Many companies design products with electronics that must function reliably at high altitude, typically 1,500m (5,000 ft) or 3,000m (10,000 ft) above sea level. Estimating the increase in operating temperatures is necessary to design and qualify such products. There are a variety of corrections used to account for this effect, many of which sacrifice accuracy for simplicity. While many companies do make reasonable adjustments for altitude, many others are needlessly using formulas that do not apply to their current power dissipation and operating temperatures.
Today’s electronics are complex. Printed circuit boards (PCBs) are often packed with variable power components, and are subject to air flow patterns with recirculation regions, dead spots, and thermal wakes of other heat sources. In spite of these analytical difficulties, any surface temperature calculation or measurement at sea level can be extrapolated to any altitude with the formula proposed in this article.
Altitude Correction
Any air-cooled surface temperature calculation or measurement at sea level can be adjusted for high altitude effects with the appropriate multiplier. This applies to any surface exposed to convection by air, such as case temperatures, board temperatures and heat sink temperatures, even if the exact power dissipation is not known. In addition, the air temperature rise inside a fan-cooled system can be scaled in a similar manner.
The multiplier is a function of the altitude and the convective environment. This concept was first conceived in Reference 1. Convective environments for electronics include: fan- or blower-cooled systems, and naturally cooled electronics in vented or no enclosures. Values of the multiplier are presented in Table 1.
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A distinction is made in Table 1 between the multiplier for general temperatures in fan-cooled systems and high power component temperatures in fan-cooled systems. The use of the general multiplier bounds all surface temperature measurements, and can be applied to temperatures such as component cases, board locations, and heat sink fins. It also applies to the air temperature rise. However, for the special case of a component whose temperature rise is dominated by its own power and not air temperature rise, the general multiplier is conservative. The high power multiplier is recommended in this case to reduce over-conservatism. Lastly, the multipliers for naturally cooled systems can be applied to surface temperatures in naturally cooled systems.
The multipliers in Table 1 can then be used to adjust the temperature rise for high altitude effects with Equation 1.
T(z) — Tamb = [ TSL — TSL,amb ] � Multiplier(z, Configuration) (1)
where:
T(z) – Tamb is the surface or air temperature minus the ambient temperature at altitude, z.
TSL — TSL,amb is the surface or air temperature minus ambient temperature at sea level.
Multiplier(z, Configuration) is the multiplier determined from Table 1.
This simple altitude correction accounts for the influence of unknown power dissipation and convective non-uniformities, by appropriately scaling the temperature rise at sea level. Once the surface temperatures are scaled for high altitude effects, other critical temperatures, such as junction temperature or temperature at a heat sink interface, can then be calculated using a traditional thermal resistance network.
A common correction for altitude that is often used is to add a fixed temperature increment to all surface temperatures, typically 5° to 7°C to account for a fixed amount of altitude, such as 3,000m (10,000ft), regardless of convective environment or power dissipation. Sometimes the adder is a function of the altitude, such as 1°C per 300m (1,000 ft). While these corrections are simple to apply and may have been appropriate for previous products, they are not accurate for the range of situations covered by Equation l and Table1, and could result in sub-optimal thermal management designs and decisions.
Effect of Altitude on Cooling
Air at high altitude is less dense than air at sea level, reducing its convective capability and overall heat capacity. Therefore, all electronics that rely on natural or forced convection to dissipate heat will experience greater air and component temperature rises for the same amount of power at high altitudes. This increase in temperatures can be predicted with commonly used convective heat transfer correlations once the change in density is known.
Derivation of Multipliers
The multipliers in Table 1 are only as good as the assumptions used to derive them, and will never be as precise as a good 3D Computational Fluid Dynamics (CFD) model or a temperature measurement at high altitude. However, in the absence of these costly resources, a very reasonable estimate for the effects of altitude can easily be obtained.
The air temperature rise in a forced-air system can be determined with an energy balance. Because the specific heat of air and the velocities will not change significantly with altitude, the air temperature rise is inversely proportional to the density of air. Thus, the multiplier for air temperature rise or low power components is simply the ratio of the air density at sea level to the air density at the altitude in question.
The temperature rise of high power components, however, is dominated by power dissipation. In this situation, the convective heat transfer coefficient can be expressed as a function of the Reynolds and Prandtl numbers. Because the Prandtl number is relatively constant, the effect of the density variation on the Reynolds number accounts for the increase in case-to-ambient resistance, which then accounts for an increase in operating temperatures.
The heat transfer coefficient in naturally cooled systems can be expressed as a function of the Grashoff and Prandtl numbers. In this case, the temperature and density dependence of the Grashoff number dictates the increase in case-to-ambient resistance, and thus, the increase in operating temperatures.
An expression for the air density ratio assuming constant ambient temperature can be obtained from Reference 2, among other sources. Typical correlations for the heat transfer coefficients can be found in Reference 3.
References
1. Azar, Kaveh, “Electronics Cooling–Theory and Applications”, Short course, 1998.
2. White, F. M., Fluid Mechanics, Second Edition, pg. 60, McGraw-Hill Book Company, New York, 1986.
3. Holman, J.P., Heat Transfer, Sixth Edition, McGraw-Hill Book Company, New York, 1986.
