Pin-fin Heat Sink Cooling by Natural Convection

A heat sink is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, thereby allowing regulation of the device's temperature. Heat sinks play an important role in electronics cooling. In computers, heat sinks are used to cool CPUs, GPUs, and some chipsets and RAM modules. Heat sinks are used with high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light emitting diodes (LEDs), where the heat dissipation ability of the component itself is insufficient to moderate its temperature.

Following the experimental work presented in Ref. 29 and numerical study presented in Ref. 2, let us consider heat transfer from an electrically heated thermofoil which is mounted flush on a plexiglass substrate, coated by an aluminum pin-fin heat sink with a 9x9 pin fin array, and placed in a closed plexiglass box. In order to create more uniform ambient conditions for this box, it is placed into another, bigger, plexiglass box and attached to the heat-insulated thick wall, see Figure 1 and Figure 2. Heat sink and enclosure geometry with their main dimensions is shown in Figure 1, where 1 - smoke inlet, 2 - enclosure under study (plexiglass), 3 - external enclosure (plexiglass), 4 - insulation, 5 - opening, 6 - substrate, 7 - heat sink, 8 - heat source (lcp x lcp x hcp). The dimension values are set as follows: length of component lcp = Ls = 25.4 mm, thickness of component hcp = 0.861 mm, height of the pin Hp = 5.5 mm, height of the substrate board Hb = 1.75 mm, size of the pin Sp = 1.5 mm, pin spacing Sps = Ls/8, length of enclosure L = 127 mm, height of enclosure H = 41.3 mm, thickness of enclosure wall Hw = 6.35 mm, ratio between opening area and the top wall area (L x L) Sv = 0, 0.4. Following Ref. 29, let us consider the vertical position of these boxes, as it is shown in Figure 1 (c) (here, the gravity acts along the Y axis).

Figure 1. The pin-fin heat sink nestled within two plexiglass boxes: (a) pin array, (b) pin size and pitch, (c) external enclosure, (d) internal enclosure.

The corresponding model used in the calculations is shown in Figure 2. In this model's coordinate system the gravitational acceleration vector is directed along the X axis. The computational domain envelopes the outer surface of the external box, and the Z = 0 symmetry plane is used to reduce the required computer resources.

Figure 2. A model created for calculating the heat transfer from the pin-fin heat sink through the two nested boxes into the environment: (a) the internal (smaller) box with the heat sink; (b) the whole model.

According to Ref. 29, both the heat sink and the substrate are coated with a special black paint to provide a surface emissivity of 0.95 (the other plexiglass surfaces are also opaque, diffuse and gray, but have an emissivity of 0.83).

The maximum steady-state temperature Tmax of the thermofoil releasing the heat of known power Q was measured. The constant ambient temperature Ta was measured at the upper corner of the external box. As a result, the value of

was determined at various Q (in the 0.1...1 W range).

The ambient temperature is not presented in Ref. 29, so, proceeding from the suggestion that the external box in the experiment was placed in a room, we have varied the ambient temperature in the relevant range of 15...22°C. Since Rja is governed by the temperature difference Tmax – Ta, (i.e. presents the two boxes’ thermal resistance), the ambient temperature range only effects the resistance calculations by 0.6°C/W at Q = 1 W, (i.e. by 1.4% of the experimentally determined Rja value that is 43°C/W). As for the boundary conditions on the external box’s outer surface, we have specified a heat transfer coefficient of 5.6 W/m2·K estimated from Ref. 17 for the relevant wind-free conditions and an ambient temperature lying in the range of 15...22°C (additional calculations have shown that the variation of the constant ambient temperature on this boundary yield nearly identical results). As a result, at Q = 1 W (the results obtained at the other Q values are shown in Ref. 2) and Ta = 20°C we have obtained Rja = 41°C/W, i.e. only 5% lower than the experimental value.

The flow streamlines visualized in Ref. 29 using smoke and obtained in the calculations are shown in Figure 3.

Figure 3. Flow streamlines visualized by smoke in the experiments (left) and obtained in the calculations (colored in accordance with the flow velocity values) (right).