A basic primer on some aspects of watercooling physics. — Mike Larsen
It’s finally here! The continuation of my last article and it’s only a little over a year late! But anyhow, on with the show!
This article will attempt, in an extremely abbreviated manner, to explain the basic physics behind flow in a water cooling system. If this seems like a lot to swallow, it most certainly is. Most mechanical engineers will endure a anywhere from one to three years studying fluid dynamics and heat transfer to learn what I am attempting to cover in a few short pages.
Laminar flow is the flow if a fluid in an organized manner in layers, or as the name suggests, laminates.
For our application, if the flow is laminar, water enters into the water block and flows through the block in nice even layers. Molecules of water stay in the same layer of water as they continue on their path. The molecules of water closest to the water block will be the hottest and moving the slowest, and those in the center of the flow will be the coolest and moving the fastest. This holds true for the entire path through the block and out the exit.
The leftmost side of this image shows a representation of laminar flow. The arrows show the flow of the individual molecules of water and how they line up in nice even layers.
Turbulent flow is just as the name suggests, very random and unorganized.
For one reason or another, the nice laminar layers of fluid somehow get mixed up and the molecules of the fluid no longer flow along nicely but rather bounce all over throughout the flow. Besides the very thinnest of layers right next to the block which remains the hottest and moves the slowest, there is not an even distribution of temperature or velocity through the majority of the flow. Everything is all mixed up and tumbling about itself.
Referencing the above image, the rightmost side shows the turbulent section. While there is an underlying thin laminar layer nearest the wall, the majority of the flow is random and unpredictable.
The boundary layer is defined as the area of the flow that has shear stress forces induced by the solid wall of the water block.
What this basically means is that the boundary layer is the part of the moving water that is feeling the friction or the ‘drag’ of the wall. The molecules of water that are closest to and touching the water block wall are not moving at all, but are stationary. As the distance from the wall increases, the molecules pick up speed until they are far enough away that the flow feels no effects from the wall; this is called the free stream velocity.
No matter the case, there will always be some kind of boundary layer.
The problem with having a boundary layer for heat transfer in a water block is that it is actually insulating the inner most layers of flow from being able to pick up the heat from the water block. This is especially true of laminar flow because the boundary layer is very thick and, in channels that are small enough, the boundary layer may extend through the entire flow.
However, in turbulent flow the random action of the water molecules breaks up the boundary layer and disperses the majority of it, thus increasing the ability of all the water molecules to pick up heat from the water block wall.
This image shows the boundary layer represented by d(x), or the thick black line. The velocity of the flow is shown by u. Before the flow gets to the wall, u is even and consistent. As the flow continues along the wall, the friction effects of the wall slow down the individual water molecules. Any molecules above the boundary layer remain at the initial entrance velocity, while the molecules next to the wall are stationary.
In this image, T represents the temperature of the fluid. Just as with the velocity, the temperature of the fluid is even and consistent until it reaches the wall. If the wall is hotter than the fluid, the fluid closest to the wall reaches near-wall temperatures, while the fluid above the boundary layer remains at the same temperature as the fluid entering the channel.
Entrance Length is defined as the length from the entrance of the water block to such a point that the flow is fully developed.
A fully developed flow is one in which the boundary layer is not changing as it moves further down the channel. When water first enters the water block, only the very closest molecules to the surface of the block feel the effects of friction. As the water moves further down the channel, more and more molecules begin to feel the friction effects.
All internal flows will have a certain entrance length and in this entrance length, the flow is laminar – exactly the opposite needed for good heat transfer. The entrance length varies with the velocity of the water entering the block, but can be up to 60 times the diameter of the channel. This could mean that the flow never becomes fully developed (thus would never be turbulent) before the water exits the water block.
Here the velocity entrance length is shown (hydrodynamic entrance region). Once the fluid has passed the entrance region, the velocity profile remains the same for the rest of the length of the channel.
The thermal entrance region is very similar to the velocity entrance region with a few exceptions. If heat is being input along the entire length of the channel, the basic shape of the temperature profile will not change, but the total average temperature will continue to increase. This can be seen by comparing the arrows representing the temperature in the middle region with those in the rightmost region.
Why Turbulent Flow is good for Heat Transfer
So why do we care about turbulent flow? Because if the flow is turbulent, the heat transferred from the water block (and thus from the CPU) is greatly increased.
If you recall from my previous article, convection in a water block takes place when heat is conducted from the solid water block into the closest molecules of water in the flow. In laminar flow (remember, nice layers of moving fluid) the heat is conducted through each layer of moving fluid with the inner layers receiving the least (if any) heat transferred into them.
In turbulent flow, the molecules are getting tossed and turned all over, with a much great number of the molecules coming in contact or near contact with the water block wall. Thus the molecules are gaining heat from the hotter source (right next to the water block) rather than from the cooler layers of the flow.
The higher the temperature differential is between two adjacent molecules, the more heat that is transferred between them. This results in the entire turbulent flow having a total average higher temperature than a laminar flow.
There have been several studies that show that for the same net flow of fluid through a channel, a turbulent flow can transfer as much as 150-500% more heat.
Turbulent Flow? How?
There are several factors that determine whether a flow will be turbulent or not: channel size and shape, velocity of the fluid, physical attributes of the fluid, etc.
In order to maximize the heat transfer, turbulent flow must be induced as soon as possible into the flow – the entrance length must be minimized.
The two best ways to do so are
To increase the flow velocity¹, or
To add turbulators at the flow entrance and/or along the entire flow length.
A turbulator would be anything that helps to induce turbulence into the flow. It could be something as simple as a rougher surface or small ridges that stir up the flow.
Care has to be taken to not introduce anything that could contribute to laminar flow. Channels with smooth walls and ridges that run parallel to the walls will tend to smooth out the flow and can take turbulent flow and turn it laminar. There has been much research done on mach level aircraft where very small ridges are run the width of a wing to prevent turbulent flow, just the opposite that water-cooling enthusiasts seek.
This article has gone over the very basics of what is happening when fluid is put in motion next to a solid body. While most of the article dealt with flow through the water block, the very same principles (with certain variations of theory) apply to water flowing though the interior of a radiator, air flowing over a radiator, or even air flowing over a heatsink.
The next article (soon to follow, I promise this time!) will deal with some specific numbers and some more in-depth theory on how to calculate whether a flow is laminar or turbulent, and how to determine what the entrance length is. It will also discuss specific things that can contribute to laminar and turbulent flow, and hopefully help in being able to predict flow behaviour.
Please send comments on what anyone would like more clarity on, or what would be best to expound on in the next article. Until then, happy overclocking!
¹ Note the positive effect of flow rates on waterblocks HERE.
All images courtesy of “Fundamentals of Heat and Mass Transfer” by Incropera and De Witt.