Convection
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Convection: As defined previously, convection is the transfer of heat from a solid to a liquid or gas. Again, I’ll present the simplest example. For convection, this is flow over a flat plate. Here air blows over an infinite flat plate. The plate surface is perfectly flat with uniform temperature and the airflow is uniform at all areas.
The convection is defined by the equation:
This equation looks very similar to the equation for conduction and some of the same observations hold true. Namely, heat transfer is proportional to the temperature differential. All other things held constant, doubling the differential doubles the heat transfer. The complication arises in the convection coefficient “h”.
Many variables affect the value of “h”. Among the most important are the fluid and surface temperatures, the fluid velocity, the fluid density, the fluid viscosity, the fluid specific heat, and the geometry of the surface. While standard engineering equations allow one to calculate convection coefficients with reasonable accuracy for simple shapes and flows, it is not possible to adequately determine the airflow through a heat sink analytically to predict performance with high accuracy. This falls under the realms of laboratory trials and a software tool called Computational Fluid Dynamics (CFD).
Even though it is not possible to determine performance precisely, knowing how a heat sink performs with a given fan allows one to approximate the change in performance given a different fan. It also allows us to dispel one of the great pervasive myths in the computing world.
Contrary to popular belief, aluminum is not superior to copper where convection is concerned. I will not claim to know how this rumor started, but I’ll do my best to lay it to rest. I can think of three facts that may have led to the conclusion that aluminum is superior to copper. Let’s take a look at these facts and explain what they really mean.
Fact 1: Aluminum has a higher specific heat and lower density than Copper. Specific heat is a measure of how densely a material can store thermal energy. If you add thermal energy to a specific mass of material, it will increase in temperature.
The specific heat of aluminum is 903 joules/kg*K at 300K while copper is only 385. The density of aluminum is 2702 kg/m^3 at 300K while copper’s is 8933. The product of specific heat and density determines how much energy may be stored in a given volume. For a given volume of material, copper will store more energy at a given temperature change than aluminum.
False Perception: Since aluminum stores less energy per volume, it must be more efficient at getting rid of heat.
Truth: During steady-state operation, there is no net energy storage in the heat sink or fins/pins; hence, specific heat plays no part in steady-state performance.
Fact 2: Aluminum has lower density than Copper. Volume for volume, aluminum is much lighter than copper.
False Perception: Weight acts as a “sink” for heat. Since copper is more dense, it absorbs heat well from the die. Since aluminum is light, it gets rid of heat more effectively than copper.
Truth: Density has no direct relationship with steady-state heat transfer.
Fact 3: A small volume of aluminum will cool more quickly than an equal volume of copper once the heat source is gone. This is due to the same reason as fact #1, namely there is less energy stored per unit volume is aluminum than copper. This is, however, a transient condition. Heat transfer from a computer is a steady-state condition where the temperature of the heat sink remains relatively constant. The specific heat of a material partially determines how a material responds to transient conditions but has no effect at all on steady-state operation.
False Perception: Since aluminum cools more quickly once a heat source is removed, it must be more efficient at convection.
Truth: The heat source driving energy into the heat sink remains in effect until you turn off your computer. If you have aluminum pins or fins, congratulations, they will cool off more quickly than copper ones after you shutdown your PC.
The only properties belonging to the solid that affect convection are geometry and surface temperature. The fluid stream has no knowledge of what lies beneath the surface of the material. If an aluminum and copper item have the same precise geometry including microscopic surface details and they have the same temperature then they will have precisely the same convection.
If you are still unconvinced, consider this little thought exercise. Imagine a magic heat sink pin. This magic pin has an adjustable conduction coefficient that allows you to dial the conduction coefficient between a range of zero and infinity. Heat enters the magic pin through its connection to the heat sink. Heat leaves the magic pin through air convection.
When the pin’s conduction coefficient is very near zero, heat has a tough time transferring down the length of the pin. The end near the heat sink gets very hot, while the opposite end remains cool. Convection can only occur with a temperature differential, thus only occurs near the hot end. Most of the pin does no useful work.
When the pin’s conduction coefficient is near infinity, there is little resistance to conduction. The pin will attain a nearly uniform temperature over its entire length and convection will occur over its entire length.
Now let us go back to the aluminum versus copper debate. Copper’s higher conductivity means is that a thinner copper fin can transmit as much heat as a thicker aluminum fin. However, on a weight-basis, aluminum can conduct more heat than copper. If weight was no object, copper holds the edge. When weight is a limitation, aluminum has the advantage. Conductivity multiplied by density is a “weighted” measure of a material’s conduction efficiency. It is this “weighted” efficiency that leads to the use of aluminum in the fins/pins of many heat sinks. It is certainly not because “aluminum gets rid of heat better than copper”.
