**2. Passive heatsink technologies**

Passive heat sinks are heat exchangers in the form of finned radiators, generally made of aluminum. They are called *passive* because they do not have any moving mechanical component (fan) designed to force airflow. Air moves through them only due to density difference: Hot air goes upward as it is replaced by cooler air. It is for this reason that passive sinks transfer heat to air essentially by natural convection<sup>1</sup> . This type of heat sinks is, by far, preferred for cooling electronic systems [2]; they are cost-effective, simple to find and assemble, and they generate no power consumption or noise.

The most widely used passive heat exchangers are *finned natural convection heat sinks*.

### **2.1 Finned heat exchangers**

In their simplest version, these heat sinks are constituted of finned surfaces. **Figure 1** shows examples of *finned heat exchangers* used as heat sinks on electronic components. They are usually constituted of materials having a high thermal conductivity, such as aluminum or copper. But other new materials, like ceramics, can also be found.

The sink is usually mounted on the electronic component, which generates heat, thus increasing its heat transfer area<sup>2</sup> with ambient air. **Figure 2** shows a transistor mounted on a finned heatsink.

**Figure 1.** *Examples of finned heat sinks. Sources [3, 4].*

<sup>1</sup> For a better understanding of natural convection see Ref. [1].

<sup>2</sup> The heat transfer area is the surface thru which energy is transferred from the electronic component to the environment.

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

**Figure 2.** *A heatsink fixed on a transistor. Source [5].*

It can be seen from this figure that this type of mounting permits to increase the heat transfer area; the heat generated by the transistor is transferred to ambient, not only through the external surface of the transistor but also through the surfaces of all the fins.

In such situations, the heat transfer process depends on several parameters such as the temperature difference between air and the electronic component, the total area of the fins and their position (vertical/horizontal), the fins spacing, etc.

## **2.2 Design fundamentals**

### *2.2.1 Thermal resistance*

Despite this complexity of the heat transfer process, design techniques usually use a simple model to represent the flow of energy through a heatsink. This simple model is based on a similarity between the way that heat moves from one medium to another and the way that electric current flows from one potential to another. We know that if a point at a potential *V*<sup>0</sup> (**Figure 3a**) is separated by an electrical resistance *R* from a second point (at *V*1), and then an electric current *i* flows between these two points, such that:

$$i = \frac{V\_0 - V\_1}{R} \tag{1}$$

Similarly, it can be shown that the power, *Q*, of heat dissipation between a point at temperature *Tc* and a point at temperature *Ta* (**Figure 3b**) is given by:

$$Q = \frac{T\_c - T\_a}{R\_{th}} \tag{2}$$

Where *R*th is called the *thermal resistance* between these points [6]. *R*th is expressed differently for conduction and convection as follows:

• For a conduction heat transfer:

**Figure 3.**

*Thermal resistance model for heat flow. (a) Electric current* i *flows between* V*<sup>0</sup> and* V*1. (b) Heat flux* Q *flows between* T*<sup>c</sup> and* T*a.*

Where *L* is the material thickness, *k* is the thermal conductivity, and *A* is the heat transfer area.

• For a convection heat transfer:

$$R\_{th}^{conv} = \frac{1}{hA} \tag{4}$$

Where *h* is the convective heat transfer coefficient and *A* is the heat transfer area.

#### *2.2.2 Electronic component without a heatsink*

Consider an electronic component with junction temperature *Tj*, in an ambient environment (air for example) at *Ta*.

As shown in **Figure 4**, the heat generated by the component is transferred by conduction from the junction to the external surface of the case. Then, heat is conveyed by convection and radiation to the ambient environment.

For normal operating temperatures, conduction and convection are the prevailing modes. The total heat transfer resistance is therefore given by the following:

$$R\_{\rm fA} = R\_{\rm fC} + R\_{\rm CA} \tag{5}$$

Where:

*RJA* is the junction to ambient resistance.

*RJC* is the conduction resistance.

*RCA* is a convection resistance.

Note that *RJC* is generally quite low, but *RCA* is usually high enough to limit heat transfer from the component to environment.

#### *2.2.3 Electronic component with a heatsink*

**Figure 5** shows the electronic component of **Figure 4** to which a finned heatsink was added in order to take advantage of its large contact area with ambient, thus permitting a better spread of the heat generated by the component.

In this case, as well, heat is transferred from the component to the ambient essentially by conduction and convection. Energy transfers are therefore represented by a series of thermal resistances:

**Figure 4.** *Heat resistance of a sink.*

**Figure 5.** *Total resistance of a heatsink.*

*RJC*, *the junction to case thermal resistance*; a conductive resistance which depends on the thickness, *eJC* (between the junction and the thermal interface), on the area *SJC*, and on the thermal conductivity *kJC*. *RJC* is given by the following:

$$R\_{\rm JC} = \frac{\mathbf{e}\_{\rm fC}}{k\_{\rm fC} \mathbf{S}\_{\rm fC}} \tag{6}$$

*RCS*, the case to heatsink thermal resistance; a conductive resistance that takes into consideration the thickness and conductivity of the case and interface material. *RCS* is given by the following:

$$R\_{\rm CS} = \frac{\mathbf{e}\_{\rm CS}}{k\_{\rm CS} \mathbf{S}\_{\rm CS}} \tag{7}$$

*RSA*, *convection resistance* between the fins and air. *RSA* is a convective resistance given by the following:

$$R\_{\rm SA} = \frac{1}{h\mathcal{S}\_F} \tag{8}$$

Where *SF* is the fins surface area in contact with ambiance and *h* is the convection heat transfer coefficient between the fins and the ambient environment (see Appendix 1).

The sum *RJC* þ *RCS* þ *RSA* represents the *heat exchanger thermal resistance* between the junction and ambient. *The thermal resistance of the heat exchanger* is then given by the following:

$$R\_{th} = R\_{\text{fC}} + R\_{\text{CS}} + R\_{\text{SA}} = \frac{e\_{\text{fC}}}{k\_{\text{fC}} \text{S}\_{\text{fC}}} + \frac{e\_{\text{CS}}}{k\_{\text{CS}} \text{S}\_{\text{CS}}} + \frac{1}{hS\_F} \tag{9}$$

Thus, the *heat exchanger thermal resistance* is a parameter, which depends on the materials constituting the heatsink, the casing, and the thermal interface material. It also depends on the surface area in contact with air, the configuration of the fins, their number, the position of the heatsink (horizontal/vertical), air temperature, etc. Its determination is somewhat complicated [6] and often necessitates the running of experiments.

Hopefully, when integrated systems are offered, values of the thermal resistance, *R*th, are given by manufacturers' data. In the case where the heat exchanger is mounted from separate pieces, the heat exchanger thermal resistance can be computed from Eq. (9). Electronic component suppliers' data sheets give the parameters necessary for the computation of *RCS*. Similarly, characteristics of gaskets

*Heat Exchangers*


#### **Table 1.**

*Values of* R*th for different heat sinks.*

(eventually), gap fillers, and other interface materials will permit the calculation of *RCS*. Finally, *RSA* can either be taken from heatsink data sheets (**Table 1** shows values of *RSA* for different heatsink makes), or calculated from Eq. (8) and Appendix 1.

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

**Figure 6.** *Dissipation power as a function of ambient air temperature.*
