﻿ Advection inside thermal hidraulics - Pirobloc

#### What is it?

When speaking about the transfer of any physical property, in general three basic concepts of transport are considered: molecular, advective and convective. The concept of convection is considered a combination of molecular transport and advective transport.

The specific definitions of each are:

Molecular Transport: Transfer of a physical property due to the behaviour of molecules in a system.

Advective transport: Transfer of a physical property attributable solely to the global movement of a fluid, which carries the property with it. Advective transport is therefore directly proportional to fluid velocity.

Convective transport: This also requires a moving fluid but involves an interface. In most cases, it is a combination of molecular transport and advective transport. Unlike advective transport, however, it is not usually proportional to fluid velocity.

We will discuss each of these properties, focusing on the transfer of heat or energy.

#### A bit of history

Historically, three basic types of heat transfer have been considered:

• Conduction: This is the transfer of heat due to the behaviour of molecules in a system or their direct interaction: this is therefore molecular transport. Molecules vibrate or move with greater speed in a region at a higher temperature. When colliding or interacting with neighbouring molecules, those at a higher temperature transfer part of their energy to those at a lower temperature.

Therefore, there must be direct contact between two media for there to be a heat exchange.

This type of transfer is usually associated with solids, such as metals.

For example, a metal bar inserted in a flame. Metals are highly conductive, with a thermal conductivity of about 50 W/m°K, so very hot molecules vibrate faster and interact with neighbouring molecules by transferring a significant part of their kinetic energy to them. Heat transfer by conduction is also possible in liquids or gases, but their thermal conductivities are lower, e.g. air is 0.024 W/m°K and water is 0.58 W/m°K, so thermal exchanges with these are primarily by other types of transfer.

• Radiation: This is heat transfer via electromagnetic waves. It could be termed as molecular transport, at least in its origin, as energy is produced by changes in the electronic configurations of constituent molecules or atoms and transported by electromagnetic waves or photons.

There is no direct contact between the two media and the intermediary or interface does not participate in the exchange functions; in most cases this is air, although there is heat transfer in a vacuum.

The heat received by the Earth from the Sun is transmitted by radiation through empty space. The heat felt in front of a campfire is also from radiation.

• Convection: This is heat transfer in which a moving fluid receives or transfers energy from or to another, whether this is the end receiver or just an interface. It occurs when a surface at a certain temperature is in contact (molecular or conduction) with a fluid moving at a different temperature (advection). It is therefore a mixture of both.

Two main types can be considered depending on the source of the fluid motion:

1. Free convection, also called natural, in which the fluid motion is due solely to differences in the density of the fluid temperature due to the variation between two points.

2. Forced convection, where the fluid movement is due to some external factor.

Heat is transferred more quickly with forced convection than with free convection.

Cooling a cup of coffee, for example, is a process of convective heat transfer. It is free convection if there is no wind. The air around and above the cup is heated; decreasing its density and making it rise, taking the heat received from the cup with it.

Once the coffee is at the same temperature as the room, it stops changing the density and the air stops moving. On the other hand, if you blow on the cup, or a fan is placed next to it, this is forced convection as the air moves due to an external agent.

Of these basic concepts, certainly advection is the least well known. So let’s try and familiarise ourselves with it.

Advection: (From the Latin advectiō, transport) is a widely used term in meteorology and its most general definition indicates it is a movement of a mass leading to a transfer of heat or other properties between different areas. The transfer of a property is attributable solely to the overall movement of a fluid. Advective transport is therefore directly proportional to the fluid velocity.

Mathematically, advection is the scalar product of the vector velocity and scalar gradient (the difference in the value of a quantity at two different points divided by the distance between them).

The most illuminating examples occur in meteorology. An iceberg washed away by a sea current will undergo a heat exchange by advection with the sea current transporting that mass of ice.

We could consider advection as a part of the heat transfer by convection, in which the fluid velocity is not determined by the temperature and within it there is mass transport, which involves an exchange of energy. Therefore, it could be considered as a kind of forced convection.

However, there are schools of thought that consider convection, whether natural or forced, is always formed by a part of the transfer due to random molecular motion or Brownian motion – called diffusion transfer – while the transfer of energy by macroscopic or massive motion is transfer by advection.

#### Other heat transfers

For the difference in the two approaches to convection, we can consider a classic example, which also illustrates other types of heat transfer:

We have a fire on which we place a vessel of water. The energy transfer from the fire to the vessel wall is basically via radiation. From the outer wall of the vessel and through the walls, energy is transferred by conduction. Obviously, if we touch the vessel, we will “suffer” a transfer of heat by conduction onto our hands.

Finally, from the inner wall of the container to the water inside, the transfer is by…

Initially, there is no doubt; we all agree. The transfer process is by conduction until a threshold of instability is reached – see Benard-Rayleigh convection and Rayleigh number.

#### Convention processes

The processes that follow have led to a difference of views.

One approach would be to say that clearly there is a transfer by convection without advection (“traditional” convection); because it is clear that the movement of water into the vessel is due to the different density of the fluid at the bottom (hotter and less dense) from the top (colder and denser).

Since fluid velocity is a function of temperature, there is no advection. If there was a transfer by advection, according to this school of thought, putting a mixer into the container would make the water inside circulate. After turning off the stirrer, the transfer would be by “traditional” convection only.

However, some authors argue that since there is a mass movement of fluid in the water – even without the stirrer – there is advection. This approach considers that, after reaching the instability threshold, a transfer occurs mainly by advection when the density difference leads to a generalised movement. If the stirrer had been in operation since the beginning of the process, advection would also exist at this initial stage.

However, it must be remembered that the difference in densities is caused by a difference in temperature.

#### Practical cases

Extrapolating these considerations to industrial heating facilities, usually with the use of an interface fluid (steam, superheated water, thermal fluids) between the main energy source (the boiler) and consumption points (exchangers, reactors), we can conclude that the heat exchange is in most cases by advection – or forced convection.

Indeed, the primary fluid (providing the energy) must be conveyed by mechanical means (usually a centrifugal pump) and therefore the velocity is independent of the temperature.

The secondary fluid (receiving the energy) circulates in exchangers also due to a process pump, regardless of the temperature. It is inside the reactors where we have the major difference between the two aforementioned approaches.

The issue is complex and certainly allows for extensive debate and profound reflection.

#### Steam

What happens in a steam plant? The steam velocity will be a function of the pressure, and therefore the temperature. Is the heat transfer therefore in a steam exchanger/natural convection process on the primary fluid side and advection on the secondary fluid side?

The clearest conclusions we can reach from a practical point of view are: heat transfer by convection, whether natural or forced, is undoubtedly the most important in industrial processing facilities. Forced convection can be considered as advection, since the fluid velocity does not depend on the temperature and therefore there is mass transport which is independent of the heat exchange.