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

Authors: R. Vidhya; T. Balakrishnan; B. Suresh Kumar; R. Palanisamy; Hitesh Panchal; Luis Angulo-Cabanillas; Saboor Shaik; B. Saleh; Ibrahim M. Alarifi
Journal: Journal of Nanomaterials
 (2022)

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## Abstract

This article experimentally and statistically reports the convective heat transfer performance of a cylindrical mesh-type heat pipe apparatus filled with ZrO2-CeO2/water-ethylene glycol nanofluids. In this regard, ZrO2-CeO2 nanoparticles were synthesized and characterized through the Scanning Electron Microscope and Powder X-ray diffraction methods followed by the preparation of hybrid ZrO2-CeO2 nanofluids of various concentrations ranging from 0.025 to 0.1%. The heat transfer features of a tubular heat pipe with a mixture of the ZrO2-CeO2 nanofluid were evaluated. A 5.33% decrease in thermal resistance value and a 41.16% increase in heat transfer ability with increased power input were observed. The potent regression models were proposed to estimate heat transfer features of the heat pipe. The ANOVA statistical method has been employed to determine the P value and the F value of the models towards enhancing the reliability and accuracy of the developed models. The outcome revealed that the proposed models are reliable and have the best fit with the experimental data for 30–60 W power. The correlations’ results were validated against the experimental data and showed high accuracy. Moreover, the accuracy of the developed models was ensured through R-squared and adjusted R-squared values.


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## Body

## 1. Introduction

Choi [1] introduced the dispersion of 1–100 nm particles into the base fluid, called the nanofluid. These nanofluids have distinct thermal and hydrodynamic properties [2–4]. 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 [10–14]. 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 [21–24]. 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 TiO2-SiO2/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 SiO2–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 [30–32]. 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 [37–39]. 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 ZrO2-CeO2 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 ZrO2-CeO2 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 ZrO2-CeO2 nanofluid for the first time.Recently, many researchers experimentally and statistically focused on investigating the thermophysical properties of nanofluids and their heat transfer behavior [42–45]. 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 ZrO2-CeO2/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.


## 2. Methodology

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


### 2.1. Synthesis and Characterization of ZrO2-CeO2 Nanoparticles

In this ZrO2 (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 CeO2 (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 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 CeO2 powder was stored in an airtight vial for further investigation.The structural characterizations of synthesized ZrO2 and CeO2 nanoparticles were carried out through the Powder X-ray 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 ZrO2 and CeO2 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 ZrO2 and 70 nm for CeO2 particles.Figure 1
SEM picture of (a) ZrO2 and (b) CeO2 nanoparticles.
(a)(b)X-ray diffraction results of zirconia and ceria nanoparticles are displayed in Figures2(a) and 2(b) with the help of the X’pert Pro instrument. The scattering angle (2θ) identification procedure has been tuned between 80° and 10° at 0.05° intervals. It clearly shows that the strong peaks at the scattering angle of 30.10°, 35.22°, 50.42°, and 60.04° correspond to (0 1 1), (1 1 1), (0 3 1), and (1 4 0), respectively, well matched with the JCPDS card no: 83–0810. These planes reveal the formation of the orthorhombic structure of ZrO2 nanoparticles. The XRD pattern shows a high intense (0 1 1) positioning peak, denoting a high crystallinity of the synthesized sample. Similarly, the diffraction peaks in Figure 2(b) at 28.53°, 33.07°, 47.56°, 56.32°, 59.15°, 69.4°, and 79.04° scattering angles are associated with (1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2), (4 0 0), and (4 2 0) planes, respectively. The CeO2 particles with a cubic structure have been observed from XRD results, which agree with JCPDS: 65-2975. The average size of ZrO2 and CeO2 crystallites (D) is measured using the following Debye–Scherrer equation:
(1)D=Kλβcosθ,where K stands for the constant shape factor (1.9), β states Full Width at Half Maximum, λ is the wavelength (1.5405 Å) of the X-ray source, and θ denotes the diffraction angle. From the XRD results, ZrO2 and CeO2 crystallites’ average size was found as 2.2 nm and 7.07 nm, respectively. Since the crystallites are very small in dimension, they will render a superior efficiency in heat transfer characteristics [49].Figure 2
Powder X-ray diffraction structure of (a) zirconia and (b) ceria samples.


### 2.2. Synthesis of ZrO2-CeO2 Nanofluids

The synthesis of ZrO2-CeO2 hybrid nanofluids has been made through a two-step approach with the prepared ZrO2 and CeO2 nanoparticles. ZrO2 and CeO2 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 [21–24]. 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 ZrO2-CeO2 nanofluids for various volume concentrations (φ) of a range from 0.0125 to 0.1% were made in room temperature using the following equation:
(2)ϕ=wnp/ρnpwnp/ρnp+wbf/ρbf∗100,where wnp and ρnp indicate the wnp mass and density of ZrO2 and CeO2 particles, respectively, and wbf and ρnp represent the mass and density of the suspension (W-EG), respectively.


### 2.3. 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 ZrO2-CeO2 hybrid nanofluids were utilized for experimentation with the heat pipe. The experiment was conducted initially with a base fluid, followed by ZrO2, CeO2, and ZrO2-CeO2 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.
(3)ThermalresistanceR=Te−TcQ,(4)Heattransfercoefficienth=QATe−Tc,where Te and Tc 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:
(5)ΔQQ=ΔVV2+ΔII2=±2.76%,(6)ΔRR=ΔQQ2+ΔΔTe/cΔTe/c2=±2.76%,(7)Δhh=ΔQQ2+ΔAe/cAe/c2+ΔΔTe/cΔTe/c2=±2.85%.


## 2.1. Synthesis and Characterization of ZrO2-CeO2 Nanoparticles

In this ZrO2 (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 CeO2 (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 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 CeO2 powder was stored in an airtight vial for further investigation.The structural characterizations of synthesized ZrO2 and CeO2 nanoparticles were carried out through the Powder X-ray 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 ZrO2 and CeO2 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 ZrO2 and 70 nm for CeO2 particles.Figure 1
SEM picture of (a) ZrO2 and (b) CeO2 nanoparticles.
(a)(b)X-ray diffraction results of zirconia and ceria nanoparticles are displayed in Figures2(a) and 2(b) with the help of the X’pert Pro instrument. The scattering angle (2θ) identification procedure has been tuned between 80° and 10° at 0.05° intervals. It clearly shows that the strong peaks at the scattering angle of 30.10°, 35.22°, 50.42°, and 60.04° correspond to (0 1 1), (1 1 1), (0 3 1), and (1 4 0), respectively, well matched with the JCPDS card no: 83–0810. These planes reveal the formation of the orthorhombic structure of ZrO2 nanoparticles. The XRD pattern shows a high intense (0 1 1) positioning peak, denoting a high crystallinity of the synthesized sample. Similarly, the diffraction peaks in Figure 2(b) at 28.53°, 33.07°, 47.56°, 56.32°, 59.15°, 69.4°, and 79.04° scattering angles are associated with (1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2), (4 0 0), and (4 2 0) planes, respectively. The CeO2 particles with a cubic structure have been observed from XRD results, which agree with JCPDS: 65-2975. The average size of ZrO2 and CeO2 crystallites (D) is measured using the following Debye–Scherrer equation:
(1)D=Kλβcosθ,where K stands for the constant shape factor (1.9), β states Full Width at Half Maximum, λ is the wavelength (1.5405 Å) of the X-ray source, and θ denotes the diffraction angle. From the XRD results, ZrO2 and CeO2 crystallites’ average size was found as 2.2 nm and 7.07 nm, respectively. Since the crystallites are very small in dimension, they will render a superior efficiency in heat transfer characteristics [49].Figure 2
Powder X-ray diffraction structure of (a) zirconia and (b) ceria samples.


## 2.2. Synthesis of ZrO2-CeO2 Nanofluids

The synthesis of ZrO2-CeO2 hybrid nanofluids has been made through a two-step approach with the prepared ZrO2 and CeO2 nanoparticles. ZrO2 and CeO2 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 [21–24]. 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 ZrO2-CeO2 nanofluids for various volume concentrations (φ) of a range from 0.0125 to 0.1% were made in room temperature using the following equation:
(2)ϕ=wnp/ρnpwnp/ρnp+wbf/ρbf∗100,where wnp and ρnp indicate the wnp mass and density of ZrO2 and CeO2 particles, respectively, and wbf and ρnp represent the mass and density of the suspension (W-EG), respectively.


## 2.3. 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 ZrO2-CeO2 hybrid nanofluids were utilized for experimentation with the heat pipe. The experiment was conducted initially with a base fluid, followed by ZrO2, CeO2, and ZrO2-CeO2 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.
(3)ThermalresistanceR=Te−TcQ,(4)Heattransfercoefficienth=QATe−Tc,where Te and Tc 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:
(5)ΔQQ=ΔVV2+ΔII2=±2.76%,(6)ΔRR=ΔQQ2+ΔΔTe/cΔTe/c2=±2.76%,(7)Δhh=ΔQQ2+ΔAe/cAe/c2+ΔΔTe/cΔTe/c2=±2.85%.


## 3. 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 [54–56]. 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 (R2), adjacent R-squared (Adj. R2), probability value (P value), and Fisher’s test (F test) value.


## 4. Results and Discussion

### 4.1. 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. Figure3 represents the values of thermal resistance against different volume concentrations at 30, 60, and 90 W heat powers. As evident, adding ZrO2 and CeO2 nanoparticles into W-EG diminishes the thermal resistance values intensely. When the surface wettability rises, fluid resistance decreases due to the settlement of ZrO2 and CeO2 nanoparticles on the wick structure of the evaporation section. 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 ZrO2-CeO2 hybrid nanofluids.Figure 3
Thermal resistance variation of ZrO2-CeO2 nanofluids with respect to volume concentrations and at different heat power input values.Figure4 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/m2K 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 ZrO2-CeO2 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) [57–61].Figure 4
Heat power input and volume concentration effects on the heat transfer coefficient by using ZrO2-CeO2 nanofluids.Table 1
Heat transfer coefficient comparative study on nanofluids at 0.1% volume concentration.
NanofluidBase fluid proportionIncrease % of heat transfer coefficient30 W60 W90 WZrO2/W-EGW-60%EG-40%25.1126.1827.19CeO2/W-EGW-60%EG-40%26.8327.1336.18ZrO2-CeO2/W-EGW-60%EG-40%27.1928.1138.16


### 4.2. 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 best-suited combination to straightforward predict the output parameters [62–67]. Therefore, the present research work has utilized the RSM method with statistical ANOVA. Table 2 denotes the model summary of the suggested quadratic models.Table 2
Developed regression model outline.
Quadratic modelStandard deviationR-squaredAdj.R-squaredPredictedR-squaredAdequate precisionThermal resistance0.0630.99970.99960.99923203.273SuggestedHeat transfer coefficient2.260.98590.98010.962234.722SuggestedIn this work, the quadratic model is the suggested model in bothR 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 of signal and noise factors that should be greater than 4 [68–72]. According to Table 2, the ratio of both models is 203.273 and 34.722, indicating satisfactory signals.Table3 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 [73–76].Table 3
Thermal resistance and heat transfer coefficient variance analysis.
SourceSum of squaresDegrees of freedomMean squareF valuePvalueprob>FThermal resistanceModel165.42533.088249.02<0.0001A: power147.691147.6936824.82<0.0001B: volume concentration0.1210.1229.900.0001AB0.02310.0235.810.0329A212.20112.203043.05<0.0001B20.04310.04310.640.0068Residual0.048124.011E-003Total165.4717Heat transfer coefficientModel4289.645857.93168.13< 0.0001A: power4050.3514050.35793.78< 0.0001B: volume concentration131.341131.3425.740.0003AB19.35119.353.790.0752A212.19112.192.390.1482B245.13145.138.840.0116Residual61.23125.10Total4350.8717


### 4.3. Developing Mathematical Models Using Regression Analysis

Regression models are formulated based on ANOVA table output. Experimental results of thermal resistance (R) and heat transfer coefficient (h) values were compared to the developed regression models in order to establish a correlation. The obtained third-order polynomial models depict the interactions between the input parameters volume concentration (A) and power (B). The R and h quadratic models are correlated by the following equations.
(8)R=19.79588−0.35376∗P−9.91874∗ϕ−0.041747∗ϕP+50.92669∗ϕ2+1.94084E−003∗P2,(9)h=2.88150+191.95901∗ϕ+0.32906∗P+1.20365∗ϕP‐1655.93390∗ϕ2+1.93960E−003∗P2.


### 4.4. RSM Model Validation with the Empirical Data

The assessment of error between the proposed model values and the experimental data of ZrO2-CeO2 hybrid nanofluids are essential to estimate the accuracy of the RSM model. The validation of empirical and predicted RSM model results is displayed in Figures 5 and 6. 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 ZrO2-CeO2/W-EG hybrid nanofluids.Figure 5
Validation of the RSM model of thermal resistance against the empirical data.Figure 6
Validation of the RSM model of heat transfer coefficient against the empirical data.Table 4
Validation of proposed regression models with experimental data.
Exp. no.Volume concentration (%)Power (W)Experimental values ofR (K/W)Regression model values ofR (K/W)Experimental values ofh (W/m2K)Regression model values ofh (W/m2K)% of deviation inR% of deviation inh103011.0610.9298414.881614.498941.176892.57140520605.575.55730428.551429.607660.227935-3.6996630903.713.67828443.320948.207660.854879-11.280340.01253010.7110.7981518.147516.81907-0.82317.32042850.0125605.415.40996733.908232.379160.0006144.50931560.0125903.563.51529255.593751.430531.2558527.48849270.0253010.710.6823918.22318.621720.164613-2.1879880.025605.45.27854434.239334.633182.249182-1.1503190.025903.553.36821456.307954.135925.1207343.857366100.053010.6410.498618.972420.674591.328992-8.97169110.05605.335.06344337.29937.588785.001075-0.7769120.05903.543.12180257.5457.9942611.8135-0.78939130.0753010.5810.3784619.741620.657531.904892-4.63966140.075605.334.91237.619238.474477.842408-2.27357150.075903.532.93904958.69659.7826816.74082-1.8514160.13010.5710.3219919.875918.570562.3463776.56737170.1605.314.82421538.444137.290239.1484953.001538180.1903.512.81995461.15359.5011819.659432.701152Mean4.7785330.022009The 3-D graphs of a response surface for heat transfer experimental measurements are shown in Figures7 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 ZrO2-CeO2 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 ZrO2-CeO2/W-EG hybrid nanofluids.Figure 7
Response surface chart of thermal resistance. Red dots are the experimental data, while the surface is the proposed model results.Figure 8
Response surface chart of heat transfer coefficient. Red dots are the experimental data, while the surface is the proposed model results.


## 4.1. 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. Figure3 represents the values of thermal resistance against different volume concentrations at 30, 60, and 90 W heat powers. As evident, adding ZrO2 and CeO2 nanoparticles into W-EG diminishes the thermal resistance values intensely. When the surface wettability rises, fluid resistance decreases due to the settlement of ZrO2 and CeO2 nanoparticles on the wick structure of the evaporation section. 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 ZrO2-CeO2 hybrid nanofluids.Figure 3
Thermal resistance variation of ZrO2-CeO2 nanofluids with respect to volume concentrations and at different heat power input values.Figure4 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/m2K 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 ZrO2-CeO2 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) [57–61].Figure 4
Heat power input and volume concentration effects on the heat transfer coefficient by using ZrO2-CeO2 nanofluids.Table 1
Heat transfer coefficient comparative study on nanofluids at 0.1% volume concentration.
NanofluidBase fluid proportionIncrease % of heat transfer coefficient30 W60 W90 WZrO2/W-EGW-60%EG-40%25.1126.1827.19CeO2/W-EGW-60%EG-40%26.8327.1336.18ZrO2-CeO2/W-EGW-60%EG-40%27.1928.1138.16


## 4.2. 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 best-suited combination to straightforward predict the output parameters [62–67]. Therefore, the present research work has utilized the RSM method with statistical ANOVA. Table 2 denotes the model summary of the suggested quadratic models.Table 2
Developed regression model outline.
Quadratic modelStandard deviationR-squaredAdj.R-squaredPredictedR-squaredAdequate precisionThermal resistance0.0630.99970.99960.99923203.273SuggestedHeat transfer coefficient2.260.98590.98010.962234.722SuggestedIn this work, the quadratic model is the suggested model in bothR 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 of signal and noise factors that should be greater than 4 [68–72]. According to Table 2, the ratio of both models is 203.273 and 34.722, indicating satisfactory signals.Table3 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 [73–76].Table 3
Thermal resistance and heat transfer coefficient variance analysis.
SourceSum of squaresDegrees of freedomMean squareF valuePvalueprob>FThermal resistanceModel165.42533.088249.02<0.0001A: power147.691147.6936824.82<0.0001B: volume concentration0.1210.1229.900.0001AB0.02310.0235.810.0329A212.20112.203043.05<0.0001B20.04310.04310.640.0068Residual0.048124.011E-003Total165.4717Heat transfer coefficientModel4289.645857.93168.13< 0.0001A: power4050.3514050.35793.78< 0.0001B: volume concentration131.341131.3425.740.0003AB19.35119.353.790.0752A212.19112.192.390.1482B245.13145.138.840.0116Residual61.23125.10Total4350.8717


## 4.3. Developing Mathematical Models Using Regression Analysis

Regression models are formulated based on ANOVA table output. Experimental results of thermal resistance (R) and heat transfer coefficient (h) values were compared to the developed regression models in order to establish a correlation. The obtained third-order polynomial models depict the interactions between the input parameters volume concentration (A) and power (B). The R and h quadratic models are correlated by the following equations.
(8)R=19.79588−0.35376∗P−9.91874∗ϕ−0.041747∗ϕP+50.92669∗ϕ2+1.94084E−003∗P2,(9)h=2.88150+191.95901∗ϕ+0.32906∗P+1.20365∗ϕP‐1655.93390∗ϕ2+1.93960E−003∗P2.


## 4.4. RSM Model Validation with the Empirical Data

The assessment of error between the proposed model values and the experimental data of ZrO2-CeO2 hybrid nanofluids are essential to estimate the accuracy of the RSM model. The validation of empirical and predicted RSM model results is displayed in Figures 5 and 6. 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 ZrO2-CeO2/W-EG hybrid nanofluids.Figure 5
Validation of the RSM model of thermal resistance against the empirical data.Figure 6
Validation of the RSM model of heat transfer coefficient against the empirical data.Table 4
Validation of proposed regression models with experimental data.
Exp. no.Volume concentration (%)Power (W)Experimental values ofR (K/W)Regression model values ofR (K/W)Experimental values ofh (W/m2K)Regression model values ofh (W/m2K)% of deviation inR% of deviation inh103011.0610.9298414.881614.498941.176892.57140520605.575.55730428.551429.607660.227935-3.6996630903.713.67828443.320948.207660.854879-11.280340.01253010.7110.7981518.147516.81907-0.82317.32042850.0125605.415.40996733.908232.379160.0006144.50931560.0125903.563.51529255.593751.430531.2558527.48849270.0253010.710.6823918.22318.621720.164613-2.1879880.025605.45.27854434.239334.633182.249182-1.1503190.025903.553.36821456.307954.135925.1207343.857366100.053010.6410.498618.972420.674591.328992-8.97169110.05605.335.06344337.29937.588785.001075-0.7769120.05903.543.12180257.5457.9942611.8135-0.78939130.0753010.5810.3784619.741620.657531.904892-4.63966140.075605.334.91237.619238.474477.842408-2.27357150.075903.532.93904958.69659.7826816.74082-1.8514160.13010.5710.3219919.875918.570562.3463776.56737170.1605.314.82421538.444137.290239.1484953.001538180.1903.512.81995461.15359.5011819.659432.701152Mean4.7785330.022009The 3-D graphs of a response surface for heat transfer experimental measurements are shown in Figures7 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 ZrO2-CeO2 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 ZrO2-CeO2/W-EG hybrid nanofluids.Figure 7
Response surface chart of thermal resistance. Red dots are the experimental data, while the surface is the proposed model results.Figure 8
Response surface chart of heat transfer coefficient. Red dots are the experimental data, while the surface is the proposed model results.


## 5. Conclusion

The present study examined the synthesis, structural, and surface characterizations of ZrO2 and CeO2 nanoparticles produced by sol-gel and coprecipitation methods. The thermal transfer behavior on a cylindrical mesh-type heat pipe using ZrO2-CeO2 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 ZrO2 and CeO2 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 ZrO2 and CeO2 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 ZrO2-CeO2/W-EG hybrid nanofluids. A cylindrical heat pipe experiment has been performed using ZrO2-CeO2/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 experimental data. In addition, the values of R2 (0.9997 and 0.9859) and Adj.R2 (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 ZrO2-CeO2/W-EG hybrid nanofluids with a cylindrical screen mesh heat pipe. it has been concluded that the hybrid ZrO2-CeO2/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.



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