such as metals, while others are poor conductors, such as insulators.
The thermal conductivity of a material depends on various factors such as temperature, pressure, and composition. At high temperatures, thermal conductivity tends to decrease due to increased scattering of phonons, which are the primary heat carriers in non-metals. On the other hand, the thermal conductivity of metals tends to increase with temperature due to the increased number of free electrons available for heat transfer.

## Principle of thermal conductivity

Thermal conductivity works on the principle of Fourier’s law of heat conduction, which states that the rate of heat transfer through a material is directly proportional to the temperature difference across it, the surface area through which heat is transferred, and the thermal conductivity of the material. The principle of thermal conductivity is based on the fact that when there is a temperature difference between two points in a material, heat flows from the hotter point to the cooler point. This heat transfer occurs through the movement of molecules in the material, which collide with neighboring molecules and transfer heat energy from one molecule to another. Materials with high thermal conductivity allow heat to transfer more easily because their molecules are more tightly packed and have more opportunities to collide with each other, while materials with low thermal conductivity impede heat transfer because their molecules are more spread out and have fewer opportunities to collide with each other. The thermal conductivity of a material depends on various factors, such as its chemical composition, density, and temperature. By understanding the principles of thermal conductivity, engineers and scientists can design more efficient heat transfer systems and select the most appropriate materials for specific applications.

## Formula of thermal conductivity

Thermal conductivity(k) = Q / (A x ΔT x t)

Where

• Q is the amount of heat transferred
• A is the cross-sectional area through which the heat is transferred
• ΔT is the temperature difference across the material
• t is the time taken for the heat to be transferred.

## Application of thermal conductivity

Thermal conductivity has many practical applications, some of which include:

1. Heat transfer: The most obvious application of thermal conductivity is in heat transfer. Understanding the thermal conductivity of a material is essential in designing efficient heating and cooling systems, such as radiators, heat exchangers, and refrigeration systems.
2. Insulation: Thermal conductivity is also important in designing insulation materials, as materials with low thermal conductivity are more effective at reducing heat transfer. Examples of insulation materials that utilize low thermal conductivity include fiberglass, cellulose, and foam.
3. Electronics: Thermal conductivity is important in the design of electronic devices, such as computer chips, where efficient heat dissipation is necessary to prevent overheating and damage to the device.
4. Building materials: Thermal conductivity is an important consideration when selecting building materials, such as walls and roofs, as it affects the energy efficiency of a building. Materials with high thermal conductivity may require additional insulation to maintain comfortable indoor temperatures and reduce energy costs.
5. Aerospace: Thermal conductivity plays an important role in the design of aerospace materials and components, where heat dissipation is critical for the safe operation of vehicles, such as spacecraft and satellites.

## Example of thermal conductivity

Followings are given some example of thermal conductivity.

1. Copper: Copper has a high thermal conductivity of about 400 W/mK, which makes it an excellent conductor of heat. It is often used in applications where heat needs to be transferred quickly, such as in heat sinks for electronic devices.
2. Air: Air has a low thermal conductivity of about 0.026 W/mK, which makes it a good insulator. This is why air is often used as an insulating material in double-paned windows, where the air between the panes helps to reduce heat transfer.
3. Wood: Wood has a relatively low thermal conductivity of about 0.04 W/mK. This makes it a good insulator and explains why wooden houses are often more energy efficient than houses made of other materials.
4. Glass: Glass has a thermal conductivity of about 1 W/mK, which is higher than many other insulating materials. This means that glass can conduct heat relatively quickly, which is why single-paned windows are not as energy efficient as double-paned windows.
5. Diamond: Diamond has an extremely high thermal conductivity of about 2,000 W/mK, which makes it an excellent conductor of heat. This property is why diamond is used in high-power electronic devices that generate a lot of heat, such as high-frequency transistors.