1. Introduction
Heat exchangers are widely applied to many industrial applications, including heating in boilers and cooling in condensers. The small heat exchangers, such as finned heat sinks, are also popular ones for instantaneous water heaters and 3C cooling devices. Since that the modern 3C electronic chips are increased in the computing speeds and narrowed in the dimensions, the operating temperature of such chips goes up greatly. In order to maintain a normal operating temperature for the modern chips, the total heat exchange surface area and the structural complexity of the heat sink installed on the chips are increased. Therefore, the overall convection heat transfer between the fluid and fin matrix can be enhanced effectively due to the increase of heat dispersion area and the improvement of fluid turbulence. The result is better reliability and a longer service life for electronic components and machinery. This kind of finned heat sink is easily manufactured and inexpensive. The key factors that influence the performance of finned heat sink include the fluid velocity, the thermal properties of the fluid and the fins, the height and cross-sectional shape of the fins, the arrangement and relative pitch for the fin array, the bypass effect, and so on.
Many studies have been made for the effects of all these factors on the heat transfer of fin arrays. Vanfossen [
1], as well as Brigham and Vanfossen [
2], discussed the heat transfer of staggered pin-fin arrays, and indicated that the long pin-fin (
H/d = 4) transferred heat better than short ones (
H/d = 1/2 and 2). The heat transfer capacity of eight-row pin-fins was slightly higher than that of four-row pin-fins, and the pin-fin surface heat transfer coefficient was about 35% higher than the end-wall surface. Metzger
et al. [
3] indicated that the heat transfer capacity of oblique pin-fins was 20% higher than that of vertical pin-fins, but the pressure drop was doubled. In addition, they evaluated the pin-fin surface heat transfer coefficient at about two times that of the end-wall surface. Zukauskas and Ulinskas [
4] established empirical correction equations for the heat transfer and pressure drop of in-line and staggered round pin arrays. Armstrong and Winstanley [
5] made retrospective comments on the effect of pin-fin height and pitch on the heat transfer and flow resistance. Jubran
et al. [
6] indicated that the optimum pin-fin pitch was 2.5 times the pin-fin diameter. Tahat
et al. [
7,
8] found that the optimum pitch of in-line pin-fin array was 1.3 times the pin-fin diameter, and the optimum pitch for a staggered pin-fin array was 2.2 times the pin-fin diameter. Babus’Haq
et al. [
9] suggested that the optimum transverse pitch of a pin-fin array was 2.04 times the pin-fin diameter, and the optimum longitudinal pitch was 1.63~1.95 times the pin-fin diameter. Sara
et al. [
10,
11] discussed the heat transfer and pressure drop characteristics of an in-line pin-fin array in a channel with a fixed transverse pin-fin pitch and a variable longitudinal pitch. Wang
et al. [
12] reviewed shell-and-tube heat exchangers. They indicated that the multi-objectives optimization for air-cooled heat exchangers should consider the heat transfer, pumper power, space usage and other economic influence factors. Chen
et al. [
13] carried out the optimizations of H- and X-shaped heat exchangers by taking the maximum ratio of the dimensionless heat transfer rate to the dimensionless total pumping power as optimization objective. They reported that the performance of the heat exchanger with X-shaped structure was superior to that with H-shaped structure. Li
et al. [
14] experimentally investigated the effects of material thermal conductivity and thermal boundary conditions (
i.e., conjugate and convective boundary conditions) on the conjugate heat transfer performance of pin fin arrays. They indicated that thermal conductivity could strongly influence the heat transfer performance. The thermal gradient along the wall thickness increased as the material thermal conductivity dropped; the temperature difference between convective and conjugate problems also raised. It would be not desirable in cooling design. Jadhav and Balaji [
15] investigated the fluid flow and the heat transfer behaviors of a vertical channel with detached pin-fin arrays arranged in staggered manner on two opposite end walls. Their results found that the volume ratio of pin fins to total channel was the most dominating variable for both the pressure drop and the thermal resistance. They also perform a multi-objective optimization by using the multi-objective evolutionary algorithm to minimize the thermal resistance and the pumping power simultaneously.
Apart from finned heat sink, metallic porous media are also employed as heat exchangers. Metal foam, with high permeability, is one of the popular porous materials. Schampheleire
et al. [
16] reviewed the available methods to study thermal applications with open-cell metal foam. Chen and Wang [
17] experimentally studied the heat transfer of the heat sink by employing non-uniform arrangements of metal foams for liquid cooling. It is found that the thermal resistance could be reduced by more than 62% as compared to that of empty plate design. For a given pumping power, the optimal metal-foam arrangement to have the best heat transfer performance is that the PPI (pores per inch) of metal foam descending from the inlet to the outlet of the heat sink. Abadi
et al. [
18] experimental explored the single-phase heat transfer mechanism of R245fa refrigerant in a metal-foam-filled plate heat exchanger. Their result demonstrated that, compared to the empty-channel heat exchanger, inserting 60-PPI metal foam promoted the heat transfer coefficient by up to 5.1 times. However, it also had the greatest pressure drop, which was 5.7 times that of an empty-channel heat exchanger. Metal foams not only extend lots of heat dispersion areas, but also increase fluid turbulence significantly, enhancing the total heat transfer capacity efficiently.
However, the porous structure reduces the effective thermal conductivity simultaneously. Inserting a metal core or fins into metal foams is one of the remedy methods to increase the effective thermal conductivity. It is a benefit to the conjugate heat transfer. Feng
et al. [
19] presents a study on finned metal foam (FMF) and metal foam (MF) heat sinks under impinging air jet cooling. They reported that the heat transfer of FMF heat sinks could be 1.5–2.8 times that of the MF heat sinks. Shih
et al. [
20] experimentally investigated the heat transfer characteristics of aluminum-foam heat sinks with the solid aluminum core under impinging-jet flow conditions. The Nusselt number of the aluminum-foam heat sink with a solid aluminum core reached a maximum of approximately 2.2 times that of the sample without a core.
This paper offers three designs of cross-runner heat exchangers. As shown in
Figure 1, there are regularly-staggered fins in a rectangular channel to form multiple cross-runners, so that the heat exchange area per unit volume is greatly enlarged, and the fluid is separated and merged continuously in the cross-runners. This increases flow turbulence to further enhance heat transfer. Three kinds of configurations employed were, (1) the aluminum alloy heat exchanger with a staggered rectangular-fin array (Model A); (2) the aluminum alloy heat exchanger with a staggered round pin-fin array (Model B); and (3) the copper heat exchanger sintered by multiple copper sheets with rectangular punched holes forming cross-runners (Model C). Among the present three configurations, Model C has the very similar open-cell structure like metal foam, but with high effective thermal conductivity. These cross-runner heat exchangers were manufactured and an air-cooled heat transfer experimental platform was built. The pressure drop characteristics and heat transfer capacity of each of these three types of cross-runner heat exchangers were investigated. The feasibility of using a cross-runner heat exchanger for instantaneous water heating was also examined.
3. Results and Discussion
Figure 8 shows the relationship between the dimensionless pressure drop and the Reynolds number for different test heat exchangers. The lowest pressure drop was found in the model A. Model B showed a medium pressure drop. Model C showed the highest pressure drop. As shown in
Table 1, Model C has the lowest porosity among the present test heat exchangers, resulting in the largest actual average aperture velocity in the cross runners of heat exchanger. Moreover, the heat transfer area (
AHT) of Model C is quite large in a fixed volume (the second one in the test heat exchangers), increasing the skin friction and form drag. Therefore, at the same Reynolds number (
i.e., the same volume flow rate), the maximum pressure drop is resulted from Model C. In addition, for the heat exchangers with the same configuration, for example Models A-1, A-2, and A-3, as well as Models B-1 and B-2, lower height would lead bigger pressure drop due to the interaction result of increasing actual average aperture velocity and decreasing heat-transfer area in the cross runners. In order to identify the effects of actual average aperture velocity and heat-transfer area on the pressure drop, the relation between the dimensionless pressure drop (Δ
P*) and the Reynolds number based on the average aperture velocity (
Re*) is plotted in
Figure 9. It is found that, for the heat exchangers with the same configuration and at the same
Re*, increasing the height of heat-exchanger promoted Δ
P* because of the increase of heat-transfer area. The Δ
P* increased with the power of
Re*. The power of
Re* ranged from 1.411 to 1.862 and the average value was 1.756. According to the relationship between Δ
P* and
Re* as well as the heat-transfer area in
Table 1, an empirical correlation of Δ
P* in terms of
Re*, ε and
AHT/W/L with deviation less than 10% is expressed as Equation (6) and Equation (7).
Figure 10 shows the experimental data and predicting results.
Figure 11 shows the relationship between the Nusselt number (
Nu) and Reynolds number (
Re) when the heat exchangers were cooled by air. The result demonstrates that for the same Reynolds number, the Nusselt number of Model C was far larger than those of Models A and B. It depicts that Model C has a much greater heat exchange capacity. Additionally, the Nusselt number of Model B was medium and that of Model A was the lowest. It should be explained as follows: for the heat exchangers herein, the heat transfer mechanism is the conjugate heat transfer combining, firstly, thermal conduction from the heated wall to the fin surface, and then series connection with thermal convection from the fin surface to the fluid. Therefore, the key factors influencing the overall heat transfer are the effective thermal conductivity (
ke), the total heat-transfer area (
AHT), the porosity (ε) and the porous-like structure. The bigger effective thermal conductivity (
ke) is desired for the better thermal conduction, while larger heat-transfer area (
AHT), lower porosity (ε) and the complex porous-like structure are necessary for obtaining more effective forced convection heat transfer. See
Table 1, the Model C is the most consistent with the above-mentioned conditions and following with Model B and Model A, sequentially. Furthermore, a semi-empirical correlation of the Nusselt number is derived according to the conjugate heat transfer mechanism.
Substituting Equations (4) and (9)–(11) into (8), one can obtain the following expression:
Rearranging Equation (12) and the solid-to-fluid Nusselt number (
Nusf) in terms of the Reynolds number based on average aperture velocity and hydraulic diameter (
ReDh) will be obtained as Equation (13):
where
Qc is the convective heat transferred to air flow;
H and
L are the internal height and length of the heat exchanger;
Tw is the average temperature of the heated wall;
Tf is the bulk air mean temperature through the heat exchanger;
A (=
W ×
L) is the area of the heated surface;
AHT and
ke are the total heat-transfer surface area and effective thermal conductivity of the heat exchanger;
kf is the thermal conductivity of fluid;
hsf is the heat transfer coefficient between the fluid and the solid fins in the heat exchanger;
Vvoid is the void volume in the heat exchanger and
Dh is the porous hydraulic diameter of cross-runners in the heat exchanger.
According to all the air-cooling experimental data in the present study, the relevant constants
C2 and
n2 are listed in
Table 2. The experimental results and the prediction by the empirical correlation Equation (13) are shown in
Figure 12. Both of the solid-to-fluid Nusselt number (
Nusf) and the average-aperture-velocity Reynolds number (
ReDh) are based on the porous hydraulic diameter (
Dh). Therefore, the present correlation can be more widely used. The Nusselt number predicted by the most popular formula of Dittus and Boelter [
23] is also plotted in
Figure 12, showing a reasonable comparison result. The average deviation between the experimental data and the present prediction is less than 1%.
Figure 13 shows the relationship between Nusselt number and dimensionless pumping power. Under the same pumping power, the heat transfer capacity of Model C is 2.27 and 1.67 times that of Model A and Model B, respectively. This makes it clear that the heat transfer enhancement of Model C is adequate compensation for the increase in flow resistance.
Figure 14 and
Figure 15 show the results of the water-cooling measurement. Models A-1, A-2, A-3, and C were selected as the typical cases.
Figure 14 displays the relationship between the temperature rise (
i.e., Δ
T, water temperature difference between inlet and outlet of the heat exchanger) and water flow rate at the thermal-equilibrium condition. The theoretical value predicted by the energy-balance method is also plotted in
Figure 14. It is found that the Δ
T of Model C, with an excellent heat transfer capacity, almost agreed with theoretical value. It means the very high heat-transfer performance of Model C almost resulted in no heat loss. In other words, almost all the input electrical power was transmitted by the Model C to the water flow. By comparing with Model C, Model A has 7.7%–15% of input heat to be lost at the present range of water flow rate from 2 to 5 L/min. In general, under the no-insulation condition, the heat exchanger with better heat transfer capacity would lead less heat loss. It would be an energy-saving device.
Figure 15 shows that the steady-state temperature can be reached in about 75 s, this conserves energy and demonstrates that the Model C can be useful as a heat exchanger in the application of instantaneous water heating. The model C heat exchanger design is a practical one that has great commercial potential.