Experimental Study on Forced Convection Heat Transfer from Plate-Fin Heat Sinks with Partial Heating

Abstract

In this study, plate-fin heat sinks with partial heating under forced convection were experimentally investigated. The base temperature profiles of the plate-fin heat sinks were measured for various heating lengths, heating positions, flow rates, and channel widths. From the experimental data, the effects of heating length, heating position, and flow rate on the base temperature profile and the thermal performance were investigated. Finally, the characteristics of the optimal heating position were investigated. As a result, it was shown that the optimal heating position was on the upstream side in the case of the heat sinks under laminar developing flow, as opposed to the heat sinks under turbulent flow. It was also shown that the optimal heating position could change significantly due to heat losses through the front and back of the heat sink, while the effects of the heat loss through the sides of the heat sink on the optimal heating position were negligible. In addition, it was shown that the one-dimensional numerical model with empirical coefficients could predict the important trends in the measured temperature profiles, thermal resistances, and optimal heating lengths.

1. Introduction

The demand for high-performance and compact products has resulted in a continuous increase in heat dissipation from electronic devices in various systems, such as power converters, supercomputers, and electric vehicles [1,2]. The high heat dissipation from electronic products results in a high junction temperature, which negatively affects the overall performance and durability of the product. Therefore, efficient cooling of these devices is essential and various cooling methods have been developed. In addition, the efficient cooling is also essential for various thermal systems such as transcritical CO₂ refrigeration systems [3], ice storage tanks [4], wind tunnels [5], and heat exchanger/reactors [6]. The most common cooling method is the use of plate-fin heat sinks under forced convection. Therefore, many previous studies have focused on plate-fin heat sinks [7,8,9,10,11]. The thermal performance of these heat sinks is best when the heated base area is equal to the total base area, because the spreading resistance is minimized [12]. However, in many cases, the total base area of the heat sink is larger than the heated base area, as shown in Figure 1. It is because the amount of heat dissipation increases as the total base area increases, and the large total base area is required to sufficiently dissipate heat from high-performance and compact electronic devices, in many cases. For example, small Insulated Gate Bipolar Transistors (IGBTs) are generally mounted on large heat sinks in power electronics [13].

Many researchers have investigated the thermal performance of plate-fin heat sinks with partial heating under forced convection. These research works are well-summarized in Yoon et al. [14]. For example, Culham et al. investigated the role of spreading resistance of the heat sink base caused by partial heating in the design and the selection of the plate-fin heat sinks [15]. They showed that the spreading resistance could be significant without proper thermal design of the heat sinks. Ellison analytically solved a three-dimensional heat conduction equation for obtaining temperature fields in the heat sink bases and for calculating spreading resistances for various heat source sizes [16]. He showed that his results could be used for designing plate-fin heat sinks. Cho et al. experimentally investigated the effects of non-uniform mass flow distributions and heat flux conditions on the thermal performance of microchannel heat sinks [17]. They observed that the microchannel heat sink should be designed by considering the heat flux conditions. Yoon et al. also experimentally investigated the thermal performance of plate-fin and strip-fin minichannel heat sinks, under partial heating [18]. Lelea analyzed the effects of the heating position on the thermal performance of a microchannel heat sink by numerically solving the conjugate heat transfer problem [19]. He observed that the heating position influences the thermal characteristics and that upstream heating has a better thermal performance than central or downstream heating. Toh et al. also numerically calculated the three-dimensional velocity and temperature fields in a partially heated microchannel heat sink by using a finite volume method [20]. Although all of these studies are systematic and provide useful results, they used water or refrigerant as the working fluid and focused on minichannel heat sinks or microchannel heat sinks. As a result, the information which these studies provide for macroscale heat sinks with air as the working fluid is limited. However, macroscale heat sinks with air as the working fluid are commonly used in various systems. Therefore, there have been several studies for investigating the thermal performance of macroscale plate-fin heat sinks under partial heating with air as the working fluid. For example, Emekwuru et al. numerically investigated the influence of three different partial heating positions on the thermal performance of air-cooled macroscale heat sinks [21]. They showed that the thermal resistance is minimized when the partial heating position is centrally located, for most Reynolds numbers. Yoon et al. extensively conducted numerical studies on the thermal performance of plate-fin heat sinks according to the partial heating position to determine the optimal heating position [14]. They showed that the thermal performance is maximized when the heating position is located on the downstream side near the center of the heat sink.

However, first, to the best of our knowledge, intensive experimental studies on the thermal performances of macroscale plate-fin heat sinks under partial heating with air as the working fluid have not been systematically conducted for various heating locations, flow rates, and channel widths. In particular, previous studies on macroscale plate-fin heat sinks [14,21] was focused on heat sinks under turbulent flows with very high flow rates, and it is uncertain whether their conclusions are applicable for heat sinks under laminar developing flows with low flow rates.

Second, heat sinks used in the practical situation showed heat losses through the front, back, and sides of the heat sink (q_loss,f, q_loss,b, and q_loss,s in Figure 1). However, there were no previous studies on the effects of these heat losses on the optimal heating position of macroscale plate-fin heat sinks under partial heating.

Third, a full three-dimensional numerical simulation could estimate the thermal performance accurately but required a time-consuming code writing process. In addition, commercial numerical simulation programs might have cost issues. Therefore, sometimes it is useful to perform several experiments and to investigate the effects of important engineering parameters on thermal performance by using a one-dimensional model that can predict experimental results.

In this study, plate-fin heat sinks under partial heating with air as the working fluid were experimentally investigated. The base temperature profiles of plate-fin heat sinks under laminar developing flows were measured for various heating lengths, heating positions, flow rates, and channel widths. From the experimental data, the effects of various engineering parameters on the base temperature profile and the thermal performance were investigated. Finally, the characteristics of the optimal heating position were investigated. It is shown that the conclusions of the previous studies [14,21] on optimal heating position of plate-fin heat sink under turbulent flow did not apply to the heat sink under the laminar developing flow examined in this study. In is also shown that the optimal heating position could change significantly due to heat losses through the front and back of the heat sink. In addition, a simple one-dimensional numerical model for predicting the thermal performances is presented.

2. Experimental Procedure

A schematic diagram of a heat sink is shown in Figure 1. The length L, width W, height H, base thickness t_b, and fin thickness t_f of the heat sink were 20 cm, 10 cm, 3 cm, 1 cm, and 1 mm, respectively. The experiment was conducted for five different combinations of heating lengths and heating positions, four different flow rates, and two different channel widths, as listed in

Table 1. Design parameters for the experiment.

N	wc [mm]	Lh/L	Lc/L	Flow Rate Q [m3/min]
25	3	1.0	0.5	0.2, 0.4, 0.6, 0.8
		0.6	0.5	0.2, 0.4, 0.6, 0.8
		0.2	0.3	0.2, 0.4, 0.6, 0.8
			0.5	0.2, 0.4, 0.6, 0.8
			0.7	0.2, 0.4, 0.6, 0.8
13	7	1.0	0.5	0.2, 0.4, 0.6, 0.8
		0.6	0.5	0.2, 0.4, 0.6, 0.8
		0.2	0.3	0.2, 0.4, 0.6, 0.8
			0.5	0.2, 0.4, 0.6, 0.8
			0.7	0.2, 0.4, 0.6, 0.8

. In this table, N, w_c, L_h, and L_c are the fin number, channel width, heated length, and the distance from the upstream end to the center of the heated area, respectively. The heat sink was made of SUS304 (k = 16.2 W/m K). As shown in Figure 2, 22 T-type thermocouples were attached to the base of the heat sink. More specifically, in order to measure the profile of the base temperature T_b along the flow direction, thermocouples were installed at 11 points in the x direction. The thermocouples were attached at two points in the y direction to check that the measured base temperature profile along the flow direction was reliable. Silver epoxy was used to minimize contact thermal resistance between the thermocouple and the base. Four other T-type thermocouples were placed at the inlet of the test section to measure the ambient temperature T_amb. As shown in Figure 3, the signals from the thermocouples were converted to temperature data using a data acquisition system (34970A DAQ; Agilent Technology) and were stored in a computer. As shown in Figure 2, five film heaters of the same size were attached to the bottom surface of the heat sink base to locally apply heat to the heat sink. The film heater was made of SUS304 and was attached using a Kapton tape. These five heaters were powered and controlled by a DC power supply (PL-3005D; Protek) to be turned on and off, independently.

The total power input to the heater was fixed at 40 W. Five different combinations of heating lengths and heating positions were investigated in this study, as listed in Table 1. As shown in Figure 3, the heat sink with the attached thermocouples and heaters was installed inside a rectangular duct in acrylic. The duct was connected to a wind tunnel system with a nozzle flow meter and a blower (TB-150; Innotech) to measure the flow rate of air while generating air flow in the duct. The nozzle flow meter consisted of the nozzle and the differential pressure meter (FCO332; Furness Controls), and it measured the volume flow rate by measuring pressure difference between the inlet and the outlet of the nozzle caused by flow restriction by the nozzle. Four different flow rates were investigated in this study, as listed in Table 1. Each measurement was repeated three times to ensure the reliability of data. The temperature was measured until the temperature change dropped to less than 0.1 °C for 10 min. After the experiment, the uncertainty of the data were analyzed, and details of the analysis were described in Reference [22] and Appendix A.

3. Results

Figure 4a–e show the profiles of the difference between the base temperature T_b and the ambient temperature T_amb, along the flow direction for five different combinations of heating lengths and heating positions and four different flow rates when the channel width was 7 mm. The various trends of the temperature profile observed in these figures were as follows.

(a)

In all cases shown in Figure 4a–e, regardless of the value of x, the base temperature decreased as the flow rate increased. This was mainly because the temperature of the fluid flowing inside the heat sink decreased as the flow rate increased. This was also because the local heat transfer coefficient, which was inversely proportional to the temperature difference between the fluid temperature and the base temperature, increased as the flow rate increased.

(b)

The extent to which the base temperature decreased with an increase in the flow rate, decreased as the flow rate increased.

(c)

The point at which the base temperature was maximized always existed in the portion where the heat sink was heated. When the size of the heating portion was equal to the size of the heat sink, the point at which the base temperature was maximized lay almost at the end of the heating portion where x was the largest. When the size of the heating portion was much smaller than the size of the heat sink, the point where the base temperature was maximized was almost at the center of the heating portion.

(d)

The base temperature at x = L_c + Δx was larger than the base temperature at x = L_c − Δx, regardless of the value of Δx. This was mainly because the fluid temperature monotonically increased as x increased.

(e)

As shown in Figure 4a, when the heat sink was uniformly heated, the base temperature increased monotonically with an increase in x. This was because the temperature of the fluid increased as x increased. This was also because the heat transfer coefficient, which was inversely proportional to the temperature difference between the fluid temperature and the base temperature, decreased as x increased.

Figure 5a–e show the profiles of the difference between the base temperature T_b and the ambient temperature T_amb along the flow direction when the channel width was 3 mm. The trends in the temperature profile were consistent with the previously described trends for the channel width of 7 mm.

Figure 6a,b show the thermal resistances for five different combinations of heating lengths and heating positions, four different flow rates, and two different channel widths. Here, the thermal resistance R was defined as the difference between the maximum temperature of the heat sink base T_b,max and the ambient temperature T_amb divided by the amount of heat q applied to the heat sink. Therefore,

$$R=\frac{T_{b,max}-T_{amb}}{q}.$$

(1)

The various characteristics of thermal resistance observed in these figures are as follows.

(a)

Regardless of the heating position and channel width, the thermal resistance decreased monotonically as the flow rate increased. This was because the temperature of the cooling fluid filling the inside of the heat sink decreased as the flow rate increased.

(b)

Regardless of the channel width and flow rate, the thermal resistance increased as the heating length decreased. This was because the heat sink base was more heavily heated locally, owing to an increase in heat flux (amount of heat per unit area) applied to the heated portion of the heat sink base as the heating length decreased. When the heat sink base was uniformly heated, heat was uniformly dissipated from the heat sink to the fluid through the heat sink surface. In contrast, only a part of the surface was mainly used for the heat dissipation in the case of the locally heated heat sink.

(c)

There was an optimal heating position that minimized the thermal resistance when the heating length was fixed. However, as shown in Figure 6a, the optimal heating position was not fixed and could be changed by changing the flow rate.

Finally, to investigate the characteristics of characteristics of the optimal heating position, we developed a relatively simple one-dimensional numerical model that could roughly predict the experimental results (further explanation on a one-dimensional numerical model is given in Appendix B). Finally, Figure 7 shows the thermal resistances for various heating positions and flow rates when the heating length was fixed. The characteristics of the optimal heating position observed from Figure 7 were as follows.

(a)

When the flow rate was fixed, there was an optimal heating position that minimized the thermal resistance.

(b)

The optimal heating position was not independent of the flow rate. In this study, the optimal heating position moved toward the smaller x as the flow rate increased. Therefore, when controlling the flow rate from the fan in an actual situation, this fact should be considered to determine the heating position.

(c)

If the heating position moved slightly in the positive x direction or in the negative x direction from the optimal heating position, the thermal resistance did not increase significantly. Therefore, in an actual situation, a slight change of the heating position from the optimal heating position was acceptable.

(d)

However, if the heating position was far from the optimal heating position, the thermal resistance could be very large. Therefore, in an actual situation, the heating position should not be close to the front or rear ends of the heat sink.

(e)

As presented earlier, Emekwuru et al. showed that the thermal resistance was minimized when the heating position was centrally located for most Reynolds numbers [21]. On the other hand, Yoon et al. showed that the thermal performance was maximized when the heating position was located on the downstream side near the center of the heat sink [14]. However, these conclusions from the previous studies did not apply to the situation examined in this study. Figure 7 indicates that the thermal performance was maximized when the heating position was located on the upstream side. In addition, Figure 6a also shows that the optimal heating position was located on the upstream side in some cases. The main reason why the conclusions from the previous studies did not apply to the situation examined in this study was that the previous study was focused on heat sinks under turbulent flows with very high flow rates and the present experiments were conducted for heat sinks under laminar developing flows. The fact that Lelea also observed that upstream heating had a better thermal performance than central or downstream heating for the heat sink under laminar flow in his study [19] supported this reasoning, although his study was focused on water-cooled microchannel heat sinks.

The heat sinks used in the practical situations showed heat losses through the front, back, and sides of the heat sink (q_loss,f, q_loss,b, and q_loss,s in Figure 1). Therefore, in this study, effects of these heat losses on the optimal heating position were investigated. Figure 8, Figure 9 and Figure 10 show the thermal resistances of the heat sinks calculated by one-dimensional models for various thermal resistances for the heat losses through the front, back, and sides of the heat sinks, respectively. In these figures, R_loss,f and R_loss,b are the thermal-resistances-related heat losses through the front and back of the heat sink, respectively. R′_loss,s is the thermal resistance per unit length related to heat loss through the sides of the heat sink, as explained in Appendix B. The characteristics of the optimal heating position observed in Figure 8, Figure 9 and Figure 10 were as follows.

(a)

The optimal heating position could change significantly due to heat losses through the front and back of heat sink. Therefore, even when the heat sink with the same dimensions was under the same flow rate, the optimal heating position could be completely different depending on how the heat sink was connected to the other devices in the thermal system.

(b)

The optimal heating position moved toward the smaller x as the heat loss through the front of the heat sink increased.

(c)

The optimal heating position moved toward the larger x as the heat loss through the back of the heat sink increased.

(d)

The optimal heating position was almost independent to the heat loss through the sides of the heat sink.

In addition, Figure 11 shows the thermal resistances for various heated lengths. As shown in the figure, the optimal heating position also did not depend strongly on the heated length, if the change in heat transfer coefficient due to the heated length was not significant.

4. Conclusions

In this study, macroscale plate-fin heat sinks under partial heating with air as the working fluid were experimentally investigated. The base temperature profiles of the plate-fin heat sinks under laminar developing flows were measured for various heating lengths, heating positions, flow rates, and channel widths. From the experimental data, the effects of various engineering parameters on the base temperature profile and the thermal performance were investigated. Finally, the characteristics of the optimal heating position were investigated.

The following were the new findings on the optimal heating position of the partially heated plate-fin heat sinks:

(a)

The optimal heating position was on the upstream side in the case of the heat sinks under a laminar developing flow that were investigated in the present study. On the contrary, as shown in a previous study [14], the optimal heating position was on the downstream side in the case of the heat sinks under turbulent flow.

(b)

The optimal heating position could change significantly due to heat losses through the front and back of heat sink. Therefore, even when the heat sink with the same dimensions was under the same flow rate, the optimal heating position could be completely different depending on how the heat sink was connected to other devices in the thermal system.

(c)

The optimal heating position was independent to the heat loss through the sides of the heat sink. The optimal heating position also did not depend strongly on the heated length.

(d)

The one-dimensional numerical model with empirical coefficients could reflect the important trends in the measured temperature profiles, thermal resistances, and optimal heating lengths.

In addition, the following are some characteristics of the partially heated plate-fin heat sinks presented in this study:

(a)

The point at which the base temperature was maximized always existed in the portion where the heat sink was heated. When the size of the heating portion was equal to the size of the heat sink, the point at which the base temperature was maximized lay almost at the end of the heating portion where x was the largest. When the size of the heating portion was much smaller than the size of the heat sink, the point where the base temperature was maximized was almost at the center of the heating portion.

(b)

Regardless of the heating position and the channel width, the thermal resistance decreased monotonically as the flow rate increased. Regardless of the channel width and flow rate, the thermal resistance increased as the heating length decreased.

(c)

The optimal heating position was not independent of the flow rate.

(d)

If the heating position moved slightly in the positive x direction or in the negative x direction from the optimal heating position, the thermal resistance did not increase significantly. However, if the heating position was far from the optimal heating position, the thermal resistance could be very large.