Thermal Management Part 2: How Hot Is Too Hot?

By Steve Somers, Vice President of Engineering

OK, since the release of Thermal Management Part 1, how many of you started using T-M Rule of Thumb #1, the finger test? I think I see a couple of bandaged fingers out there. I'm sure that many of you have some interesting stories about overheated equipment and systems. Yes, those stories are just the thing that would entertain engineers on a Saturday night, aren't they? It just goes to show that any story of experience is always interesting to some. But, isn't it always true that a story with a catastrophic ending appeals to a much wider audience?

For example, as an engineering student, I repaired TVs, radios, and audio systems in my father's television sales and repair shop. Telling most people about the times I powered up defective equipment only to blow the fuse isn't very exciting. Oh, but how about the time I applied power to a defective five-tube clock-radio while the customer looked on? The clock-radio suffered from a blown fuse (I bypassed with a clip lead) and a shorted AC rectifier. Anyone remember those radios? They had no power transformer; just a series line capacitor connected to the hot side of the power line via a wired fuse, then onward into a half-wave rectifier that works only half time charging up the main electrolytic capacitor to produce about 150 volts DC. Now, here's a thermal management folklore gem.

To access the line fuse, I had to remove the chassis and invert it on the bench. After bypassing the fuse with the clip lead (now don't do this at home), I plugged the radio into the AC outlet and switched it ON. In the blink of an eye, and with all the excitement of a July 4th aerial starburst, the main electrolytic capacitor ignited under the heavy AC current inrush. A platoon of flames shot skyward bolstered by the brusque low frequency buzz note that only an overloaded AC line can create. The amazement on my face and the customer's was deadlocked into a photo finish. Here before us was a prime example of inadequate thermal management under stressful conditions. The transfer of energy and heat orchestrated itself within a time span of only milliseconds; thus demonstrating a forthrightness that would have easily launched the cylinder-shaped electrolytic capacitor into suborbital heavens was it not for its sturdy mounting. As the final sacrificial element to this dazzling display, wisps of the capacitor's magic smoke were forever lost to the environment. And, my recovery comment to the astonished customer (along with my incredibly obvious troubleshooting naiveté)? "I believe I have isolated the faulty component."

Watts in the Box

Figure 1 (High Resolution Image)

Seriously, the thermal management of real interest to us is the heat energy transfer process, albeit much slower, that is expected in functional integrated systems. Thermal Management Part 1 discussed units of energy and some rules of thumb for first order thermal management. This installment intends to describe methods for implementing good thermal management in real applications. In most open room applications, we seldom consider thermal effects since the mass of circulating air usually more than overcomes any heat rise contribution from electronic products unless either or both of two things happen: 1) the room itself overheats; 2) the product produces more heat than that which can be dissipated via radiation or available air convection. Small box products may be tucked into tight spaces such as podiums, desk recesses, or other equipment cabinets, if space permits. This creates new challenges to reliable operation. Let's put this situation into terms we can relate to. When the surrounding ambient conditions are able to absorb all the power (watts) generated by an equipment item (the heat load), the ambient is a heatsink. When the generated heat is not absorbed, the ambient is a heat contributor. For this discussion, I'll define the power generated by the installed equipment as the input power and define the heat conduction capability into a cooler environment as the output power. Let's call the ratio of the output power divided by the input power the "heat transfer ratio". As long as the resulting ratio value is greater than one, the ambient environment is a heatsink and reliable operation should be possible. If the ratio value is less than one, the ambient is a heat contributor and will further stress equipment within its environment. See Figure 1 for an illustration of this concept. Further, if the ratio of output to input equals one, the current amount of heat generated (watts/hour) will be the maximum allowable for reliable operation. Let's look at how we can use this concept to pre-calculate realistic heatsink environments for enclosed equipment prior to installation.

Fourier Is Your Friend

Suppose you must place an electronic equipment item in some type of non-vented enclosure such as a wooden podium. Space is a premium and there is likely to be very limited air space surrounding the equipment. How can we predict whether the equipment will survive in this environment? I'm going to show you an easy way to calculate the answer with reasonable certainty. First, we need to make some assumptions based on what we've learned about thermodynamics so far. Our assumptions are:

During the initial operating period, the limited internal podium air volume will heatsink the equipment until equilibrium is attained.
Eventually, the equipment, the internal air, and the internal walls of the enclosure will equalize at some temperature, providing the equipment's power input remains constant.
At thermal equilibrium, heat conduction will occur through the walls of the wooden podium into the external environment. At this point, we can consider the equipment exterior, the podium air, and its internal walls to be at the same temperature.

In order to move ahead, we must become acquainted with Fourier's Law of Conduction (see Figure 1) so as to calculate the heat transfer to the external environment1. Fourier's Law will tell us if the equipment is likely to survive by conduction or require cooling augmentation, such as forced air. Don't be put off by Fourier's equation. It's just the product of some basic terms divided by the wall thickness of the enclosure… in this case, a wooden podium. The minus sign indicates heat travel direction (i.e., hot to cold). The "q" term represents watts per hour that may be transferred through our podium. The "k" value for thermal conductivity we'll take from Table 1 of Part 1 of this series (wood = 0.130 watts/m-°C). The "A" represents the area (in square meters) of the enclosure walls that conduct heat outward. Measure the internal podium space and convert to square meters (assume a volume of 3"x10"x12" which converts to a surface area of 0.24 sq. meters). We need the podium wall thickness (say, .75 inch or 0.019m) and the difference in temperature between the internal space where the equipment rests and the average outside air temperature. Further, we'll assume that heat conducts through all podium walls evenly, but your actual situation may vary.

In Part 1, I mentioned the manufacturer's maximum operating environment for equipment as being about 40°C to 50°C. We will assume that if we use the manufacturer's maximum value, the podium internal air must be at that value and no higher. Let's use 40°C. If the outside environment is normal room temperature, or about 25°C, our temperature differential is 40 - 25 = 15°C.

Plugging all the previous numbers into Fourier's formula, we have:

q = -((0.13)x(0.24)x15)/0.019 = -24.6 watts.

This tells us that the wooden podium is capable of transferring up to 24.6 watts into the external environment with an internal temperature of 40°C. Suppose the equipment item is a computer video interface that only uses 12 watts. We have a 2:1 design factor or we know that the internal podium temperature will be lower. No fan is required.

Towers of Power

Great information, but you say "I mostly build equipment racks for my projects. How do I thermally manage my rack designs?" Rack enclosures can be both good and bad from a temperature management point of view. Properly designed rack installations may actually extend equipment life by providing better air circulation than the original equipment would otherwise receive. Equipment racks with improperly designed cooling can significantly shorten equipment life by creating hot spots, trapping heated air, and focusing heat from hotter products onto other products.

(High Resolution Image)

We already know that heated air rises and cooler air falls. By now it is clear that heat flow conducts only one direction: from the hotter body to the colder body. So, let's think only in terms of removing hot air…colder air will automatically follow to fill the void. With this in mind, it is typically easier to "pull" the hot air away than to "push" cold air into a hot environment. Pushing colder air into a warmer environment increases the chance that condensation may occur at an inappropriate time or place. In addition, it is highly probable that the cooler air may bypass some equipment in such a way as to create eddy currents, or dead circulation areas, where air flow becomes stifled. This latter situation ensures the shortening of equipment life.

From a weight distribution perspective, good design practice recommends placing larger, heavier equipment at the bottom of the rack. Larger equipment usually produces the most heat and this heat affects equipment above. For example, audio power amplifiers most times produce more heat during operation than much of the combined power requirements of the remaining equipment collection in the rack. While these larger items will heat other items, placing them in the bottom of the rack will more readily produce an upward convection to facilitate cooling overall. However, where room ambient temperature is high, it may be better to place hotter equipment at the top of the rack. This tradeoff can become problematic for areas of seismic activity or for transportation of rack systems to the job site.

The designer must attempt to position equipment to minimize hot spots and provide an overall chimney effect within the rack so as to move as much air through as possible. Practically, there are other facets of equipment layout that must be considered, such as placement of products in ergonomic locations within the rack for user interface. The system designer must rationalize many aspects of the rack build between user access, safety, thermal management, and servicing. Placement of equipment in a rack having proper thermal design is one consideration, but equally important is the circulation of air within the room where the rack is located2.

The external room environment of the equipment rack must have a lower average temperature than the internal rack environment; otherwise, there will be no heat flow from the rack into the environment. Electronic equipment is not much different than people, when it comes to the temperature of the environment. Most of us perform well and feel comfortable in a room of about 23°C (73°F). It's good practice to keep the equipment room environment within normal bounds too. As shown by Fourier's Law of Conduction, the key to good heat transfer is a high temperature differential between the body of air surrounding the hotter item to be cooled. As the warmer air rises from the equipment, ideally cooler air should easily stream into the rack and set up a natural air flow. This action describes the process of natural convection.

Convection cooling is the lowest cost and lowest maintenance form of thermal management, but is not always easy to implement such that all equipment is cooled equally. Rack-mounted equipment produces nearly 400 BTU/hour of heat for every one ampere of line current at 117 volts AC (one half ampere at 230 VAC) 2. Since the power consumption of most equipment items is relatively constant during operation, this is a straightforward heat calculation. Where heat generation varies most is with products delivering power on a variable basis. Such is the case with large audio power amplifiers. (Class D audio power amplifiers may be an exception where their worst-case power usage occurs typically when idling, as opposed to hard use where their power usage is lowest.) Your ability to calculate heat load for larger equipment items will rest with having the manufacturer's specs and estimating an average value under normal and worst-case use conditions.

Venting IS Critical

What about vent sizing? Whether you use convection or resort to forced air cooling, air intake and outtake openings are very important. In most cases, unless equipment perimeters are completely sealed, air ingress may be expected at various points around equipment items and through lower vents in the rack assembly. It is generally good practice to pull cooler air in from the front of the rack around each item and exhaust through the top of the rack. In this scenario, the sources for air ingress are likely to be equivalent to a large opening. The exhaust vents must then be carefully designed. Since this is a series system of air moving in and moving out, the exhaust vent must be at least equal in opening area.

Calculation of actual vent efficiency is not always as simple as adding up the areas of the holes or slots. For convection, larger thermal gradients between the internal air and the outside air generate more rapid air convection. Rapidly moving air will more easily overcome vent airflow resistance. Vent openings exhibit resistance to air flow depending on their dimensions and number. Air flow is characteristically laminar and will "see" vent resistance as it relates to the vent openings' physical geometry. For example, long slot-shaped vents conduct airflow better than bulkheads perforated with small round holes. Although both geometries may have the same vent area, air flow will tend to be reflected by the bulkhead of round holes while it will more easily flow through the wide slots. Any air reflected back into the rack will encounter the normal air upflow convection and create eddy currents, which are stagnating air patterns that hinder cooling performance.

A common question is: Should I separate each item in the rack by at least one rack unit space? Rack space is at a premium in many system designs. Certainly, if you can separate items, it's usually a good idea, but there is no single correct answer here. The right answer depends on several factors, such as:

Whether adjacent items are significant generators of heat, since the resulting heat will physically transfer from a hotter box to a colder box.
How items are vented individually. If there are no vents on top or bottom, then chances are that separating them will provide no additional heat relief, unless your plan is to pull cooler air through front panels between items. If there are vents on top and/or bottom, do not defeat them by stacking the item.
The power rating on each item. Keep in mind the 400 BTU/hour per ampere of line current (115VAC), which translates to 115 watts draw.

Let's say you have a short stack of 1U pizza-box-sized items that each use 50 watts. For each two you stack, you'll be generating nearly 400 BTU per hour. Pizza box type products tend to extend into the rack space and block air flow past smaller, less deep products that might be located above or below them. This situation is ripe for establishing eddy currents, particularly when the equipment above does extend deeper into the rack. The overall profile of equipment extension into the rack's air space is another consideration for good thermal management. To destroy the eddy, allow air to pass through the front of the rack, and just below, the smaller items.

Forced Into Forced-Air

In many cases, equipment type and density will not allow proper cooling via convection, so forced-air cooling must be implemented. Of course, forced-air implies use of fans. Even with forced-air, the best approach is to pull hot air out and not attempt to force downward airflow into an enclosure. Pushing the air into the enclosure tends to set up internal currents which are deflected in uncertain directions and does not necessarily move air into all the areas where needed.

When using equipment items with internal fans, pay particular attention to the direction of the exhaust so as not to disturb the normal convective flow within the rack, even though you may or may not use fans for the rack itself. There are many scenarios for the management of forced-air cooling. Depending on circumstances, any one of several approaches may be appropriate. I highly recommend reading the white paper on "Controlling the Temperature Inside Equipment Racks" by Bob Schluter of Middle Atlantic Products2. It covers a wide variety of installation scenarios and design calculations too numerous to explore here.

Key points to remember with forced-air cooling are:

Make temperature measurements at various points in the rack to determine if the temperature gradient from bottom to top is normal (linear).
Avoid extra equipment vents near the top of the rack in front or back as they tend to short-circuit air flow.
Fan airflow ratings in CFM (cubic feet per minute) represent the maximum volume of air per unit time that may be moved and does not account for any vent resistance or other obstructions.
Static pressure describes the suction or pressure the fan is capable of developing so as to overcome the resistance to airflow.
Fans with ball bearings have a significantly longer life…as much as 50% longer than low cost sleeve bearings.
Typically, the best location for fans is at the top of the rack with airflow oriented upward to pull cooler air from the bottom of the rack and expel hot air through the top.

Forced-air cooling requires more maintenance. In high dust and dirt environments filters are required to extend fan and equipment life. Clogged air filters are a common cause of system failure when not serviced regularly. One way to extend fan life is to design the rack for the best convective flow possible without the fan. Then, install the fan with a proportional controller so that the fan runs only when needed and at a speed appropriate for attaining the minimum cooling required. These days, proportional controllers may have integral thermostats to enable and disable fan operation. On a grander scale, connection of an internet-enabled interface, such as Extron's IP-Link, provides the ability to control system cooling from afar and, minimally, be warned via email should the fan fail and rack temperature rise to a destructive level.

The possibilities are endless. Thermal management plays a key role in designing reliable system installations. As this installment concludes my discussion on thermal management, I hope both Part 1 and Part 2 provided some insight and understanding of the measurement units and physical concepts guiding good thermal management decision-making. Unlike the poor example I set as a troubleshooter during the five-tube radio story, don't allow your system designs to go up in smoke due to inadequate thermal management planning. Remember, once the magic smoke is lost, it's virtually impossible to replace.

References

"Conductive Heat Transfer" from the Engineering Tool Box web site at:
http://www.engineeringtoolbox.com/conductive-heat-transfer-d_428.html
"Controlling the Temperature Inside Equipment Racks" by Bob Schluter, President and Chief Engineer, Middle Atlantic Products, Inc. © 2002-2004.
Download this paper from: http://middleatlantic.com/pdf/ThermalManagement.pdf