An Experimental Study of ZrO2-CeO2 Hybrid Nanofluid and Response Surface Methodology for the Prediction of Heat Transfer Performance: The New Correlations

PG and Research Department of Physics, Bishop Heber College (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli 620017, Tamilnadu, India Crystal Growth Laboratory, PG and Research Department of Physics, Thanthai Periyar Government Arts and Science College (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli 620023, Tamilnadu, India Department of Mechanical Engineering, K.Ramakrishnan College of Technology, Samayapuram, Tiruchirappalli, Tamil Nadu 621112, India Dept. of EEE, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203, India Mechanical Engineering Department, Government Engineering College Patan, Gujarat, India Universidad Nacional Santiago Antunez de Mayolo, Huaraz, Peru School of Mechanical Engineering, Vellore Institute of Technology, Vellore, 632014 Tamil Nadu, India Mechanical Engineering Department, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al-Majmaah, Riyadh 11952, Saudi Arabia

Nanofluids reduce energy consumption in the industries by decreasing the heat losses within the heat exchangers. Therefore, nanofluids attracted the attention of many researchers in the latest years because of their enhanced hydrodynamic and heat exchanging phenomenon. A heat pipe device is one of the modest heat exchangers that work on the capillary action and phase change principle. It transfers a massive quantity of heat [5]. The nanofluid is a potential fluid with a high thermal conductivity and stability compared to other fluids like water, EG, oils, and microfluids [6,7]. Hence, nanofluids are used as heat transfer liquids in various heat exchanging systems, such as computers, solar collectors, cooling electronic devices, and microelectronics [8].
Chien et al. [9] first analyzed the heat pipe efficiency using nanofluids, followed by many experimental studies to estimate the heat transfer proficiency on various heat pipes [10][11][12][13][14]. Solomon et al. [15] determined that adding 0.1% Cu/W nanoliquid increased the heat transferring ability by about 20%. Akbari and Saidi [16] examined the pulsating type heat pipe's thermal performance and flow regimes using graphene and titania nanofluids, reporting that the nanofluid improved thermal performance by 70% flow regimes at 70 W. A two-phase thermosyphon's heat transfer behavior charged with Ag/W nanofluid had shown the augmented result by applying a strong magnetic field [17]. Ghanbarpour et al. [18] performed experimentation with a silicon carbide nanofluid in a tubular heat pipe and originated the thermal resistivity value of 30% for 1.0% particle weight concentrations. Zeinali Heris et al. [19,20] tested the heat transfer proficiency of the thermosyphon and car radiator with oxidized CNT/water and CuO/EG-W nanofluids. It is noticed from the literature that high heat transfer appearances with nanoparticles in aqueous EG deliver significant outcomes over the traditional base liquids [21][22][23][24]. Keshavarz Moraveji and Razvarz [25] found that the sintered wick pipe's heat transferring characteristics were improved when using an alumina nanofluid, especially at 3% particle concentration. Noie et al. [26] analyzed the alumina nanofluids in the thermosyphon, resulting in enhanced system efficiency with respect to power and particle weight concentration. Using TiO 2 -SiO 2 /W-EG hybrid nanofluids, Nabil et al. [21] observed 22.8% enrichment in thermal conductivity at 3% weight concentration as the weight concentration increases. Akilu et al. [22] achieved the augmented thermophysical properties 1.15 times and 26.9% higher with the SiO 2 -G/EG nanofluid than the base fluid.
Ghalambaz et al. [27] demonstrated the increment in the thermal performance of the double-pipe heat exchanger using alumina nanoparticles. They have also observed the enhancement in the Nusselt number for alumina nanoparticles and twisted tape inserts with the help of a two-phase nanofluid model. Due to the enhanced thermal features of nanofluids, nanocoolants have been utilized to transfer a large quantity of heat more efficiently in car radiators [28,29]. A great part of the literature is devoted to the investigation of nanofluid-based nonconcentrating collectors. The analysis of nanofluids based nonconcentrating solar systems especially in solar collectors has been found to increase thermal efficiency [30][31][32]. The researchers also recommended that nanofluids in mechanical operations such as cutting and drilling reduce the production of excessive heat during the machining operations [33,34]. Nanofluids hold great significance in biomedical industries such as antibacterial cases, cryopreservation, dressing of wounds, and drug delivery also [35,36].
Based on the above literature, additional investigation is required on the potential applications of the hybrid nanofluids as the working medium in heat pipes. We chose zirconia nanofluids because they have significant thermophysical features and have recently been used for various heat transfer applications [37][38][39]. Ceria nanofluids also exhibited improved efficiency in flat-type solar collectors [40]. Mary et al. [41] evaluated the improved transport properties with cerium oxide/ethylene glycol nanofluids. However, the thermal transfer performance of ZrO 2 -CeO 2 nanofluids dispersed in the W-EG fluid in a screen mesh heat pipe has not been examined so far. In addition, it is expected that anomalous thermal features can be accomplished by applying the heat transfer of a hybrid ZrO 2 -CeO 2 fluid with a wick-structured heat pipe. Therefore, in the current research, an investigation is conducted for estimating the thermal resistance attributes of the tubular heat pipe filled with a ZrO 2 -CeO 2 nanofluid for the first time.
Recently, many researchers experimentally and statistically focused on investigating the thermophysical properties of nanofluids and their heat transfer behavior [42][43][44][45]. Response surface methodology (RSM) is a more suitable technique than the genetic algorithms (GA) and artificial neural networks (ANN) to obtain all information among input variables from minimum experimental data [46]. Moreover, RSM provides acceptable precision compared to GA and ANN algorithms [47,48].
The present study analyzes the experimental and statistical thermal resistance and heat transfer coefficient of a tubular heat pipe filled with ZrO 2 -CeO 2 /W-EG nanofluids. RSM with the ANOVA technique was engaged to examine the influence of input variables on thermal resistance and heat transfer coefficient properties. In addition, two new regression correlations on considered responses were proposed with the regression analysis.

Methodology
The first part of this section explains the nanofluid preparation, and the second one deals with the experimental arrangement used for measurements.

Synthesis and Characterization of ZrO 2 -CeO 2
Nanoparticles. In this ZrO 2 (zirconia) nanoparticle preparation, zirconium oxychloride was used as the precursor solution via the sol-gel method. 0.6 M of aqueous ammonia solution was slowly added to the precursor solution (0.7 M) for 30 minutes under constant stirring. Then, a slurry gel with white color was procured. Finally, it was calcinated for five hours at the temperature of 750°C in a muffle furnace to obtain the zirconia nanoparticles.
In the CeO 2 (ceria) nanopowder synthesis, an aqueous ammonia solution (0.8 M) was slowly added to the ceric nitrate solution (0.8 M) for 30 minutes at ambient temperature under constant stirring. The colloidal suspension was heated up to 100°C overnight and then washed thrice with EG and distilled water to remove the contaminants. The 2 Journal of Nanomaterials precipitate obtained was calcinated at the temperature of 650°C using a muffle furnace for four hours and finally powdered using a mortar and pestle. The pale yellow CeO 2 powder was stored in an airtight vial for further investigation.
The structural characterizations of synthesized ZrO 2 and CeO 2 nanoparticles were carried out through the Powder Xray diffraction (PXRD) method and surface morphology through a Scanning Electron Microscope (SEM). SEM analysis is used to identify the surface structure of the nanoparticles. The SEM pictures of zirconia and ceria nanoparticles recorded with the JEOL, JSM 6390 instrument, are depicted in Figures 1(a) and 1(b), correspondingly. SEM pictures show that both ZrO 2 and CeO 2 nanoparticles have a spherical shape, white color, and slight agglomeration with the neighboring nanoparticles. ImageJ software is used to determine the nanoparticle size, and it was found as 80 nm for ZrO 2 and 70 nm for CeO 2 particles.

Synthesis of ZrO 2 -CeO 2
Nanofluids. The synthesis of ZrO 2 -CeO 2 hybrid nanofluids has been made through a two-step approach with the prepared ZrO 2 and CeO 2 nanoparticles. ZrO 2 and CeO 2 nanoparticles (50 : 50) were suspended in the W-EG fluid (60/40%) in the first step. A 60 : 40 proportion of the W-EG mixture exhibited superior and significant performance with regard to the thermal characteristics of nanofluid production [21][22][23][24]. A small amount (2.5 g) of cetyltrimethylammonium bromide surfactant (CTAB) was added to the above combination with the preparation of the nanofluids of all particle weight concentrations to attain the stability of the fluids [25,26]. An ultrasonicator (50 Hz, 170 V AC-270 V AC, 50 Hz) was utilized to prepare all volume concentrations of nanoparticles to avoid nanoparticle settlement in the base fluid [22]. Thus, hybrid ZrO 2 -CeO 2 nanofluids for various volume 3 Journal of Nanomaterials concentrations (φ) of a range from 0.0125 to 0.1% were made in room temperature using the following equation: where w np and ρ np indicate the w np mass and density of ZrO 2 and CeO 2 particles, respectively, and w bf and ρ np represent the mass and density of the suspension (W-EG), respectively.

Experimental Apparatus and Process.
The schematic and working principle of a cylindrical heat pipe device fabricated for inspecting heat transfer operation was reported earlier in our previous work [50]. The six various particle weight concentrations (0%, 0.0125%, 0.025%, 0.05%, 0.075%, and 0.1%) of ZrO 2 -CeO 2 hybrid nanofluids were utilized for experimentation with the heat pipe. The experiment was conducted initially with a base fluid, followed by ZrO 2 , CeO 2, and ZrO 2 -CeO 2 hybrid nanofluids. The position of the heat pipe was set up at 45°orientation since the efficiency of the heat pipe is enriched at this position [51,52]. The heat transfer rates were calculated for the three heat power inputs in the range of 30-90 W. The following equations (3) and (4) are utilized to determine the heat pipe's heat transfer characteristics.
Heat transfer coefficient h where T e and T c stand for the temperature of the evaporator and condenser sections, respectively. Q = I * V represents the input heat power and A = πdl (d: internal diameter; l: overall length of tubular heat pipe device). Uncertainty of all the quantities used in this heat pipe experimentation was estimated using standard procedure [53]. The current, area, and voltage uncertainty values were found as ±0.2, ±0.25%, and ±0.25%, respectively. The maximum uncertainty value of power (Q), thermal resistivity (R), and heat transfer coefficient (h) was determined as ±2.76%, ± 2.76%, and ± 2.91%, respectively, using the following equations:     Journal of Nanomaterials

Response Surface Methodology (RSM)
RSM remains a powerful method to recognize the impacts of input factors on the measured outcomes coupled with the mathematical and statistical methods [25]. In general, the RSM approach is widely utilized in engineering, especially in nanofluids' heat and mass transfer applications [54][55][56]. This study develops a regression model using the experimental data acquired from the heat pipe to assess the response parameters combined with RSM. Variance analysis denotes such substantial values amongst the various input factors and responses. To evaluate the consistency between recommended RSM models and measured data, it is important to inspect the statistical elements, i.e., R-squared (R 2 ), adjacent R-squared (Adj. R 2 ), probability value (P value), and Fisher's test (F test) value.

Experimental Results of the Heat Transfer Properties of
Heat Pipe. The volume concentration of nanofluids, heat power input, and positioning of the heat pipe are the significant factors inducing the features of heat transfer. To assess such factors, it is necessary to examine heat transfer characteristics. Figure 3 represents the values of thermal resistance against different volume concentrations at 30, 60, and 90 W heat powers. As evident, adding ZrO 2 and CeO 2 nanoparticles into W-EG diminishes the thermal resistance values intensely. When the surface wettability rises, fluid resistance decreases due to the settlement of ZrO 2 and CeO 2 nanoparticles on the wick structure of the evaporation section.

Journal of Nanomaterials
Similarly, thermal resistance decreases with the rise of heat power input. The minimum resistance value of 3.51 K/W is detected for 0.1% concentration at the heat input of 90 W, which shows a 4.8% reduction in the thermal resistance value over the base fluid. This demonstrates the augmented efficiency of heat pipes using ZrO 2 -CeO 2 hybrid nanofluids. Figure 4 depicts the heat transfer coefficient values as a function of volume concentrations and heat input. The maximum and minimum heat transfer coefficient values are 14.88 and 61.15 W/m 2 K for 0.0125% and 0.1% particle weight concentrations. At 90 W, a supreme enhancement is observed that is 41.16% more than the base fluid mixture.
This enhancement (41.16%) is better than the W-EG fluid mixture and better than other reported nanofluids [30]. Table 1 represents the heat transfer value comparison between hybrid ZrO 2 -CeO 2 nanofluids and other fluids. The maximum of 38.16% rise in heat transfer coefficient value is obtained for the 90 W input heat power at 0.1% volume concentration over the single-component fluids (0% concentration) [57][58][59][60][61].

RSM Approach with ANOVA Technique.
In the response surface method, the empirical data obtained through the experimentation are fixed as input variables. For analyzing the empirical data, the Design-Expert software is utilized in this study. RSM with regression analysis would be the bestsuited combination to straightforward predict the output parameters [62][63][64][65][66][67]. Therefore, the present research work has utilized the RSM method with statistical ANOVA. Table 2 denotes the model summary of the suggested quadratic models.
In this work, the quadratic model is the suggested model in both R and h, and the developed models also have good predictability because the quadratic models have a significantly closer R-squared value as 1. As it is clear from Table 2, R-squared values of the resistance and heat transfer coefficient are 0.9997 and 0.9859, respectively, showing the developed models' precision. R-squared values indicate that 99% of the experimental data confirm the responses forecasted by both models. The matching of "predicted R -squared" values 0.9622 and 0.9992 with "Adj. R-squared" values 0.9801 and 0.9996, respectively, is almost good with each other. "Adequate precision" is described as the ratio    Journal of Nanomaterials of signal and noise factors that should be greater than 4 [68][69][70][71][72]. According to Table 2, the ratio of both models is 203.273 and 34.722, indicating satisfactory signals. Table 3 summarizes the variance analysis responses of the thermal resistance quadratic model and heat transfer coefficient quadratic model. It is identified that the models are significant as the F value is 8249.02 and 168.13 for the thermal resistance and heat transfer coefficient, respectively. The F values of 8249.02 and 168.13 denote the significance of the models. If "Prob > F" falls below 0.05 and above 0.1, then the model terms are supposed to be substantial terms. All responses acquired with these models are closer to standard values representing the models' high accuracy and consistency with the experimental responses [73][74][75][76] Table 4 lists the validation results of the RSM regression model and experimental values with the percentage of deviation. The mean originality of models from the experimental data is estimated to be 4.8% and -0.02% for thermal resistance and heat transfer coefficient, respectively, which is minor. The validated percentage of deviation assured the high predictability of both of the proposed models. These low margins of deviation prove that the proposed RSM models have higher predictability on the responses of heat pipes using ZrO 2 -CeO 2 / W-EG hybrid nanofluids.
The 3-D graphs of a response surface for heat transfer experimental measurements are shown in Figures 7 and 8. It can be seen that the surface formed with the new regression correlations and the collected data from the experimental setup on R and h values (of ZrO 2 -CeO 2 hybrid nanofluids) are closely taking place, demonstrating an excellent agreement of the proposed models with the experimental data. These results recommend that the RSM correlations accurately evaluate heat transfer characteristics of heat pipes that use ZrO 2 -CeO 2 /W-EG hybrid nanofluids.

Conclusion
The present study examined the synthesis, structural, and surface characterizations of ZrO 2 and CeO 2 nanoparticles produced by sol-gel and coprecipitation methods. The thermal transfer behavior on a cylindrical mesh-type heat pipe using ZrO 2 -CeO 2 nanoparticles in W-EG suspension was investigated. Further, the RSM technique was employed to design experiments, model process variables, and validate the results. The following major conclusions have been drawn through this examination.
The average sizes of ZrO 2 and CeO 2 nanoparticles were found to be 80 nm and 70 nm, respectively, and the shapes of the particles were found to be spherical for both samples through the SEM studies. From the XRD pattern of ZrO 2 and CeO 2 samples, the crystallite sizes were determined to be 2.2 nm and 7.07 nm, respectively.
A statistical approach using a response surface methodology combined with ANOVA was engaged to predict the heat transfer attributes (R: thermal resistance; h: heat transfer coefficient) of the heat pipe of ZrO 2 -CeO 2 /W-EG hybrid nanofluids. A cylindrical heat pipe experiment has been performed using ZrO 2 -CeO 2 /W-EG hybrid nanofluids at different particle weight concentrations for various temperatures. It showed 5.33% and 41.16% enhancement in thermal resistance and heat transfer coefficient, respectively, over the base fluid mixture. The developed regression models for R and h can predict the heat transfer performance with the average deviation of 4.8% and 0.02% over the experimental data at a heat input power in the range of 30-90 W and volume concentrations in the range of 0.0125-0.1%. The validation of both the modeling results is well matched with the experi-mental data. In addition, the values of R 2 (0.9997 and 0.9859) and Adj:R 2 (0.9801 and 0.9996) demonstrated the accuracy of the proposed RSM models vs. the experimental data. Moreover, the ANOVA technique showed significant results with the developed correlations. Hence, it is emphasized that these proposed mathematical models can be utilized for prediction of heat transfer coefficient and thermal resistivity of ZrO 2 -CeO 2 /W-EG hybrid nanofluids with a cylindrical screen mesh heat pipe. it has been concluded that the hybrid ZrO 2 -CeO 2 /W-EG nanofluid has superior potential for thermal performance and is highly suitable for heat transfer applications in various heat exchanging systems. In this work, major investigations had been carried out on the most commonly used cylindrical-shaped screen mesh heat pipe in industrial applications due to simplicity in construction, handling, filling, and refilling of the working fluid. Future research direction may focus on the study on variation of heat pipe performance using different types of wick structure, different cross-sections of heat pipe such as square and triangle, various hybrid nanofluids, etc. A heat pipe with enhanced thermal performance has major applications in the field of refrigeration and air conditioning system, satellite equipment, electronic component cooling, automobile radiator, high power LED cooling, microreactors, phase change materials (PCM), etc. These are some of the probable directions on which work can be performed on hybrid nanofluids by researchers in the future for dissemination of their use in different applications.

Data Availability
Data are available upon journal request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.