General Heat Transfer Guide

Heat Sink Material and Geometry

This content was originally featured on Amdmb.com and has been converted to PC Perspective’s website. Some color changes and flaws may appear.

The heat sink’s job is to transfer heat from the die to its own fins or pins where convection can remove it. This means that the heat sink needs to have excellent conductivity, the shortest path possible from the die to the fins/pins, and copious fin/pin area to allow good convection. While the first criteria is a matter of material selection, the second and third are sort of mutually exclusive. The trick is to balance the amount of material used with the amount of surface area present.

In this respect, more material (weight) does not always make for a better heat sink. Copper has a density of 8933 kg/m^3. The typical heat sink has a length and width of 60 mm. A solid chunk of copper 60 mm on a side would only be about 9.3mm tall to weigh 300 grams (maximum AMD recommend weight). This solid chunk of copper would be an awful heat sink because of very little surface area for convection.

Now consider the other extreme. If the heat sink is only pins or fins with no base, there would be no means to get the heat from the die to the pins/fins. A good heat sink has a solid enough base to transfer heat to all pins/fins and enough surface area to convect the heat away efficiently while still remaining relatively light.

At the time of this writing (July 2001), the top heat sinks are constructed from solid copper and cost in the range of $30 to $70. Some are plated with silver. The primary benefit offered by the silver is not its higher conductivity. The plating is too thin to substantially affect conduction. The advantage is the ability of the silver to fill small voids between mating pieces of the non-plated heat sink.

Fan Flow and Direction

The easier of these two is fan flow and its effect on temperature. The convection coefficient depends on many air properties, but the most significant is the velocity of the air. This in part determines the Reynolds number. The convection coefficient is highly influenced by the Reynolds number. If you swap a 19CFM fan for a 38CFM fan, the flow doubles and the convection coefficient will increase by roughly 40 to 60%.

This will decrease the temperature differential between the heat sink and the air feeding the fan by about 30%. Because the same energy is transferred, the differential across the heat sink remains unaffected. The overall temperature decrease will be somewhat less than 30% of the previous differential. For example, if the CPU temperature with a 19CFM fan was 50°C with an air temperature feeding the fan of 24°C, then the original differential between the CPU and air is 26°C. The original temperature differential between the heat sink and air will be somewhat less, perhaps 18°C. Installing a 38CFM fan will decrease the 18°C differential by about 30% to 12.6°C. This difference of 5.4°C is the decrease in CPU temperature you may expect by replacing the low CFM fan with the high CFM fan.

It is critical at this point to acknowledge just how complex convection is. Turbulence plays a large factor in convection and can’t be adequately predicted given the complexity of airflow around a heat sink. Additionally, the system temperature is not the same as the air temperature surrounding the heat sink’s fan. The following equation may estimate the impact of changing fan flow, but should not be viewed as an absolute.

The effect of fan direction is even more difficult to determine. As air flows over the heat sink, the air warms. The hottest part of the heat sink is where it contacts the die. The temperature of the heat sink drops the farther out the fins/pins you go. When a fan “blows”, it pushes air through the heat sink. The coolest air contacts the coolest part of the heat sink and the air warms as it nears the hottest part of the heat sink. The air tends to keep a relatively high differential against the heat sink because the air gets hotter as it nears the hotter parts of the heat sink. This is the most efficient use of the airflow. When a fan “sucks”, it pulls air through the heat sink. The coolest air contacts the hottest part of the heat sink and the air warms quickly. By the time the air reaches the coolest part of the heat sink, it may be nearly the same temperature as the heat sink and will no longer gain additional heat. This improves heat transfer near the base of the heat sink at the expense of overall convection efficiency.

Which is better? It depends on the design of the heat sink. For most, it’s better to blow. For some that don’t have efficient fins/pins, it may be better to suck. The Alpha 6035 is an example of a good one to suck. Its aluminum pins are not particularly good at getting heat away from the base of the heat sink, though its copper base gets heat to the bottom of the pins very well. It also has a shroud around the top of the pins to ensure that air entering the fan flows over the full pin length. The shroud prevents air from short-circuiting to the fan intake.

Air Temperature Feeding the Fan

Heat transfer is all about temperature differentials. Conduction through materials and convection away from surfaces is proportional to the temperature differential that exists. If the temperature in the air feeding the fan goes up by 5°C, the CPU temperature will go up by about 5°C. The difference will not precisely equal 5°C because air properties vary, but the difference will be very close to 5°C.

Again, note that the system temperature is not the same as the air being fed to the heat sink’s fan. Since the system measures temperature near the south bridge, the air around the CPU is normally warmer by a couple of degrees Celsius.

Should I Consider a Peltier?

Before you consider one you need to know a little about how they work. In simplest terms, a Peltier may be considered as a heat pump. It doesn’t get rid of heat, but merely moves it from point A to point B. Like a piston-pump, it also has a fixed displacement and won’t handle more heat than specified. If the chip puts out more heat than the Peltier can transfer, the chip will die. If the HSF can’t handle all the heat the Peltier transfers, the Peltier will warm up and the chip may die.

A Peltier has a cool side and a hot side. The cool side contacts the die while the hot side contacts a conventional heat sink cooled by air or water. As long as the hot side doesn’t get too hot, the Peltier can transfer a fixed maximum power from its cool side to its hot side. The cool side can get very cool to the point of causing condensation in humid environments.

If the chip produces more heat than the Peltier can handle, the cool side will no longer be so cool. Simple rule, select the Peltier capacity to handle a little more than the peak power output of the chip at the conditions you intend to run.

Once the heat reaches the hot side, a heat sink needs to transfer it to air or water. This begs the question, “What is the advantage of a Peltier if I still need a heat sink?”

The answer goes back to temperature differentials. A Peltier may have a temperature of 10°C on the cool side and 50°C on the hot side. The CPU will love the 10°C while the 50°C of the hot side will make it easy for an air-cooled heat sink to get rid of the heat. By contrast, a conventional HSF without the Peltier will have a “cool side” contacting the CPU at 50°C. Now the logical question is, “Why doesn’t everyone use one?” The answers include cost, necessity, and complexity. Air-cooling can allow people to hit 1.5GHz without too much strain, so why bother with the added cost and complexity that a Peltier brings?

How About Water Cooling?

Water and air both cool solids via convection. The primary difference is the convection coefficient of water compared to air. At the same conditions (temperature, flow velocity, etc.), water is on the order of twenty times more efficient at convection than air is. Air holds about 1000 joules of energy for every degree Celsius that a kilogram of air changes temperature. Water holds about 4000 joules for every degree in a kilogram. Liquid water is about 1000 times as dense as air. This means a smaller mass and much, much smaller volume of water is required to contain the same energy as air.

The only things holding back water-cooling from the masses are the same as for a Peltier: cost, necessity, and complexity. People that demand to be on the edge of speed will spring for the cost. Rather than discuss this in depth for the few willing to pony up the cash, I’ll move on to more air-cooling considerations.