### Categorized |Power Design, Thermal Management

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Posted on 21 January 2019

# Forced Air Cooling of Power Modules

In contrast to natural air cooling, forced air cooling can reduce the thermal heatsink resistance to 1/5...1/15. Figure 1 compares the Zth(s-a) characteristics of natural and forced air cooling up to the final Rth(s-a) value using the example of a SEMIKRON P16 heatsink in different lengths.

Figure 1. Zth(s-a) (t) characteristics for different P16 heatsink lengths in [mm], number of heat sources n; a) in case of free convection with different power dissipation values; b) for forced air cooling

α is much higher with forced air cooling than with free convection. The rated surface temperature of forced air cooled heatsinks should not exceed 80...90°C at a supply air temperature of 35°C (condition for datasheet ratings). Since convection is mainly responsible for the dissipation of heat, coating the heatsink black will have virtually no effect in the case of forced air cooling.

### Cooling profiles

The heatsink material must display optimum heat conductivity and heat spreading (high coefficient of thermal conductivity λ) at reasonable material and processing costs. For this reason, aluminium is often preferred (λ = 247 W/K·m for pure Al), but copper is also used to meet particularly high requirements (λ = 398 W/K·m). The dependence of heat spreading on the production process and the alloy used is remarkable. In practice, heatsinks display λ values of between 150 W/K·m (Al-die cast alloy) and 220 W/K·m (AlMgSi extruded material). Heat spreading in the material has a considerable influence on the thermal efficiency of the heatsink. Therefore, optimized dimensioning is important for root thickness, number of fins, fin height, and fin thickness:

• The root of a heatsink is the unfinned part of the mounting surface for the power modules where the heat is spread.
• The fins of an air heatsink are used to dissipate the majority of the heat to the environment by convection.

To determine optimized conditions for forced air cooled heatsink profiles, heat conduction and convection can also be integrated by way of the fin height layout, which will result in the following formula on the condition of some simplifications:

$R_{th(s-a)} = \frac {1}{n \sqrt {\alpha \cdot U \cdot \lambda \cdot A} \cdot \Big [ \frac{1}{1+e^{-2k}} - \frac{1}{1+e^{2k}} \Big ]}$

where $k =h \cdot \sqrt {\frac {\alpha \cdot U}{\lambda \cdot A}}$

(α: heat-transfer coefficient, U: fin circumference, λ: coefficient of thermal conductivity of heatsink material, A: cross-section of fins, h: fin height)

Table 1 provides a rough overview of the design features of various types of heatsink.

 Thin root Thick root Many fins Few fins Lower Rth(s-a) Higher Rth(s-a) But: Low overload capacity (e.g. for pumps) High overload capacity (e.g. for lifts) Short time constants Long time constants Little heat spread Good heat spread High pressure drop – less air Low pressure drop – more air Sensitive to dirt Less sensitive to dirt

Table 1. Properties and selection criteria for different heatsink profiles

### Pressure drop and air volume

Rth(s-a) continues to be mainly determined by the rate of air flow per time Vair /t depending on the average cooling air velocity vair and the transfer cross section A:

$V_{air} /t = v_{air} \cdot A$

Instead of the assumed laminar air flow, air swirling on the fin surfaces will induce turbulent flow conditions which will improve heat dissipation to air, provided the fin surfaces are set out accordingly. Of course, it is not just the static, but also the transient thermal resistance (thermal impedance) Zth which is reduced by forced air cooling. Figure 1 shows Z th(s-a) characteristics up to the final Rth(s-a) value for natural and forced air cooling in a SEMIKRON P16 heatsink. Time behavior also changes by a power of ten. While for natural air cooling the static end value will only have been reached after 2,000…3,000 s, in the case of forced air cooling this process is completed after just 200...300 s.

Increasing the number of fins and fin width will reduce the transfer cross section of the heatsink. As with increased heatsink length, the pressure drop in the cooling air Δp rises and the volumetric flow rate decreases. This is a counter-effect to extending the cooling surface. For this reason, each fan has an optimum with regard to flow cross section, heatsink length, and volumetric flow rate. Heat dissipation is dependent on the fan properties, which are described in the fan characteristic Δp = f(Vair /t) (Figure 2).

The intersection of the characteristic fan curve and the pressure drop curves for the heatsinks Δp = f(Vair /t, L) enables the volumetric flow rate at the operating point to be determined according to Figure 2. When integrating the fan characteristic, the permissible operating voltage fluctuation (e.g. 230 V ± 10%) must also be taken into account. Sufficient cooling has to be ensured even when a minimum voltage is applied, i.e. when there is less air flow. The heat transfer resistance Rth(s-a) of the heatsink layout (Figure 3) is a function of the determined volumetric flow rate.

Figure 2. Cooling air flow of a Px16 heatsink profile for various heatsink lengths and fan characteristics

Nearby a known operating point, Rth(s-a) can be determined as a function of the volumetric flow rate according to the following equation:

$R_{th(s-a)}2 = R_{th(s-a)1} \cdot \Big ( \frac {\dot{V}_1}{\dot{V}_2} \Big )^k$

where k = 0.7…0.9

Figure 3. Characteristic curve of the Px16 heatsink as a function of the volumetric flow rate

### Fans (ventilators, blowers)

Fans produce the air flow required for air cooling. Depending on the kind of heatsink and application, different fan types are used (Figure 4):

### Axial flow fans

The spin axis of the axial rotor runs parallel to the air flow. The air is moved through the axial rotor which acts similar to an airscrew. The advantages of axial flow fans are their relatively small dimensions in relation to the high air flow rate handled. Their disadvantage is the increase in pressure compared to radial flow fans.

### Radial flow fans or centrifugal fans

Radial flow fans (Figure 5) are used whenever, unlike axial flow fans, a higher pressure increase for the same amount of air is important. The air is sucked in parallel or axial to the drive axis of the radial flow fan, and deflected by 90° as a result of the rotation of the radial rotor and blown out in a radial direction. In order to minimize pressure losses due to the high exit velocity of air out of the radial flow fan, care must be taken to continue the air chanelling, e.g. by using a diffuser.

### Tangential or cross flow fan

Cross flow fans have an intake and blow-out slot across their entire length. Air is sucked into the interior of the rotor through the intake slot, where it is swirled, deflected and blown out highly homogenously. Cross flow fans provide a high air flow rate even at low speeds and can therefore be constructed to emit relatively low noise. The rotor length and the outlet slot are matched to the heatsink width.

Figure 4. a) Axial flow fan, b) Radial flow fan, c) Cross flow fan

Figure 5. Set of 3 diode half bridge modules in a three phase rectifier circuit on a cooling profile with radial flow fan

### Operating height

The amount of heat to be dissipated depends on the atmospheric pressure and the density of the cooling air. Air density, and hence cooling efficiency, decreases as the operating height increases. Decreasing air density deteriorates heat dissipation. Heatsink efficiency also deteriorates. To factor this in, it is necessary to reduce the inverter power, or to multiply Rth for thermal rating by a correction factor in accordance with Table 2.

 Height [m / ft] Performance reduction Correction factor for Rth(s-a) 0 / sea level 1 1 1000 / 3000 0.95 1.05 1500 / 5000 0.90 1.11 2000 / 7000 0.86 1.16 3000 / 10000 0.8 1.25 3500 / 12000 0.75 1.33

Table 2. Impact of operating height above sea level on thermal resistance

These performance constraints also apply to water coolers if the cooling water temperature is regulated by means of an air cooled heat exchanger.

Heat Transfer in Power Semiconductor Devices

Cooling Methods for Power Semiconductor Devices

Thermal Modeling of Power Module Cooling Systems

Cooling Low Power Components

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