**3.2 Heat exchanger verification**

In this case, it is desired to verify if a given heatsink will permit the safe operation of an electronic component at a known surroundings temperature.

The verification procedure is carried out in four steps.

STEP 1: From data sheets (component, thermal interface, and heatsink) get the values of *Qmax*,*Top*, *RJC*, *RCS*, and *RSA*.

STEP 2: Calculate *R*th from Eq. (12): *R*<sup>∗</sup> *th*. STEP 3: Calculate *R*<sup>∗</sup> *SA* from Eq. (13) as follows:

$$R\_{\rm SA}^{\*} = R\_{th}^{\*} - \left(R\_{\rm fC} + R\_{\rm CS}\right) \tag{13}$$

STEP 4: If *RSA* ≤*R*<sup>∗</sup> *SA* then the heatsink will do the job. *Illustration 2*

*You bought an electronic component with a heatsink mounted on, thus constituting a heat exchanger ready to use. The heatsink is the one shown under N° 10 in Table 1.*

*The data sheet of the electronic component gives the following information: Qmax = 10 W and Top = 115°C.*

*Will this system operate safely at a surrounding temperature of 27°C? Solution STEP 1: Qmax = 10 W,Top = 115°C and N° 10 in Table 1 gives: Rth = 14°C/W. STEP 2: Eq. (11) gives: R*<sup>∗</sup> *th* <sup>¼</sup> <sup>115</sup>�<sup>27</sup> <sup>10</sup> <sup>¼</sup> 8, 8° *<sup>C</sup> W : STEP 3: Rth* > *R*<sup>∗</sup> *th: the mounted heatsink will not do the job.*

#### **3.3 PCBs optimal assembly**

A typical passive heat exchange problem is encountered when one needs to assemble a set of circuit boards on a rack.

**Figure 7** shows a number of boards of the same size, *H*, placed on a rack of length *L* and width *w*. The spacing between the different circuit boards is assumed to be constant, *δ*, whereas each board releases a constant flux density, *q* (W/m<sup>2</sup> ). The cooling of the circuit boards is ensured by natural convection.

In such a configuration, the temperature of the boards is not uniform, rather it increases with height, reaching its maximum value at *H*. The spacing *δ* needs to be such that heat evacuation is optimum.

**Figure 7.** *Assembling a set of circuit boards on a rack.*

## *3.3.1 Optimum spacing of PCBs*

A frequent question is; *how should the boards be placed on the rack for optimum heat evacuation?* In other words, *what is the optimum spacing, δ\* ?*

The optimal spacing is given by [17]:

$$\delta^\* = 2,12 \frac{w}{Ra\_q^{0,2}} \tag{14}$$

*Raq* being the Rayleigh number for, *q*, given by:

$$Ra\_q = 2,12 \frac{w^4 \mathcal{C}\_p \rho^2 \mathbf{g} \beta q}{\mu k^2} \tag{15}$$

Where

