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## What is heat? - Part 2

March 17, 2023
by
Niels Verdijck

In the previous article, “What is heat? - Part 1”, we covered the basics of thermodynamics, including the concepts of heat and temperature, their relationship, and energy conservation. It also discussed an example use case of a lighting fixture and the importance of understanding heat transfer mechanisms.

For today’s article, we will glance at the heat transfer modes. Let’s begin!

### Heat transfer modes

There are three ways in which heat can flow from one object to another: conduction, convection and radiation. The explanation is carried out separately, but you should know that all of them can operate simultaneously:

#### Conduction

Conduction is the mode of heat transfer everyone should be very familiar with. If you leave a metal spoon inside a bowl of soup, you’ll notice that the handle also becomes hot, even though it doesn’t directly touch the hot soup.

The molecules inside the hot part of the spoon (the part submerged in the soup) have high kinetic energy, while the molecules inside the colder handle (the part sticking outside the soup) will have less kinetic energy. The molecules with higher kinetic energy will collide with their slower-moving neighbors. This collision will result in an energy transfer between these molecules.

Conduction is thus the heat transfer due to collisions of high-energy molecules with lower-energy molecules.

Conduction can be expressed in the following equation:

$\dot{Q}=-\kappa\:A\:\frac{dT}{dx}$

The heat flow rate is thus dependent on the cross-sectional area A of the object. The higher the area, the more collisions between high- and low-energy molecules. It also depends on how close the hot and cold ends are to one another. The closer the hot and cold ends are, the bigger the energy difference between neighboring molecules, thus the easier the heat transfer.

The final influencing parameter is the thermal conductivity value $$\kappa$$. This is a material property of how easily molecules can transfer heat to their neighbors. The higher this value, the more energy is transferred. Metals usually have very high thermal conductivity values and are thus often used in heatsinks. Materials like Rockwool or asbestos have very poor thermal conductivity values and are therefore referred to as insulators. Gases have also pour conduction characteristics due to the relatively large space between molecules.

The negative sign is included because the heat goes from high to low temperatures (per definition), while the temperature gradient is positive from low to high temperatures.

In our LED lighting fixture, the heat produced inside the LED will conduct through the PCB towards the heatsink.

#### Convection

Convection can only occur if the molecules inside a substance can move over large distances. This is the case for liquids and gases. The molecules take on energy when next to the heat source and carry that energy away over a large distance, where they can deposit that energy to a colder region to potentially repeat the cycle.

The following equation can express convection:

$\dot{Q}=h\:A\:\Delta T$

Where A is the area over which the convection occurs, the higher the contact area, the more heat can be convected away. Similarly to conduction, the larger the temperature difference between the heat source and the coolant, the more energy can be transferred to the molecules. Finally, the heat transfer coefficient specifies how easily the heat can be convected away and depends on multiple factors.

There are two dominant ways to convection:

• forced convection
• natural convection

Those concepts deserve their own articles, but the main difference relates to how fluid motion is established. For forced convection, mechanical energy drives the flow (through a fan or pump). This results in high heat transfer coefficients.

For natural convection, fluid motion is caused by rising hot fluids and sinking cold fluids. This will, therefore, result in a lower heat transfer coefficient than forced convection cooling.

In our lighting fixture example, once the conduction has carried the heat from the LED to the surrounding air. The heat is passed on to the air molecules and carried away.

The final heat transfer mode is called radiation. This is the process by which heat is emitted and transmitted through electromagnetic waves. This type of radiation does not require a medium, such as air or water, to travel through, making it different from conduction and convection.

Heat radiation is emitted by all objects with a temperature above absolute zero (-273.15°C), and it is a direct result of the random motions of atoms and molecules in a substance. The hotter an object is, the more energy its atoms and molecules have and the more heat radiation it emits. The wavelength of the heat radiation depends on the object's temperature, with hotter objects emitting radiation with shorter wavelengths.

This can be expressed in the following equation:

$\dot{Q}=\epsilon\:\sigma\:T^4$

As explained above, the hotter the object, the more heat is radiated away. Sigma is the Stefan-Boltzmann coefficient and has a fixed value. Epsilon represents emissivity, a characteristic of the surface of the radiating material, and is a value between 0 and 1. Very dark surfaces have an emissivity close to 1, whereas shiny metal surfaces have an emissivity closer to 0. The emissivity also relates to how good of an absorber it is. A good absorber is also a good emitter.

Heat radiation is responsible for the warmth we feel from the sun, and it is also used in a variety of applications, such as heating buildings, cooking food, and drying clothes. It is also used in some medical treatments, such as phototherapy, where light is used to treat skin conditions.

In our lighting example, if you hold your hands below, for example, an old halogen lamp without touching it, you clearly feel the warmth of the lamp. This warmth is due to the heat radiating away from it.

### Fun fact

The 18th-century scientists thought that heat behaved similarly to a fluid flow. They believed that caloric, a fluid substance, was how heat transferred from one object to another.

We know now that this is not true since the caloric fluid was never found. But still, we refer to heat as flowing from one object to another.