Research PaperDesigning a microchannel heat sink with colloidal coolants through the entropy generation minimisation criterion and global optimisation algorithms
Introduction
Thermal management is a well-known and widely studied problem in many engineering application areas. An increasing interest in our days has been focused on solving this heat transfer problem on modern electronic devices. Thus, there exist a vast number of reported solutions that include theoretical and experimental studies [1], [2], [3], [4], [5], [6]. A common solution for this problem requires implementing heat sinks attached (or embedded) to the microelectronic component [7]. Microchannel heat sinks, proposed by Tuckerman and Pease in 1981 [8], have been broadly used in high thermal power dissipation applications due to their higher capacity for convective heat transfer phenomena [7], [9], [10], [11]. Recently, Seko et al. [12] reported a virtual screening of a library containing thousands of compounds, with the purpose of selecting some of them with a low lattice thermal conductivity. As the authors suggest, this sophisticated selection methodology could be used in getting a material, for the present case, with very high thermal conductivity that may perhaps be used for the assembly of a microchannel. For many years, water, air and some oils were used as working fluids, because their thermal properties offered a good performance with contemporary electronic devices [13], [14]. Nonetheless, electronics evolve quickly, requiring coolants with improved heat transfer properties [15], [16], [17]. For example, interest on nanofluids has boosted research on them because their physical properties enhance the heat transfer process of the base fluid with just a slight increase of viscosity. A nanofluid is a colloid composed of the mixture of a liquid phase or base fluid and a solid phase or a powder of a material with high thermal conductivity [18]. Several examples exist where nanofluids have been employed in microchannel heat sinks [18], [19], [20], [21]. For example, Chein and Chuang carried out an experimental study using a colloid of H2O–CuO flowing through a silicon microchannel heat sink. They found that a volume fraction in the range of 0.2 to 0.4 wt/wt%, and a lower volume flow rate (), allowed the system to absorb more energy than if no nanoparticles were used [22]. Later on, Adham et al. analysed two kinds of nanofluids, H2O–SiC and H2O–TiO2, confirming that nanofluids increase the overall performance of the system [23]. Moreover, they observed that TiO2 nanoparticles are better than SiC, and also noticed that system efficiency is highly susceptible to variations of the channel inner geometry.
Even so, a remarkable working fluid is insufficient to ensure an optimal power dissipation. In fact, over-cooling an electronic component wastes energy (by pumping the extra fluid flow) and also represents an increased manufacturing cost of the thermal system. Hence, optimum design of heat sinks should aim at augmenting the thermal efficiency of the heat flux from the electronic device, to the surrounding media [15], [24], [25], [26]. Specifically, several approaches based on modelling, simulation and experimentation have been developed [8], [24]. One of them is the entropy generation minimisation (EGM) criterion, proposed by Bejan as a design alternative [27]. Still, EGM just provides a model of the system related to the entropy generation rate of its operation, so an optimisation approach has to be implemented to obtain the optimal system design. The application of this methodology for the design of microchannel heat sinks was pioneered by Khan et al., though they used traditional optimisation approaches [28]. Eventually, use of the EGM criterion in designing heat sinks became widespread [29], [30], [31]. Furthermore, a natural evolution of the field focuses on analysing nanofluids as feasible coolants for heat sink [32], [33], [34], [35], [36].
As of late, optimisation has focused on solving problems via novel algorithms. This preference derives from their simplicity and ease of use. Moreover, these algorithms are free of derivatives and of continuity concepts. Literature is bountiful with examples regarding their implementation on engineering problems, including the design of heat sinks [15], [37], [38], [39], [40]. More recent works incorporate this criterion with non-conventional optimisation algorithms. For example, Khan et al. designed a rectangular microchannel using Genetic Algorithms (GA) and claimed a better performance of such strategy when compared to traditional Newton–Raphson–Lagrange results [41]. Later, Adham et al. employed EGM-GA, but analysing the effect of several design features over the entropy generation rate of the heat sink [42]. Nevertheless, literature lacks works related to the entropy generation minimisation criterion for the design of heat sinks that include nanofluids as working fluids, using non-conventional optimisation algorithms.
This work summarises results from different scenarios in designing rectangular microchannel heat sinks based on the EGM criterion. A comprehensive model for the equivalent thermal resistance is implemented, where three metaheuristic algorithms were selected to minimise the objective function, based on their remarkable characteristics: UPSO, SO, and Cuckoo Search (CS). In order to reduce body thermal conductive resistance, High Thermal Conductive Graphite (HTCG) was selected as the material of the heat sink, because it has a thermal conductivity in the range 1300–1900 W/m⋅K [43]. Likewise, a working fluid of a water based nanofluid with particles of TiO2 was chosen, and several values of nanoparticle volume fraction were used. The performance of this colloidal coolant was compared against traditional working fluids such as air and ammonia gas.
This paper begins by describing the mathematical model and the optimisation techniques used in the current work, followed by a summary of the methodology, and a discussion of the results. Finally, the main conclusions are laid out.
Section snippets
Mathematical model
Fig. 1 shows a scheme of the system used in this work, which is composed of a rectangular microchannel heat sink, a thermal interface and a pair of supply tubes of fluid flow. The heat sink has a total volume given by , since tt and tb are the thicknesses of the upper and the lower parallel plates that enclose the array of fins, respectively. Also, the system contains microchannels with width 2wc, height Hc, length Ld, and spacing or wall thickness 2wp.
Methodology
In this work, the influence of using a nanofluid as coolant on designing a rectangular microchannel heat sink was analysed through the entropy generation minimisation (EGM) criterion, and powered by three non-conventional optimisation methods: Particle Swarm Optimisation (UPSO), Spiral Optimisation (SO) and Cuckoo Search (CS). This aim requires, however, a procedure integrated by two sequential phases, i.e., preparation and execution. Furthermore, the first one also incorporates a dual stage
Results and discussions
In spite of the vast amount of data available, we present just the one related to the Cuckoo Search algorithm. This is done considering space restrictions and because data slightly differ throughout the algorithms used in this work. Fig. 3 shows the tendency of the minimal entropy generation rate () as a function of the volume flow rate (Gd); the latter was considered as a design specification. Several working fluids were used, such as air, NH3 and H2O–TiO2, with different nanoparticle
Conclusions
An entropy generation minimisation (EGM) procedure in a rectangular microchannel heat sink (MCHS) was carried out. Several assumptions were made, such as heat sink body made of High Thermal Conductive Graphite (HCTG); air, ammonia gas (NH3) and H2O–TiO2 as working fluids; nanoparticle volume fractions of and 0.9 wt/wt%; and volume flow rates (Gd) between and throughout the first stage of this work, and as a design variable later on. Also, it was
Acknowledgement
This work has been supported by the Consejo Nacional de Ciencia y Tecnología (CONACyT) of Mexico, under the grant number 687900.
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