Plate Fin Heat Sink Cooling by Forced Convection

The calculations are based on the experimental results from Ref. 15, where several flow regimes were considered.

Heat sink geometry with its main dimensions is shown in Figure 1. The dimension values were set as follows: fin height (H) of 10 mm, thickness of 1.5 mm and fin-to-fin distance (d) of 5 mm while the heat sink width (B) and length were 52.8 mm and the base thickness was 3 mm. The wind tunnel width (CB), height (CH) and length were 160 mm, 15 mm and 200 mm respectively.

Figure 1. Geometry model of the heat sink.

The model of heat sink is made of solid aluminum (thermal conductivity 200 W/(m∙K)). It is heated by MINCO Thermofoil™ electrical heater with a heat load of 10 W. The bottom of the heated foil is insulated with a 25 mm Polystyrene brick (thermal conductivity 0.033 W/(m∙K)). The heat sink is placed in a rectangular wind tunnel duct with the walls made of Plexiglass (thermal conductivity 0.2 W/(m∙K)). It is mounted in such a way that the fin base is flush with the duct wall as shown in Figure 2.

Figure 2. Vertical cut view of heat sink: (1) heat sink, (2) thermocouple, (3) electrically heated foil, (4) insulation, (5) bottom of wind tunnel.

The performance of the heat sink is estimated by a thermal resistance defined as:

where Ths is the temperature of the heat sink base, T0 is the temperature at the wind tunnel inlet and q is the total power input of the heat source (10 W). In Ref. 15, the Ths value was measured by averaging the reading of four thermocouples (two of them can be seen in Figure 2) placed symmetrically at the corners of the heat sink base.

Table 1 shows air inlet flow conditions specified for the calculations, inlet temperature is constant and equal 20°C. To perform the calculations, five cases are considered, each with a different inlet velocity uin that was determined as follows:

where A = 24 cm2 is the wind tunnel cross sectional area; is the volumetric air flow rate at standard conditions defined as

where w is the average air velocity; Afront = 1.4 cm2 is the front area of the fins; Redh is the Reynolds duct number; dh is the hydraulic diameter of the wind tunnel; μ is the dynamic viscosity of air; ρ is the density of air.

The outlet static pressure is set to 1 atm.

The heat exchange between the outer duct surfaces and the ambient medium with the temperature of 20°C is defined by a Newton's law of cooling with the heat-transfer coefficient of 3 W/m2∙K.

Since the geometry model has a symmetry plane, only a half of the model is used to generate the computational mesh.

The automatically generated mesh with RRL = 3 contained approximately 26 000 cells for cases 1-4 and with RRL = 5 contained approximately 109 000 cells for case 5. Figure 3 shows the mesh generated in the fluid region in one of the heat sink cross-sections. One can see that there only about 3-4 cells generated between two adjacent fins.

Figure 3. The computational mesh (cases 1-4).

The values of thermal resistances predicted by Flow Simulation and the corresponding values measured experimentally from Ref. 15 are shown in Figure 4. According to this plot, the difference between the calculations and the experimental measurements is less than 10%.

Figure 4. Thermal resistance of the Heat Sink versus Reynold number in comparison with the experimental data.

This indicates that the sufficient accuracy of the results is maintained even on a coarse mesh generated inside the narrow channels.