Computers, Materials & Continua DOI:10.32604/cmc.2022.019048 | |

Article |

Utilization of Machine Learning Methods in Modeling Specific Heat Capacity of Nanofluids

1Sustainable and Renewable Energy Engineering Department, University of Sharjah, P. O. Box 27272, Sharjah, UAE

2College of Engineering and Technology, American University of the Middle East, Kuwait

3Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

4Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

5Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

6Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

*Corresponding Author: Thabet Abdeljawad. Email: tabdeljawad@psu.edu.sa

Received: 31 March 2021; Accepted: 01 May 2021

Abstract: Nanofluids are extensively applied in various heat transfer mediums for improving their heat transfer characteristics and hence their performance. Specific heat capacity of nanofluids, as one of the thermophysical properties, performs principal role in heat transfer of thermal mediums utilizing nanofluids. In this regard, different studies have been carried out to investigate the influential factors on nanofluids specific heat. Moreover, several regression models based on correlations or artificial intelligence have been developed for forecasting this property of nanofluids. In the current review paper, influential parameters on the specific heat capacity of nanofluids are introduced. Afterwards, the proposed models for their forecasting and modeling are proposed. According to the reviewed works, concentration and properties of solid structures in addition to temperature affect specific heat capacity to large extent and must be considered as inputs for the models. Moreover, by using other effective factors, the accuracy and comprehensive of the models can be modified. Finally, some suggestions are offered for the upcoming works in the relevant topics.

Keywords: Specific heat capacity; nanofluid; artificial neural network; concentration

Literature demonstrates that by suspending solids with nanodimension in traditional operating fluids, heat transfer rate can be improved, mainly due to increment in the effective thermal conductivity [1–3]. Addition of solid phase in the base fluid results in changes in different thermophysical properties such as density, thermal conductivity and specific heat capacity [4–6]. Variations in these properties are contingent on different items including concentration of solids, temperature and properties of the base fluid [7,8]. In general, increase in volume fraction of nanostructures causes increase in both viscosity and thermal conductivity [9,10]. Despite the advantages of high thermal conductivity for heat transfer purposes, the increase in dynamic viscosity is unfavorable; consequently, there is an optimum concentration in the majority of the cases [11,12]. In comparison with specific heat capacity of nanofluids, more attentions have been attracted by dynamic viscosity and thermal conductivity; however, several studies have focused on this property of the nanofluids due to its substantial role in heat transfer of operating fluids.

Nanofluids are employable in different energy-related mediums and technologies for performance enhancement including renewable energy systems, air conditioners and heat pipes, as shown in Fig. 1 [13–17]. For instance, Hosseinzadeh et al. [18] applied three different nanofluids in an indirect solar cooker and compared the performance with a case of using thermal oil without any nanoparticle. They observed that with the thermal oil, utilizing

Different approaches have been applied for modeling the properties of nanofluids including regressive correlations, artificial neural networks (ANNs) and support vector machines (SVMs). Studies have demonstrated that employing artificial intelligence for modeling results in higher accuracy compared with the correlations. For instance, Komeilibirjandi et al. [23] applied both GMDH NN and correlation for predicting thermal conductivity of nanofluids with CuO particles. The determined values for R-squared of the models based on ANN and correlation were 0.9996 and 0.9862, respectively. Higher accuracy of the models based on ANNs in comparison with correlations has been observed for the predictive models used for dynamic viscosity of nanofluids [24].

There are some review papers on the models proposed for predicting thermal conductivity and dynamic viscosity of nanofluids [25,26]; however, there is not any up to date review article on the specific heat capacity. In this work, studies carried out on specific heat of nanofluids are reviewed; afterwards, the proposed models with focus on artificial intelligence are reviewed and represented. Finally, some suggestions are recommended for upcoming works in the relevant topics.

2 Specific Heat Capacity of Nanofluids

Specific heat capacity of nanofluids is one of the properties that play substantial role in heat transfer ability of nanofluids. Mainly, suspension of solid materials with nanodimensions in the base fluid changes the overall specific heat. Depending on the intended application, decreased or increased specific heat would be desirable. Variation in specific heat depends on several elements that are discussed and reviewed in this section. For instance, concentration of the particles notably influences the variation in the specific heat [27–29]. Tiwari et al. [30] measured the specific heat of graphene nanoplatelet/water-EG for various concentrations of solid phase. As shown in Fig. 2, they noticed that the increase in the volume fraction resulted in a reduction in the specific heat of the nanofluid. In addition to the volume fraction, other factors including base fluid and temperature influence specific heat capacity of nanofluids. In a study done by Akilu et al. [31], the effect of dispersion of

Contrary to the nanofluids with conventional base fluids, specific heat capacity of the ones with molten salt base fluids can be increased by adding solid particles with nanometer dimensions [33]. Qiao et al. [34] measured the specific heat capacity of molten nitrate salt-based nanofluids with

In another work [37], the effect of dispersing

Hybrid nanofluids, that are composed of nanostructures with two dissimilar materials, have gained attentions in recent years for various purposes [41,42]. In this regard, the specific heat of these nanofluids, similar to their other properties, has been investigated by some researchers. Wole-Osho et al. [41] carried out a work on specific heat capacity of

3 Proposed Models for Specific Heat Capacity

Similar to dynamic viscosity and thermal conductivity [45], variety of methods have been applied for modeling specific heat of nanofluids. There are two general methods that are applicable for rough estimation of specific heat capacity [46]. The first one is based on the idea of mixing theory for ideal gases (model I) which is defined as follows [47]:

where subscripts nf, n and bf refer to nanofluid, nanoparticle, and base fluid, respectively. Another correlation is proposed based on the thermal equilibrium of nanoparticles and base fluid, which is defined as follows (model II) [47]:

where

where

The determined values of the coefficients are mentioned in Tab. 1. The maximum error of this correlation in determining the specific heat capacity of the nanofluid is 0.86%.

There are some correlations with higher degree of comprehensiveness by including more inputs. For instance, Vajjha et al. [51] proposed a correlation for specific heat capacity of nanofluids with different particles including ZnO,

The coefficients of the above mentioned correlation are presented in Tab. 2. Average error of their model is around 2.7%.

In addition to the conventional nanofluids, the specific heat capacity of hybrid nanofluids could be modeled by using correlations [52]. Tiwari et al. [53] compared the specific heat capacity of three hybrid nanofluids with CuO-MWCNT, MgO-MWCNT, and

where

In addition to correlations and ANNs, other intelligent methods are applicable for specific heat capacity modeling of nanofluids [57,58]. Alade et al. [59] compared performance of support vector regression and ANN with the classical models for modeling specific heat capacity of CuO/water nanofluid. As shown in Fig. 5, based on the values of root mean squared error (RMSE), using support vector regression led to the highest accuracy which was followed by ANN. In another work, Alade et al. [47] applied support vector regression (SVR) for modeling the specific heat capacity of EG-based nanofluids with different metal oxide particles including CuO and

4 Suggestions for Upcoming Studies

Based on the performed literature review, several models have been introduced for determination of the specific heat capacity of nanofluids; however, the provided models have some defects or restrictions which necessitate some modification and further attempt. First of all, the majority of the models are limited to special type of nanofluids with certain number of particles. In this regard, the applicability of the models can be broadened by using more variables such as properties of the base fluids and nanostructures. By including these parameters as the inputs, specific heat capacity of more nanofluids could be modeled and predicted. Moreover, there are few studies that applied ANN despite their desirable performance in modeling complex system. It is suggested to develop various types of ANNs, such as GMDH, for proposing models which are simple to use [63]. Furthermore, due to the dependency of ANN performance on the architecture of network, it is crucial to examine different structures to obtain more precise and reliable models [64]. In addition, utilizing various functions in the architecture of the ANNs would be useful for upcoming research.

Besides ANNs, other intelligent methods with different structures and algorithms can be used for specific heat capacity modeling. Adaptive neuro-fuzzy inference system (ANFIS) [65] and least square SVM (LSSVM) [66] would be appropriate and attractive options for modeling this property with remarkably high accuracy. Coupling novel and powerful optimization algorithms with the currently used intelligent methods for minimizing error is another idea for proposing better predictive models. Finally, performing sensitivity analysis would be very useful since detailed and brilliant insight into the effect of each factor can be provided. Summary of the suggestions for upcoming research are shown in Fig. 7.

In this article, parameters influencing the specific heat capacity of different nanofluids in addition to the proposed models are reviewed. The main findings of the study are as follows:

• For the nanofluids with conventional base fluids, in contrary to molten salts, increase in the volume fraction of nanostructure leads to reduction in the specific heat capacity.

• Temperature of nanofluids influences the specific heat capacity and its increasing or decreasing trend with temperature is dependent on the base fluid.

• Analytical models, based on thermal equilibrium or ideal gas idea, could be applicable for rough estimation of nanofluids specific heat capacity.

• Several correlations have been proposed for modeling specific heat capacity of nanofluids with higher accuracy compared with analytical models.

• Different intelligent models have been proposed for modeling the specific heat of nanofluids with higher precision compared with correlations.

• Including more parameters in the models improve comprehensiveness of the models.

• Different optimization algorithms can be coupled with models for minimizing the errors.

• It is suggested to consider other intelligent methods such as ANFIS and LSSVM for upcoming studies with similar topics.

Funding Statement: This work was supported by College of Engineering and Technology, the American University of the Middle East, Kuwait. Homepage: https://www.aum.edu.kw.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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