Second law analysis of a hybrid nanofluid in tubes equipped with double twisted tape inserts
Graphical abstract
Introduction
Nowadays, due to high demands and growing the consumption of energy, efficient use of energy is an important issue. Increasing performance of the thermal devices such as heat exchangers, solar collectors, refrigerators, heat pipes and so forth, can be beneficial way to saving the energy. In the recent decades, several techniques have been developed to improve the heat transfer rate in thermal systems, and many researchers have employed these methods to increase the performance and efficiency of thermofluidic processes in various applications [1]. Typically, these approaches are termed Heat Transfer Enhancement (HTE) techniques, and the main purpose of applying them is to increase the heat transfer rate and reduce size and cost of the thermal systems. Utilizing these methods in many engineering and industrial applications such as steam generation [2], heat recovery processes [3], cooling of thermal equipment [4], refrigeration, electronics cooling [5], and air conditioning is very effective for efficient use of energy. Design of more efficient thermal equipment can be achieved via these techniques in various engineering arenas. Generally, heat transfer enhancement approaches can be classified into two different categories, i.e. active and passive. Active methods need extra energy during the process, while the passive ones do not require any external power source. The passive methods are based on the modification in the configuration of devices that results in generating the higher flow mixing that leads to smaller thermal boundary layer and consequently greater heat transfer rates [6].
One of the most promising passive techniques which has recently become important to improve the heat transfer rate and increase the efficiency of thermal devices for different applications, is to employ the swirl flow generators. The swirl flow generators providing great mixing of flow with the low cost are effective and economical to use as heat transfer improvement equipment. The twisted tapes are one of the most used swirl generators which are commonly used to improve the heat transfer rate, especially in heat exchangers [7]. The twisted tapes have various configurations and are able to disturb the thermal boundary layer with generating severe swirl flows that lead to strong flow mixing and consequently higher heat transfer coefficients [8]. In addition, employing the twisted tapes can adversely affect the pressure drop and cause higher pumping power values. As a result, designing a twisted tape with the reasonable pressure drop is one of the main concerns of researchers to improve the heat transfer with low pumping power.
During the past years, various designs of twisted tapes have been investigated by many researchers. Chang et al. [9] experimentally studied the effects of utilizing serrated twisted tape on heat transfer improvement in a circular tube. They reported that by decrease of twisted ratio, the Nusselt number and friction factor increase. The heat transfer enhancement of tube equipped with the serrated twisted tape was around 1.25–1.67 times higher than that of the tube fitted with the smooth twisted tape. A numerical simulation was carried out by Eiamsa-ard et al. [10] on heat transfer enhancement using loose-fit twisted tapes. The tube wall was under constant temperature condition, and the flow regime was turbulent. The authors found that in the case of twisted ratio of 2.5, by increase of clearance ratio from 0 to 0.3, the heat transfer enhancement drops from 73.6% to 20% and friction factor augmentation decreases from 330% to 160% compared to the empty tube. Chokphoemphun et al. [11] examined flow and heat transfer of air flow through the tube enhanced with quadruple counter twisted tape. They reported that the tube equipped with the quadruple counter twisted tape shows greater thermal performance than that fitted with the quadruple co-twisted tape. Bhuiya et al. [12] studied the heat transfer and flow characteristics of air inside the heat exchanger tube equipped with double counter perforated twisted tape. They showed that the Nusselt number and friction factor increase by reduction of porosity. Furthermore, their results demonstrated that the maximum heat transfer enhancement was around 290%. Hasanpour et al. [13] researched optimization of heat transfer rate in a corrugated tube heat exchanger enhanced with twisted tapes using neural networks. They showed that the maximum heat transfer rate occurs in the corrugated tube fitted with the v-cut twisted tape, while that fitted with the perforated twisted tape showed the minimum pressure drop. Liu et al. [14] numerically studied the heat transfer improvement using a new type of the twisted tape, named coaxial twisted tape. They stated that utilizing the coaxial twisted tape can enhance the heat transfer greatly, such that the Nusselt number increased 151–195% compared to the traditional twisted tapes. Sheikholeslami et al. [6] reviewed the investigations carried out on employing the swirl flow generators for enhancement of the heat transfer rate. They concluded that the twisted tapes can increase the heat transfer rate with a reasonable increment in pressure drop.
The conventional working fluids possess poor thermal conductivity and therefore, replacing them with the fluids having higher thermal conductivities can be effective method to improve heat transfer rate. Introducing nanofluids was a milestone in heat transfer improvement techniques. Nanofluids are suspensions of solid nanoparticles in conventional liquids. Utilizing nanofluids as working fluids in many industrial and engineering applications is another approach to reduce the wasting of energy and enhance the overall performance of thermal devices. Recently, many researchers [[15], [16], [17], [18], [19], [20], [21]] experimentally and numerically investigated the merit of using nanofluids instead of common fluids in different thermal systems. Higher thermal conductivity of nanofluids compared to the common fluids decreases the temperature gradients and leads to higher heat transfer rates. Various studies have been conducted for using nanofluids in various thermal applications, and several scholars have reviewed these investigations in different areas such as employing nanofluids in heat sinks [22], heat exchangers [23], solar systems [24], microchannels [25], refrigeration systems [26], etc. Most of the performed reviews have demonstrated the superior merit of employing nanofluids instead of ordinary fluids.
So far, several nanofluids have been introduced with different types of nanoparticles and base fluids. Nanoparticles with high thermal conductivity are the excellent choices for utilization as solid phase in nanofluids, because even at the low particle volume fractions, lead to great heat transfer rates. Graphene, which has recently attracted the attention of many researchers owing to its great thermal properties, is an appropriate option to reach this goal. During recent years, a few investigations have been performed with considering graphene in nanofluids [[27], [28], [29], [30], [31]]. Ranjbarzadeh et al. [32] conducted an experimental analysis on heat transfer and flow characteristics of water–graphene oxide nanofluid in an isothermal heat pipe. They reported that the thermal conductivity of nanofluid at the maximum concentration (0.1%) is 28% greater than that of the base fluid, which causes 40% improvement of heat transfer rate. Zhou et al. [33] researched the heat transfer characteristics of oscillating heat pipes using a graphene nanoplatelet nanofluid. They found that the thermal resistance decreases 83.6% in the case of using 2 vol% nanofluid in comparison with distilled water.
All thermal devices impose irreversibilities and thus, analyzing the second law of thermodynamics is of significant importance for thermal equipment in order to figure out the contribution of irreversibilities on destruction of available energy. According to the relevant studies, there are several papers that have analyzed the second law of thermodynamics for nanofluids [[34], [35], [36], [37], [38], [39]], but the research investigations on evaluating the irreversibilities for graphene based nanofluids are insufficient, and most of the scholars have adopted the first law of thermodynamics to assess the heat transfer features in these nanofluids. Bahiraei and Heshmatian [40] studied the entropy generation and efficiency of a hybrid nanofluid with graphene–silver nanoparticles in various liquid blocks for cooling of electronic processors. Their results revealed that utilizing this nanofluid significantly reduces temperature gradient in the liquid block and leads to reduction of the overall irreversibility because of the great thermal conductivity of graphene. Bahiraei and Mazaheri [41] carried out a numerical investigation on the entropy generation due to flow of the hybrid nanofluid containing graphene–platinum nanoparticles inside a chaotic twisted minichannel. They illustrated that the thermal entropy generation rate and Bejan number reduce by concentration increment. Also, it was reported that adding nanoparticles into the base fluid causes augmentation of frictional entropy generation but owing to the low contribution of the frictional entropy generation in total entropy generation, overall irreversibility reduced with the concentration increase.
According to the author's knowledge, nanofluids containing graphene nanosheets have not so far been used in tubes enhanced with twisted tapes. Additionally, most of the investigations have considered only the first law of thermodynamics, while evaluating the second law of thermodynamics can have even more importance in thermal equipment. Indeed, all thermofluidic devices involve irreversibilities which reduce the performance of systems, and entropy generation is a measure of irreversibility amounts occurred during each process. Owing to importance of studying the value of irreversibilities in such geometries, which helps to design more efficient thermal systems, the main objective of the present investigation is to examine the entropy generation rates to evaluate thermal, frictional and total irreversibilities for flow of a hybrid nanofluid containing graphene–platinum nanoparticles inside the tubes improved with different twisted tapes. Effects of nanoparticle concentration and twisted tapes arrangement are presented regarding counter and co-swirling flow generators.
Section snippets
Definition of geometry and nanofluid
In this research, it is attempted to determine the best double twisted tape configuration in view of the second law of thermodynamics. The geometries simulated in this study consist of the tubes enhanced with double co-twisted tapes (CoTs) and double counter twisted tapes (CTs) with various twisted ratios (y/w). Parameter w is the tape width, and y indicates the tape pitch which is defined as the length of one complete rotation of the tape. Such a configuration can be employed instead of smooth
Governing equations
The single-phase approach is adopted for this investigation. In the other words, it is assumed that the thermal equilibrium is established between the base fluid and nanoparticles. Besides, it is supposed that the nanoparticles and the base fluid have a same velocity. It should be noted that many researchers [43] have verified the validity of the single-phase approach for nanofluids in which the nanofluid is considered as homogenous fluid, and effective models are employed for thermophysical
Entropy generation
There are two factors which commonly cause irreversibility and entropy generation, i.e. friction and heat transfer. Sum of entropy generation rates due to these factors is called total entropy generation rate and is obtained as [[44], [45], [46], [47]]:where represents the total entropy generation rate, while and are frictional and thermal entropy generation rates, respectively, which are determined as below:
Numerical method and validation
In order to solve the governing equations in the tube equipped with the double twisted tapes, numerical simulations are employed through the finite volume method. The pressure-based method is considered, and the governing equations are solved by using the second order approach, while the SIMPLE method is utilized for velocity–pressure coupling. Convergence criteria for all equations are considered 10−6.
The grid independency tests are adopted to reach the optimum cell number, reduce the
Results and discussion
The numerical investigations are carried out for two different inserted twisted tape configurations including double counter twisted tapes (CTs) and double co-twisted tapes (CoTs) with various twisted ratios (y/w). The nanofluid concentration varies from 0 to 0.1%, and the Reynolds number is considered 15,000 for all simulations. In this section, the results related to investigating the flow pattern in presence of the twisted tapes are firstly presented and thereafter, entropy generation rates
Conclusions
Thermal, frictional and total entropy generation rates for flow of the hybrid nanofluid containing the graphene–platinum nanoparticles in the tubes equipped with the double twisted tapes are evaluated. The double co-twisted tapes and double counter twisted tapes are examined at various twisted ratios. The findings obtained in this study can be summarized as below:
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The flow pathlines in the tube fitted with the CTs are more affected by the twisted tape, and experience a more intense path change.
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