Increasing the efficiency of a Peltier device by assessing the thermal performance of liquid-cooled microchannel heat sinks

Water is, arguably, Earth's most valuable and vital resource. Devices that extract water from the atmosphere have been intensely researched as a means of harvesting potable water in environments where it is otherwise scarce. One such device is a Thermoelectric Cooler (TEC); a device that utilises the Peltier effect to cool a system. TECs are a promising solution for atmospheric water generation (AWG) over their competitors due to their simplicity and refrigeration capabilities. Despite these advantages, TECs are still considered mostly inefficient as they demand relatively high costs and energy consumption. This meta-analysis focuses on optimising the efficiency of small-scale Peltier devices. It explores the means of optimising the liquid cooled heat sink by using a specific flow field microchannel configuration such that less pumping power is required to push the coolant and more energy can be saved. A combination of optimal operating current of the Peltier device and of a novel flow liquid-cooled microchannel heatsink configuration with bifurcated fins using Galinstan as a coolant promises a significant increase in water production per unit of energy consumption for the AWG system.


Qc
Cooling of a TEC, which behaves as a heat pump redistributing heat from the cold side to the hot side [13]. A TEC typically features a p-n semiconductor array (junction) encased in ceramic plates on both the top and the bottom frames for the hot and cold sides of a Peltier device, illustrated in Figure 1. The flow of direct current through the device will produce a temperature gradient between the two plates which in turn, generates a thermal flux, transferring heat from one side to another [10,14]. To prevent overheating, a heatsink must be attached to the hot side to dissipate the heat produced by the module and the Joule heat produced consequence of the electricity supply [13,14].  Simplified schematic of an Atmospheric Water Generator where a thermoelectric cooler drives the heat from the Cold Side to the Hot Side, allowing for water condensation and collection. Hot, humid air is passed over the heat sink, creating an electric current that further cools the opposite side. The water vapour in the hot air is cooled to its dew point and allowed to condense. Power input is connected to the semiconductor array.
When the cold side of the device reaches the ambient dew point, the contacting water vapour condenses into water droplets [10,15]. Figure 2 illustrates a simplified schematic of an AWG based on a TEC module, showing the main components and the direction of air flow.
The temperature distribution of the TEC's hot side is impacted by the design of the microchannels [16]. The standard topology is a Parallel network design; however, benefits have been noted in U-Shaped and S-Shaped designs that surpass those of the former [16]. Although these shapes generate somewhat even temperature distributions on the surface, they also reduce the temperature gradient across the device [17]. Overcoming this, river-like microchannel designs with bifurcations have been shown to not only normalise the temperature across the TEC more evenly but also reduce the change in pressure from the inlet to the outlet, removing the need for extra work in the form of pumping power to be applied to the system [17]. The performance of a river-like microchannel design is more effective than that of a Parallel, U-Shaped, or S-Shaped network as it reduces the thermal resistance R, cooling the cold side more efficiently [17].
Thermoelectric cooling applications have specific heat sink requirements. Often, there will be different mechanical necessities that convolute the design. Considering each case is unique, it is impractical to propose the same heat sink design for both, large and small Peltier devices. Nevertheless, the most common applications are based on forced convection, whereby fans are used to move air around the system [14]. Cooling air is passed through the length of the heat sink and directed to the focal point of the fins, egressing it through both open ends, similar to the large Peltier device in Figure 2. Most experiments that model realistic scenarios use a temperature range like that of what a TEC may experience in a desert environment; between 296 K and 388 K. Ultimately, determining the efficacy of the TEC's cooling process is the Coefficient of Performance (COP). It is defined as the ratio of cooling capacity, Qc, to the total power input, Win [5]:

Liquid-Cooled Heat Sink
Liquid cooled heat sinks provide the highest thermal performance per unit volume and, when optimally designed, can exhibit a very low thermal resistance. Among all the various types of heat sink modules, the microchannel heat sink has garnered attention for its ability to remove high heat flux density ranging from 100 to 1000 W cm -2 [18]. To quantify the cooling performance of a heat sink, its performance is evaluated by the ratio of the difference between the maximum and minimum surface temperature, + , against the heat flux, --, applied as shown in Eq. 2 [19], where /"0 11 # is the maximum temperature difference on a heating surface per unit of heat flux (K W -1 m -2 ).
However, a more accurate analysis of the heat sink can be obtained when using the average temperatures rather than individual data points. The average low temperature is an important variable and should be monitored, and as a result, a parameter forms as shown in Eq. 3 [19].
PAM Review 2020 7 R represents thermal resistance and is the ratio of the difference between the average surface temperature, + , $$$ and the temperature of the input fluid, 5 (6 , against the applied heat flux, --. An efficient heat sink will provide better heat transfer, resulting in a lower average surface temperature and in turn a lower thermal resistance [19]. An ideal sink with the greatest heat transfer will have both /(0 11 ) and R at the lowest possible values [19]. Nonetheless, achieving both minima is practically impossible due to both variables strongly influencing each other. Therefore, to optimise the efficiency of a heat sink without any drawbacks, other design elements should be studied carefully, such as the input pumping power required to drive the coolant through the heat sink.
Where v is the volumetric flow rate of the coolant in the heat sink and is the pressure drop across the microchannel, the pumping power P is [17]: The smaller the microchannels the greater the heat transfer area, however, if the flow distribution of the fluid is not facilitated appropriately, the heat sink's efficiency decreases due to the thermal stress and increase in pumping power [19]. The local heat coefficient is: where ℎ &(() is the local heat transfer coefficient of the microchannels (W m -2 K -1 ), is the heat flux (W), ; represents the heat transfer area (m 2 ). (() is the local temperature of the microchannel wall surface, and 5 is the local mixed-mean fluid temperature between the inlet and the outlet, both measured in degrees Kelvin [17].

Microchannel Topology
In microchannel topology, Parallel, U-Shaped, and S-Shaped patterns are very practical to manufacture, however, their designs produce high temperature gradients and high hydraulic resistance, two factors that negatively impact heat transfer [20]. To overcome these disadvantages to the heat exchange process, non-uniform microchannels can be used as they prove more efficient in heat dissipation than conventional uniform microchannel designs [20,21]. Additionally, multistage bifurcations improve thermal performance, whereas nil stage bifurcations do not as they require large pumping forces when compared to natural flow designs, and at higher Reynolds numbers [16]. In order to maximise the heat transfer across a heat sink, the heat exchange area must be increased [22]. This process is most effectively done by creating organic microchannel topologies that, by extension, create small islands that redistribute the heat to areas of the heat sink being underutilised or not utilised at all [22].

Reynolds Number
The Reynolds number (Re) is the ratio of inertial forces to viscosity, both pertaining to a liquid [23]. Where u is the flow speed (ms -1 ), L is the characteristic linear dimension (m), and v is the kinematic viscosity (m 2 s -1 ), the Reynolds number can be calculated as follows [23]: This ratio is significant in deducing the efficiency of a liquid-cooled heat sink as it describes how a fluid will flow through the microchannels, and by extension, how heat will be transported out of the system [23]. A lower Reynolds number, in the order of hundreds, suggests laminar flow and a stable flow rate [23]. Both flow resistance and heat transfer increase with the flow rate, and in maximising these properties, so does the efficiency, as the improvement of heat exchange is more cost-effective when compared to the reduction in power consumption [20].

Objective
A forced convection technique is not viable for smaller heat sinks as there is simply not enough space. Here, a liquid cooled microchannel heat sink can be advantageous as it requires a much smaller space, is suitable for high flux heat dissipation, and offers a higher heat capacity and thermal conductivity when compared to generic convection methods [19,24]. Investigations have been conducted on microchannel heat sinks, however, there is limited focus on the distribution of flow within the microchannels [19]. Less uniform flow distribution of the microchannels not only decreases the heat sink's efficiency by raising local thermal stress, but also generates high pressure losses between the inlet and the outlet requiring greater pumping power consumption for operation [19]. Considering this, our meta-study investigates the optimal coolant fluid and flow distribution design for an efficient Peltier device, whilst also comparing microchannel topologies.

Method
The aim of this meta study is to aggregate results and conclusions from multiple studies regarding the optimisation of liquid cooled heat sink that are used in TEC modules, synthesising an analysis. Information was obtained from academic sources such as, SCOPUS, Science Direct, IEEE Xplore, and INSPEC, with a publishing date within the past decade. Imposing this limitation provides contemporary solutions from contemporary technologies.
Furthermore, the research scope was restricted to thermodynamics, utilising keywords such as thermoelectric cooling, thermoelectric generators, and atmospheric water generation, eliminating the possibility of using irrelevant information. Combining these limitations ensured that the sources used are of adequate quality, presenting theoretical information and experimental data with the following benchmarks: it contains theoretical knowledge of the thermodynamic process in a Peltier module, it contains experimental data which quantifies the translation and distribution of heat in the heat sink, and it explores the implication of optimisation in real-world application. The data presented in Figure  9a was calculated using Eq. 5, where Q is 300W, and the data Figure 8. Each hm was calculated as an average of each bifurcations' respective parameters, (area and temperature difference), and presented as a line graph. Figure 9b also represents averages, presenting the average temperature difference across the microchannels in each case. Figures 3-6, 8, and 10 were derived by manually reading the data points from the actual graphs in the respective paper hence there may be slight discrepancies with the position of the plot points but the trends for each case are carefully preserved. Figure 7 was adapted from the simulations run by Li et al. and Koga et al. It should be noted that the impact of the heat sink's material has been ignored for this study and is a variable recommended by the authors for further study.

Single vs Bifurcated Microchannel Heat Sinks
To understand the significance of microchannel topology in the design and performance analysis of a heat sink, the experimental study of heat sinks with and without bifurcations in the microchannel is referred to [17]. It can be stated that bifurcation poses a potential advantage when designed properly. To explore this, four cases of bifurcations along with one case of non-bifurcation (single continuous microchannel), as shown in Table 1, were investigated [17]. The microchannel length and the number of microchannels in the 1 st and 2 nd segments are given by > & ? and > & ? respectively. The ratio of the lengths, Ψ C and the ratio of the number of microchannels Ψ A is also given. Variables such as the microchannel height, substrate thickness, cover plate thickness, and wall thickness are all constant in each case [17]. To understand the significance of improving the design of bifurcation three constructal designs of inlet bifurcation microchannel are also considered for comparison as described in Table 2 [25]. The microchannel heat sink with two bifurcations, the second being in the front part 4 The microchannel heat sink with bifurcations, the second being in the back part The heat transfer coefficient, hm, of the microchannel increases with the increase in flow rate as per Eq. 5 [17]. However, at a high inlet velocity, the drop in the pumping pressure also increases. According to Figure 3a, Case 5 has the highest pressure drop with Case 1 being the lowest. This is because at the first segment of the junction the pressure decreases slowly and linearly but then increases at the position of split and then again decreases sharply and linearly. This happens since velocity gradually becomes smaller before approaching the bifurcated position and then gradually becomes larger after reaching the bifurcation position [17]. Hence, the flow pressure in the bifurcated heat sink is always higher than the singular continuous microchannel. As a result, according to Eq. 4 the bifurcated microchannel requires a greater pumping power for generating this high pressure to push the coolant through the microchannels.
Furthermore, the experimental result with the constructal inlet design also supports the fact that the velocity gradually reduces before approaching the bifurcation position and then gradually increases after passing it [25]. This can be seen in Figure 3b where it is found that the pressure-drop of the two-stage bifurcation microchannel (Cond. 2, 3 & 4) is higher than that of the one-stage bifurcation microchannel (Cond. 1). Moreover, for the two-stage bifurcation microchannel where the shorter plate is inserted at the front (Cond. 3) of the entrance region, the pressure drop is slightly less than that for the other type of the two-stage bifurcation microchannel.   To assess the thermal capability of the microchannel heat sinks at a fixed Re value, the average thermal resistance is taken into consideration. The connections between the average thermal resistance and Re are given in Figure 5. From Figure 5a, it is indicative that the average thermal resistance is inversely proportional to the Re for all cases. Likewise, for a constant microchannel length ratio, C , the thermal resistance is also inversely proportional to the bifurcation ratio, A . In addition, Figure 5 represents the relationship between thermal resistance and pumping power P. According to Figure 5b, the thermal resistance decreases within increasing pumping power for all cases. For a given microchannel number ratio, Ψ A , the overall thermal resistance of the bifurcating microchannel with a shorter length of the first segment (Cases 4 and 5) is always lower than that with a longer length of the first segment (Cases 2 and 3) at identical pumping power. This analysis indicates that the thermal performance of the microchannel heat sink operates more efficiently with bifurcations, as splitting the flow will reduce more the thermal resistance when compared to a singular continuous microchannel. However, this justification is only applicable if the bifurcations are designed considering other variables, such as the pumping power. As the demand for pumping power increases, the overall thermal performance of the inlet design can be assessed to identify an ideal bifurcation design i.e. an ideal balance between a low thermal resistivity and a low required pumping power [25]. From Figure 6, we can conclude that at a constant pumping power, the two-stage bifurcation microchannel with shorter plate at the back (Cond. 4) of the sub-microchannel provides lower overall thermal resistance than the other type of two-stage bifurcation microchannel. To summarise, bifurcated microchannel heat sinks with a larger bifurcation ratio may be better for heat dissipation given the length ratio is fixed [17]. The drawback of this attribute is the requirement of a greater pumping power which invalidates the initial purpose of optimisation. To avoid this drawback, the implementation of two bifurcation by placing a short plate at the back of the microchannel which splits the flow into two can reduce the pumping pressure required as shown in Cond. 4 in Figure 6 [25]. Therefore, an amalgamation of a larger bifurcation ratio and an optimal constructal inlet design will result in an idealised heat sink.

Non-Uniformly Structured Microchannels & Heat Transfer Performance
In reference to Eq. 6, when u and v are unchanging across iterations, the Re becomes dependant on bifurcation length only. From Figure 3(a), Figure 5(a) and (b), it can be noted that a lower Reynolds number implies less pumping power and input voltage is needed, creating an overall more thermodynamically efficient system, particularly if energy efficient fins are attached to the heat sink. Across the investigated experiments, a Reynolds number at or between 150 and 200 performed best. The topologies that correspond to these Reynolds numbers are non-uniformly structured, having branched microchannels, and small islands throughout, as can be seen in Figure 7a and 7b. The organic shape arrangements led to a lower maximum surface temperature, Tsurface, when compared to inorganic shape designs, e.g. parallel microchannels, shown in Figure 7c.

(b) (a) (c)
In the case of Figure 7a versus Figure 7c, the Tsurface of 7a maximised at 349.38 ºK, which is 8.1% lower than that of the uniform parallel microchannel, which maximised at 380.16 ºK. Agreeing further, in the case of Figure 7b versus Figure 7c, the Tsurface of 7b maximised at 335.65 ºK, which was 11.7% lower than that of the uniform parallel microchannel. These promising results can be attributed to the improved flow rate that non-uniform microchannels can provide. The lack of an organic-like flow design in Figure 7c results in heat accumulation along three of the seven parallel microchannels. This heat does not egress out of the system via the coolant, but rather, transfers out of the system through the surroundings as waste heat. Although the fin design of the heat sink is also very important in redirecting waste heat, these investigations have showed that an average 9.9% reduction in surface heat is achievable when adjusting solely the microchannels' topology. From this, it can be understood that, both the quantity of and length of bifurcations, positively impact the thermal performance of the heat sink module. Figure 8 below illustrates the temperature changes of six cases where bifurcations have been added to the microchannels along the streamwise direction Z. The complete length of the microchannels from left to right is 35 mm, with a constant width of 1.3 mm. Where a vertical is present on the horizontal axis, there is a bifurcation in the microchannel. Note that not all cases utilise all bifurcations. In Case 1, there is no bifurcation present, i.e. a single flow microchannel. For Cases 2 and 3, a single bifurcation is added but the distance from the inlet is altered. Cases 4 and 5 apply the same conditions however with two bifurcations. Finally, Case 6 has three bifurcations, evenly spread along the microchannel. The results from this experiment imply that when fluid flow is disrupted within the microchannels, i.e. bifurcated, the local heat transfer coefficient is increased.  per section, with an overall Q of 300 W, a positive trend is attained as is shown in Figure 9a below. The cases are defined as follows: Case 1 had no bifurcations (single continuous microchannel), Case 2 had 1 bifurcation with a length ratio of 3:7, Case 3 had 1 bifurcation with a length ratio of 6:4, Case 4 had 2 bifurcations with a length ratio of 3:4:3, Case 5 had 2 bifurcations with a length ratio of 3:3:4, and Case 6 had 3 bifurcations with a length ratio of 3:3:3:1. An R 2 value of 0.9833 is attained from the data for Figure 9a, suggesting that there may be an outlier. However, the information is only calculated over six data points, implying that the expected hyperbolic fit may be correct should more data be obtained. Quick comparison of Figure 8 and Figure 9a shows that cases with lower temperature gradients do produce higher heat transfer coefficients, agreeing with Eq. 5. However, further study is required to observe more valid results. illustrates the temperature gradient across each bifurcation and the corresponding heat transfer coefficient. As expected, it follows a hyperbolic curve, implying that the smaller the difference between the inlet and outlet temperatures, the greater capacity of the system to dissipate heat. The heat coefficients values are multiples of 10 7 .
As illustrated in Figure 9a, the heat transfer coefficient hm increases with the number of bifurcations, and the more evenly spread out they are along the microchannel. Revisiting Eq. 5, it can be assumed that the increase in the thermal performance is attributed to the redistribution of heat that occurs when a fluid flow is disrupted. This can be seen in Figure 8, where the coolant temperature immediately drops at a bifurcation in the microchannel.
Not only is hm dependant on contact area, but it is also dependant on the temperature difference across the bifurcation. Considering hm follows a hyperbolic curve in Figure 9b, it can be assumed that as the temperature difference across the microchannel approaches 0, the coefficient increases exponentially. Realistically, the temperature difference cannot be exactly 0 as the laws of thermodynamics disallow this, hence, there must be a limit to the heat dissipation capacity of the system. An R 2 value of 0.991 is attained from the data for Figure 9b, suggesting that Eq. 5 correctly models this system. More data points are needed to further validate the experiments. Combining the information from Figures 7 -9, and Eq. 5, the bifurcations and microchannel topology heavily influence the overall thermal performance of the heat sink. Furthermore, when accounting for the Reynolds number in Eq. 6 and knowing that a lower Re improves thermal performance, should the kinematic viscosity of the fluid (v) be constant, the Re will reduce when the length L of the microchannel reduces, and/or when the fluid velocity (u) reduces. Qualitatively, the data agrees with and is coherent with the theory provided by the literature.

Coolant
Coolants are passed through a heat sink at a constant rate to collect the heat and then remove it from the system. As mentioned previously, the heat sink in the AWG system is placed at the hot side of the TEC in order to dissipate and remove some of the waste heat from the system. The ideal coolant would have a low thermal resistance and a high thermal conductivity and viscosity such that liquid would absorb the waste heat and carry it away from the TEC. A high inlet flow velocity increases the performance of the heat sink; however, it also requires a higher pumping power. The pumping power also increases as the viscosity of the coolant increases, due to a liquid with low viscosity not being able to flow as quickly as one with a higher viscosity. Seven different coolants have been compared through analysing the aforementioned properties utilising experimental data from five articles. Table 3. Properties of the coolants, as collected from articles utilising the coolants to obtain experimental data. This gives a preliminary insight as to which coolants are better for use in the AWG system's heat sink. The papers which used the Al2O3/H2O Nanofluid, Transcritical CO2, Supercritical CO2 coolants for their experiments, did not provide such data for analysis [26][27][28][29][30] Table 3 demonstrates that the coolants TiO2/water nanofluid [28], nanofluid [27] and EGalSn [27], all possess properties which should allow them to perform as a more superior coolant than water. Galinstan has the highest thermal conductivity of all the coolants with data provided making it a better coolant than the nanofluid tested in the same paper. The TiO2/H2O nanofluid coolant also has a high thermal conductivity although still not as high as that of Galinstan. The Galinstan has a much higher dynamic viscosity than the water and nanofluid meaning the pumping power required to effectively pump the coolant through the system would be greater. The TiO2/H2O nanofluid's dynamic viscosity was not provided and thus, it cannot be concluded from this data whether it is a more suitable coolant than the Galinstan. In Figure 10(a) above, the cross-sectional area of the microchannel is stated as 1 x 1.5 x 50 mm = 0.0075 cm 3 for the Al2O3/H2O Nanofluid coolant [29]. The fluid flow rate can be converted to the velocity by executing the following equation: This allowed for a more direct comparison of the effect of the coolant's velocity of the thermal resistance for Figure 10(a). Figure 10(a) demonstrates that as the velocity is increased, the thermal resistance of the coolant decreases and whilst the comparison cannot be completely direct as the velocities at which the thermal resistance was tested were vastly different, the thermal resistances Pumping Power (W) recorded for the Galinstan coolant were far lower than that of the Al2O3/H2O Nanofluid coolants. As previously mentioned, the lower the thermal resistivity in the heat sink, the more efficient the heat sink. Thus, through this comparison of the thermal resistivity of Al2O3/H2O Nanofluid and Galinstan as depicted in Figure 10(a), it can be determined that Galinstan, with a minimum recorded thermal resistance of approximately 0.054 K W -1 , would act as a superior coolant to Al2O3/H2O Nanofluid which has a minimum recorded thermal resistance of approximately 0.08 K W -1 . Conversely, the pumping power increases as the velocity increases however, a low pumping power is ideal for a high efficiency heat sink. Although the minimum point of thermal resistance corresponds with the higher velocity and pumping power for Figure 10(a), the Galinstan coolant remains the better coolant with a lower maximum pumping power of 0.001 W than Al2O3/H2O Nanofluid at all concentrations with a maximum pumping power of 0.11 W. Figure 10(b) above illustrates the effect of the fluid inlet temperature on the thermal resistance of water, supercritical CO2, transcritical CO2 at a pressure of 8 MPa and transcritical CO2 at a pressure of 9 MPa. From this direct comparison it is demonstrated that the thermal resistance of water is unaffected by change in the coolant inlet temperature while all variations of CO2 coolant are. This result suggests that supercritical CO2 would be the most suitable coolant in for the heat sink with the lowest recorded thermal resistivity of 0.094 K W -1 . Figure 10(c) depicts the effect of the thermal resistance on the pumping power of supercritical CO2 at a velocity of 2 m s -1 [30] and thus can be compared against Figure 10(b) to determine whether supercritical CO2 or Galinstan is the most superior coolant for the heat sink. In Figure 10(b), at the lowest point of thermal resistance, 0.054 K W -1 for Galinstan, the pumping power is at a maximum of 0.001 W. From Figure 10(c), the lowest point of thermal resistance for supercritical CO2 is 0.064 K W -1 where the pumping power is also at a maximum, at approximately 0.277 W. These values demonstrate that to achieve a low thermal resistivity, supercritical CO2 requires approximately 0.276 W more pumping power than the Galinstan coolant.

Optimal operation characteristics of Peltier device
The experimental results from the below studies show that the ambient temperature and relative humidity of the air around the Peltier device are the largest factors which determine the water production rate. Trends indicate higher relative humidity and higher airflow rate leads to an increase in water production [5,9]. This leads to the explanation that the cold side temperature of the Peltier device, Tc, is lower with increasing airflow, which is demonstrated by the works of Shourideh et al., Kadhim et al. and Eslami et al. [5,9,10].
Comparing experimental data from Jradi et al. and Joshi et al. [31,32] show the water production rate is clearly shown to increase with increasing current. Figure 11 displays this relationship. Due to the difference in cold side area and number of TEC's used in experimentation, the nominal rate of water production is drastically different however the trend remains relatively similar.  Figure 12 shows COP versus input current to two difference Peltier device models. The trend remains similar across models, with the COP peaking at lower input currents and slowly dropping off as current increases. The COP has a dramatically smaller peak for larger difference in temperature across the Peltier device, denoted ΔT, demonstrated by Eslami et al. [9] in Figure 12(a) and (b). The cooling capacity slowly increases with current and is increased with a decrease in ΔT. These results indicate it is imperative to achieve the smallest ΔT to improve the overall efficiency as both the cooling capacity and power efficiency increase with decreasing ΔT.  [5,9], using different TEC module parameters. Furthermore, both Figure 11 and Figure 12 suggests an optimal current should be verified experimentally on a case by case basis. While the COP decreases with increasing current, an optimal operational current can be determined by finding a midpoint between the peak of the COP and peak of Qc.