*4.1.2 Forced convection heatsink design*

An important parameter in the design of a forced convection heatsink is the flow rate of the cooling fluid (e.g., air) going through the fins of the sink [2]. As a matter of fact, the flow rate generated by the fan actually impacts the heat transfer coefficient: A higher flow rate will mean a greater cooling fluid velocity, leading to a better convection heat transfer [1]. The flow rate also impacts the pressure drop across the heatsink given that for a given fin configuration, higher flow rates generate higher pressure drops<sup>4</sup> .

Consequently, the proposed design procedure will search for *a balance between a reduced thermal resistance and an acceptable pressure drop*. It can be organized in the following seven-step procedure.

*STEP 1: Collect heatsink pressure drop data.*

Flow over a fanned heatsink generates a pressure drop that depends on several parameters including the number of fins, the distance between two fins, the value of the flow rate, etc. [26]. Suppliers of heat sinks will generally be able to provide, for the different models they propose, plots of the pressure drop versus the cooling fluid (air) flow rate. These plots are referred to as *heatsink working diagrams* where the flow rate is generally expressed in cubic feet per minute (CFM: ft3 /mn).

**Figure 11** shows an example of such plots.

**Figure 11.** *Heatsink working diagram.*

<sup>4</sup> For laminar flow, the pressure drop is proportional to the square of the flow velocity [26].

*STEP 2: Get the fan curves.*

Similarly, fan suppliers provide plots that give, for each model proposed, the flow rate achievable by the fan under a given pressure drop. These plots are often referred to as *performance curves of the fans*.

**Figure 12** presents examples of performance curves for four fans. *STEP 3: Select heatsink candidates based on their working diagrams.* The selection criterion here is the individual thermal resistance, *R<sup>s</sup> th*. *STEP 4: Define the allowable coolant temperature rise.* The *coolant temperature rise* is defined as follows:

$$
\Delta T = T\_o - T\_i \tag{17}
$$

where *Ti* and *To* are, respectively, the inlet and outlet temperatures of the coolant.

*Ti* being known (generally, the coolant enters the heatsink around ambient temperature: *Ti*≈*Ta*Þ, the definition of Δ*T* permits to calculate*To*:

$$T\_{\sigma} = T\_i + \Delta T \tag{18}$$

*STEP 5: Determine coolant flow rate for each heatsink candidate.*

For each heatsink s under evaluation, the thermal resistance, *R<sup>s</sup> th*, is known. This makes it possible to calculate the coolant flow rate by combining Eq. (9) and a heat balance on the cooling fluid:

Equation (9) gives:

$$Q\_s = \frac{T\_c - T\_a}{R\_{th}^{\prime}} \tag{19}$$

The heat balance for the cooling fluid gives the following:

$$Q\_s = \dot{m}\_s C\_p (T\_o - T\_i) = F\_s \rho C\_p \Delta T \tag{20}$$

Where:


**Figure 12.** *Performance curves of fans.*


Substituting for *Qs* in Eq. (19) and extracting the coolant volume flow rate, *Fs*:

$$F\_s = \frac{T\_c - T\_a}{\rho C\_p \Delta T \ R\_{th}^s} \tag{21}$$

#### *STEP 6: Determine the pressure drop for each of the heatsink candidates.*

Injecting the values of flow rates into the working diagram gives the pressure drop which will be generated by each of the heatsink candidates. **Figure 13** shows this procedure for the first two heat sinks considered in **Figure 10** (*R*th = 1.5°C/W and *R*th = 15°C/W), which permits the determination of pressure drops Δ*P*<sup>1</sup> and Δ*P*<sup>2</sup> generated by when *F*<sup>1</sup> and *F*<sup>2</sup> flow over sink 1.

*STEP 7: Determine compatible fans using the performance curves.*

For each heatsink candidate, s, inject the pressure drop, Δ*Ps*, determined in the previous step in the performance curves. This will generate the series of flows, *Ffani <sup>s</sup>* , which will be delivered by fan i, operating against the pressure drop Δ*Ps*.

**Figure 14** shows that, for fan 1, all performance curves cross the line Δ*P*1. This means that any of the fans under evaluation can be used. The choice will then be made on price and volume criteria.

## *4.1.3 Cold plate heat exchangers*

Cold plate heat sinks could be considered as a particular class of *plate heat exchangers* [27]. They are used when thermal powers released by electronic systems (smartphones, electric cars, onboard avionics systems, TGV, etc.) become so important that forced convection heat sinks are no longer sufficient [28–30]. They are constituted of plates that are fitted with pipes (see **Figure 15**) through which cooling fluid passes. They are attached to the surfaces of the electronic component or to the board to be cooled. The coolant is conveyed by means of a pump. The coolant itself is, in turn, cooled using a compact exchanger [27].

**Figure 13.** *Determination of pressure drops for heat sinks 1 and 2.*

**Figure 14.** *Determination of deliverable flows under Δ*P*1.*

**Figure 15.** *A cold plate heatsink and its thermal scan. Sources [28, 29].*

### *4.1.4 Microchannel heat exchangers*

Microchannel heat sinks can be considered as a particular subclass of *printed circuit heat exchangers* [27]. These are indeed very small exchangers with overall dimensions not exceeding a few millimeters.

In contrast to their very small dimensions, they allow heat transfers in the order of 800 W/cm<sup>2</sup> [30–33]. The cooling fluid (generally air) circulates in microchannels, of microscopic equivalent diameters (approximately 10–60 μm), formed by etching on metal plates or in composite materials [34]. These microchannels have heights of the order of 0.5 mm. The modules thus formed are placed under the electronic components to be cooled [35]. **Figure 16** illustrates such an assembly where the circuit board to be cooled is shown in semi-transparency, above the microchannels.

However, microchannel cooling suffers from several drawbacks: complex implementation, significant pressure drops associated with microchannel flow. Moreover, it does not quite meet the requirements of thermal management in power electronic systems [36].

#### *4.1.5 Refrigerated heat exchangers*

Significant efforts have been devoted during the last 10 years to the development of a new kind of heat sinks. These are constituted of heat exchange plates associated with refrigeration cycles and a refrigerant as the heat transfer fluid [37–39]. Such refrigerated heat exchangers are used to cool power electronic

*Heat Exchangers for Electronic Equipment Cooling DOI: http://dx.doi.org/10.5772/intechopen.100732*

**Figure 16.** *Overall dimensions of a micro-channel heatsink.*

systems such as laser power supplies and their optical systems. They are able to extract heat flux densities exceeding 1000 W/cm<sup>2</sup> while keeping microchips at temperatures below 65°C [39–44].

Note, however, that mounting this type of heat exchanger on electronic equipment remains difficult due to the fact that all the components of a refrigeration cycle (compressor, expansion valve, evaporator, and condenser) must be assembled in rather tiny spaces (**Figure 17**).

These systems must therefore meet an important challenge: the miniaturization required by designs favoring small sizes [21, 42, 43].
