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Maximum Heat Dissipation for
Natural Convection Cooled PCBs |
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Introduction
Questions about natural convection limits are very common.
Thermal designers are confronted with them repeatedly. The reason
is apparent. Everybody wants to stay with natural convection as
long as possible because it is both a simple and reliable cooling
method.
There are several ways to approach natural convection problems.
Flow simulations with various degrees of sophistication are
quite popular. Empirical correlations based on case to case
studies are another possibility. Regardless of the method
eventually used, the first step should nevertheless be an
estimate. That is what this article is about.
The suggested procedure is quite simple. The drawback is that
the uncertainty is quite high. The answers will therefore never
be exact. The method should rather be looked at as a traffic
light that signals in either a red, a yellow and a green colour.
If the distribution is a 1/3 of each, the net result is that
2/3 of the cases can be eliminated form the agenda. That is
not a bad outcome for a method that only takes a few minutes
to apply.
Figure 1
The maximum PCB temperature is a function of many parameters.
The parameters
Figure 1 shows a theoretically exact equation for the maximum
heat that can be dissipated from a PCB. There are lots of
parameters involved. Most of them are just simple measures and
temperatures. The air velocity, the cooling efficiency and the
heat transfer coefficient are however somewhat difficult assess.
The air velocity is rarely dealt with in natural convection
theory. For PCB applications it is nevertheless an important
parameter. The article
Natural Convection and Equivalent Velocity
explains one way to estimate it. It is a somewhat complicated
procedure but once in place it facilitates things considerably.
The cooling efficiency is basically a ratio that relates the
actual PCB case with a simple and well-defined reference case. A
more in depth explanation can be found in the article
The Cooling
Efficiency Concept, part 1. Typical values are around 70%. The
value can however exceed the 100% limit if there are heat sinks
involved.
The heat transfer coefficient is only easy to get for simple
cases. There are correlations available for
isothermal parallel
plates in free air but not much more. The approach here is to
use
forced convection values based on the equivalent air velocity.
Figure 2
Some ways to arrange natural convection in telecom racks.
| Case | Stacked racks |
W [m/s] |
h [W/m2K] |
Q [W] |
Qrel [%] |
Air eff [%] |
| Free | 1 | 0.16 | 6.0 | 11.8 | 100 | 36 |
| Enclosure 1 | 2 | 0.21 | 5.6 | 8.3 | 70 | 48 |
| Enclosure 2 | 1 | 0.07 | 3.1 | 6.0 | 51 | 54 |
| Enclosure 3 | 8 | 0.35 | 7.0 | 5.1 | 43 | 71 |
Heat dissipation data for 200x200 mm PCBs, 20 mm pitch, 70% cooling efficiency and 35 K temperature difference. Radiation included. The velocities are approximate.
Table 1 shows some PCB cooling data for enclosures of the types in figure 2. They are based on case to case correlations for the equivalent velocity. The free PCB case is included for comparisons and it should be noted that this case refers to parallel PCBs in free air with no flow restrictions.
The air velocity spans over a factor 5. The highest value is found for the 8 stacked sub rack case. The general tendency is that stacked sub racks tend to increase the air velocity. This tendency is also reflected in the heat transfer coefficient.
The heat dissipation levels for the enclosure cases are all below 10 Watt. It is far below the typical capacity needed today. This is also why natural convection to a large extent has been abandoned.
The relative cooling capacity is a measure of the performance relative to the free PCB case. It is on the 45% - 70% level. It can be concluded that heat transfer coefficients for ideal textbook cases not can be used for PCBs in enclosures.
The air efficiency is also of some interest. This parameter can never exceed 100%. For the enclosure cases it is on the 50% - 70% l evel. Heat sinks, or any kind of other surface enhancement, can therefore only have a modest impact -- unless the air efficiency somehow could be decreased. One way to do this is to increase the PCB spacing, which opens up some possibilities.
One difficulty when making these comparisons is that radiation can have a significant impact. The net radiation exchange between two parallel PCBs having the same temperature is zero. There is however always a radiation contribution from the openings around the PCB edges. For the free PCB case it is on the 20% level. For the enclosure cases it is lower because the surfaces absorbing that radiation are above the ambient temperature. That particular radiation is difficult to exclude experimentally and this is why radiation has been included in table 1.
Figure 3
If the PCB spacing is larger than optimum, there is a potential that can be used to enhance the cooling.
The volumetric approach
Natural convection between parallel plates, inside or outside enclosures, is always characterised by an optimum surface to surface distance. It is at this distance that the heat dissipation density has its maximum value. The optimum spacing can be found at the point where a line drawn from the origin touches the curve in a heat dissipation - PCB spacing diagram, figure 3.
A somewhat less strict interpretation of the optimum spacing concept is that a volume is characterised by an optimum total heat transfer surface. Two PCBs placed on a larger than optimum spacing must therefore have a cooling enhancement potential, figure 3. This potential can be exploited by introducing additional heat transfer surfaces. The condition for a good function however, is that these surfaces are carefully spaced. Unless that, they can be either parallel or perpendicular to the PCB.
Figure 4
A couple of ways to exploit the cooling potential for PCBs placed on larger than optimum distance.
Figure 4 shows two ways to add heat transfer surfaces. One is a parallel cooling plate and the other a heat sink. In both cases, it is important that the surfaces catch as much of the approaching air as possible. They should therefore ideally stretch over the entire PCB. The heat sink should in addition be placed as low on the PCB as possible, (to take advantage of the chimney effect).
Figure 5
The optimum fin pitch increases when the air velocity decreases.
Heat sinks
Heat sinks that are optimised for free air, are not automatically the best for PCBs in enclosures. They are therefore somewhat complicated to design.
On way to tackle this problem is to use a forced convection approach. The typical tendency for heat sinks in bypass flow is that the optimum fin spacing increases when the air velocity decreases, figure 5. In view of the different air velocities shown in table 1 it is apparent that heat sinks must be adapted to the actual conditions. It is therefore recommendable to use forced convection rather than natural convection design procedures.
A related matter is if the heat sinks should be designed for bypass flow or not. The ideal is that they cover as much of the channel cross-section as possible, which could suggest that the bypass is small. There are however many other alternative air flow paths in sub racks. A somewhat conservative rule of thumb is therefore to assume a large bypass flow.
Figure 6
Natural convection heat dissipation increases faster than linear with the temperature difference.
The temperature difference
A particularity with natural convection is that the heat dissipation increases more than linear with the temperature difference. There are two cases. The given surface spacing case and the optimised case, in which the spacing is adjusted when the temperature difference is changed.
The temperature difference is given by the available space between the maximum PCB temperature assumed and the environmental specification. Changing one of these two can sometimes result in considerable gains. Switching from components of commercial quality to components of industrial quality could for example increase the available temperature difference with a factor 1.4. The corresponding heat dissipation gains are in the 50% - 65% range.
The temperature difference impact should not be neglected for heat sinks. They should be given as high surface temperatures as possible. The problem with arrangements such as in figure 4 is that there is a thermal coupling between the PCB plate and the heat sink. It might therefore not be possible to run the heat sink at a considerably higher temperature than the PCB.
Figure 7
Radiation to side PCBs can contribute significantly to the cooling.
Side PCBs
As mentioned above, radiation can have a significant impact. The most important surfaces in this respect are the side PCBs. If they have the same heat dissipation as the main PCB, there will be no net exchange. If they are completely passive, they will typically contribute with a cooling enhancement on the 30% level. This is not a radical impact but a well-planned mixture of hot and cold PCBs in a sub rack can sometimes save critical cases.
It can in this context also be noted that even if there is no net radiation exchange between identical PCBs, there is indeed an exchange. The hot parts of one PCB radiate heat to the colder parts of the other PCB and vice versa. This is a beneficial impact that tends to increase the cooling efficiency. It is therefore important to use software tools that consider it.
Example
Estimate the spacing needed to cool 15 W on a 265x160 mm, (height x depth), PCB with natural convection. The maximum PCB plate temperature is 85 C when the room temperature is 50 C.
Solution
The information given is not detailed enough to enable any high precision answer. The best that can be done is a coarse estimate.
The available maximum temperature difference is 85-50 = 35 C. Assume that the PCB, without any surface extensions, has a cooling efficiency of 70%. Some surface extension will undoubtedly be needed. Assume that these surfaces can be kept at maximum PCB temperature. Given this, an assumption that the average heat transfer surface temperature difference is 80 % of the maximum temperature difference can be justified, 35x0.80=28.0 C.
Go to the natural convection between parallel plates calculator. Use 0.1 mm for the PCB thickness, (the lowest value possible), and check the radiation-included checkbox. The maximum heat dissipation/pitch is calculated to 1.25 W/mm. Assume that it is possible to achieve 50% of that value in an enclosure, (supported by table 1), 0.62 W/mm. The free air spacing needed is 15/0.62=24 mm. Add 2 mm to compensate for the PCB thickness, 3 mm for the component heights and 4 mm for the solid parts of the heat sink, 24+2+3+4=33 mm. This value requires that a perfect surface extension of the type shown in figure 4 can be arranged. That is quite optimistic. Given all kinds of restrictions a more realistic answer would be 35 - 50 mm.
Note. A good overview is not achieved unless this estimate is made for a range of assumptions. A slightly more elaborated analysis will for example reveal that the average temperature difference assumption in this case is a critical parameter.