# Influence of Process Parameters and Convective Heat Transfer on Thermophysical Properties of SiO2 Nanofluids by Multiobjective Function Analysis (DFA)

Authors: R. Suprabha; C. R. Mahesha; C. E. Nanjundappa
Journal: Journal of Nanomaterials
 (2023)

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## Abstract

From the requirements, high-performance cooling systems in the applications of solar, heat exchangers, and chemical industries are needed to improve efficiency. The metal-oxides-based nanofluids composed the better thermal properties with exchange of heat-transfer mechanisms. Therefore, this study mainly focused on nanosilicon dioxide materials to produce the nanofluids with blending of water-base medium by two-step techniques. The scanning electron microscope was used to analyze the presence of silicon dioxide nanoparticles from the procured material. During the two-step method input aspects like weight fraction of silicon dioxide (1.5–4.5 wt%), particle sizes (10–30µm), pH range of water (5–9), and sonication process time (2–4 hr) were considered. The outcomes like thermal conductivity, specific heat capacity, and viscosity were selected as thermal physical properties. The desirability techniques were implemented to identify the best optimal input parameters from the nanofluid processing. From the desirability outcomes, the processed nanosilicon dioxide fluids with respective input parameters were 0.9623 W/mK for thermal conductivity, 688 J/kg K forspecific heat capacity, and 0.00162 for viscosity, respectively. The heat-transfer coefficient was successfully identified with processed nanosilicon dioxide fluids, and the Nusselt number and Reynolds number were attained with respective heat-transfer coefficients.


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## Body

## 1. Introduction

In the last decades, energy crisis is more consumed with requirements of energy applications such as electronic products, chemical industry, power plant engineering, food and beverage industries [1]. The subsequent achievements are highly influenced by the requirements like greater efficiency, multimode function, less weight, and compact shape [2]. The enhanced superior heat-transfer medium, or liquid, and the thermic liquid have significant scopes in the thermal-related engineering fields [3]. Thermal fluids have played an essential role in the process and system-based maintaining industries and employed with ideal running temperature [4]. Therefore, to improve the mechanical thermal efficiency, nanofluids are rich medium for heat-transfer liquid [5]. Due to this, it has secured colloidal scattering as compared with the solid-based nanoparticles; these particle sizes must be in the range of 1–100 nm during liquid process [6].Some unique requirement is needed to select appropriate nanofluids. Those characteristics are compatibility, availability, thermal attributes, stability in chemical process, and less in price [7]. The conventional heat-transfer technique is insufficient to exchange the heat resulting in less thermophysical properties. To overcome this issue in the thermal- and heat-transfer managing led to identification of the effective nanofluid, and it is the most admired objective in this research [8]. Therefore, nanofluid is utilized to increase heat transfer and enhanced thermophysical properties. Hence, the thermalophysical properties fully depends up on the efficiency of cooling systems. So the researchers were highly involved in finding the better thermal conductivity in the presence of nanofluids [9]. The medium of nanoparticle with metal oxides have different concentrations to achieve the nanofluids by the conventional technique. The different nanomaterials are graphite, carbon nanotubes, metal oxides, graphene oxides, metals, diamonds, carbides, graphenes, and nitrides [10]. Normally in the metal-based nano-fluids for nanoformulations, the thermal conductivity is lesser when compared with the base metals, and settling issues were developed during the nanofluid formulations [11]. In comparison with metals, metal-oxide-based nanomaterials showed better thermophysical properties. Formulation of nanofluid is very effective to produce maximum thermal conductivity and never compensates the pressure drop [12]. Therefore, the increasing of thermophysical properties enhances the heat-transfer mechanism. The hybrid nanofluid is composed between two or more than two metal oxide nanoparticles when suspended with traditional base liquids. Single- or mononano fluids were prepared from one nanoparticle of metal oxide dispersed in the base fluids [13]. Many techniques like glycols with water, glycols without water, and oils and water were used to compose the nanofluid formulation [14]. Among these methods, water was the majorly used to act as a coolant, and various investigations are focused more on water-based nanofluids by various authors [15]. The overview of experimental plan is displayed in Figure 1.Figure 1
Experimental layout.Abu-Hamdeh et al. [16] investigated the nanofluid of SiO2 in various preparations in the heat exchangers. The main objective was to improve the efficiency in the solar power plant systems. It is concluded that the efficiency was increased at 25% when using SiO2. Singh et al. [17] analyzed the various nanofluids like aluminum oxide, silicon dioxide and magnesium oxide to identify the thermal behaviors. The latent heat thermal energy storage system was used to complete the investigations properly. Among the metal oxides, SiO2 provided better efficiency in this study. Jang et al. [18] studied the nanocoated SiO2 on the steel in the concrete technology to improve the tensile and interfacial bonding. A comparision between the plain steel and coated nano-SiO2 steel to improved the corrosion rate. Finally, the coated SiO2 steel increased the bonding strength at 50%. Yu et al. [19] increased thermophysical properties in the thermal storage applications by the influence of SiO2 nanofluids. The specific heat was enhanced at 2.58 times than the eutectic nitrate. Iqbal et al. [20] addressed the performance of engine-oil flow by using the nanosilicon carbide and silicon dioxide powders. These two nanopowders were suspended in the base fluid of engine oil and, in addition to that, the heat mechanism was migrated through the temperature conditions. Esfe et al. [21] studied the improvement of viscosity in the engine oil with help of multiwall carbon nanotubes and silicon dioxide nanoparticles. The engine performance was improved by 42.53% in the statistical analysis. The response surface methodology was used to forecast the experimental values. Awais et al. [22] enhanced the thermal conductivity in the kerosene oil with help of silicon dioxide and titanium dioxide. The Riga wedge technique was used to create the fluid formulations. SiO2 nanofluid provides better thermal conductivity. In this research, two-step technique was implemented to produce the nanofluids with utilization of sonication and mechanical stirring process. The even dispersion of nanoparticles is very significant to enhance the interfacial bonding with maximum stability in the base fluids and was accomplished in the two-step technique [23]. These stability controls were fully influenced by the frequency, temperature, and time of sonication method. The rising of nanoparticles and its concentration volumes improves the thermal conductivity in the prepared nanofluids. Based on the detail literature reviews, SiO2 was considered for nanoparticle material and to produce the nanofluids along with water-base fluid by two-step technique. This research work aims to investigate the optimum process parameter of nano silicon dioxide materials to produce the nanofluids with the blending of water-base medium by two-step techniques.


## 2. Material and Preparation of Nanofluids Aspects

In this study, silicon dioxide has been chosen as a base metal oxide element with water (H2O). It is suspended in base fluids. The particle size analyzer was used to check the size of the nanoparticle and selected sizes were 10–30 nm. The silicon dioxide was purchased at Coimbatore Metal Mart. The thermophysical properties of SiO2 and water were as follows: 2,220 and 3,885 kg/m3 densities, 703 and 731 J/kg K specific heat capacities, 1.2 and 40 W/mK thermal conductivities, respectively. The SEM analysis was employed to identify the presence of particle elements which is displayed in Figure 2. From Figure 2, it is clear that the silicon dioxide particles were observed.Figure 2
SiO2 SEM micrograph.The appropriate weight machine was used to measure the weight of SiO2 particles from the manufacturers of Nitiraj. The two-step technique was used to conduct the nanofluid preparation accompanying the mechanical stirring and ultrasonication process to vanish the agglomerated particles in the working base fluid. To evaluate the essential volume concentration, 0.5 ml measuring flask was used. The parameters like amplitude (123 µm), 130 W and 40 kHz power was maintained in the ultrasonic mixer.In this study, it is required to consider, by technically improving the efficiency of heat transfer systems, that the influencing properties are specific heat capacity (SHC), thermal conductivity, pH range, viscosity, and dynamic viscosity. These properties were measured with calorimeter with differential scanning, thermal meter (KD2-Pro), pH meter, and viscometer (Brookfield), respectively. Before that the volume concentrations are significant aspects to measure the quantity of particles blended with base fluid or working fluid to maintain the thermophysical properties. The forecasted thermal conductivity of prepared nanofluids was not uniform [24].Various techniques like transient hot wire (TWH) method, temperature oscillation, steady-state parallel plate, and optical beam and deflection were used to verify the thermal conductivity of nanofluids. Among these techniques, THW is a suited method to find out the thermal conductivity of composed SiO2 nanofluids. The clustering and maximum temperature were highly impacted with modifications of thermal conductivity [25]. Similarly, the pH value was fine-tuned to improve the nanoparticles’ dispersion evenly with the working fluid during the process. Finally, the thermal conductivity was carried with thermal meter (KD2-Pro) with Fourier’s law in support of transfer-heat conduction [26]. Normally, the working base fluid thermal conductivity was much finer with lesser viscosity, and this viscosity is related with pumping force to affect the pressure fall. This test was conducted by the Brookfield viscometer (plate and cone type). The pH range and SHC were measured with pH meter and the differential scanning calorimeter. Meanwhile, simultaneously thermal conductivity has enhanced with moderate pH values [27]. The weight fraction of SiO2, particle sizes, pH range, and sonication process time are the input factors which are displayed in Table 1.Table 1
Input factor for preparing nanofluids.
Process runsWeight fraction of SiO2 (vol.%)SiO2 reinforcement size (µm)Water pH rangeSonication processing time11.5105223207334.53094


## 3. Results and Discussion

### 3.1. Desirability Function Analysis on Processed Nanofluid Parameters

Based on the detailed processing procedures, thermophysical properties are obtained with appropriate processing parameters. There is need to validate the processing parameters to enhance the physical properties. Therefore, desirability approaches were used to identify the optimal process parameters. The composed nanofluids contain conditions like maximum thermal conductivity, minimum SHC, and viscosity [28]. The influenced process parameters are weight fraction of SiO2, particle sizes, pH range, and sonication process time, and outcomes are thermal conductivity, SHC, and viscosity. The Taguchi L9 design was utilized to frame the processing levels [29]. The input aspects and its outcomes are displayed in Table 2 as per the L9 Taguchi technique.Table 2
Outcomes of thermal properties with L9 input.
RunsWeight fraction of SiO2SiO2 sizepH range (H2O)Sonication processing time (hr)TC (W/mK)SHC (J/kg K)V (Cp)121050.20.91016860.00145231070.40.92136790.00168341090.60.95286810.00194422090.40.91226900.00159532050.60.93576950.00174642070.20.92126890.00152723070.60.91856960.00146833090.20.91196910.00151943050.40.96236880.00162


### 3.2. Contour-Analysis of Thermal Properties with Input Factors

#### 3.2.1. Contourplots of Weight Fraction and SiO2 Particle Size on Thermal Properties

The contourplots of weight fraction of SiO2 and particle size on the thermal conductivity, SHC and viscosity are displayed in Figures 3(a) and 3(b), respectively. From the figures, the thermal conductivity was increased at increasing of weight fraction 3%–4% and sizes of the particles were increased from 20 to 30 nm. Similarly, SHC, was enhanced with increase of weight fraction 3%–4% and low-level particle size 10 nm, and viscosity was improved at low-weight fraction and increase of particle sizes from 10 to 30 nm, respectively.Figure 3
(a) Weight fraction and SiO2 particle size on TC; (b) weight fraction and SiO2 particle size on SHC; (c) weight fraction and SiO2 particle size on viscosity.
(a)(b)(c)


#### 3.2.2. Contourplots of Particle Size of SiO2 and pH Range on Thermal Properties

The contourplots of SiO2 particle size and pH range on the thermal conductivity, SHC, and viscosity are displayed in Figures 4(a) and 4(b), respectively. From the figures, increase of particle size of SiO2 and pH range from 7 to 9 improved the thermal conductivity. Meanwhile, decreasing the particle size of SiO2 at 10 nm and raising the pH range from 7 to 9 enhanced the SHC. The viscosity was improved when the particle size was increased from 10–30 nm and pH range from 7 to 9.Figure 4
(a) SiO2 particle sizes and pH range of water on TC; (b) SiO2 particle sizes and pH range of water on SHC; (c) SiO2 particle sizes and pH range of water on viscosity.
(a)(b)(c)


#### 3.2.3. Contourplots of pH Range of Water and Sonication Processing Time on Thermal Properties

Figure5(a)–5(c) displays the contourplots pH range of water and processing of sonication on the thermal conductivity, SHC, and viscosity, respectively. From the figures, increase of pH range from 5 to 9 and processing time from low level (0.2) to medium level (0.4) enhanced the thermal conductivity. The SHC was improved on increasing the pH range from 7 to 9 and with low-level processing time. The viscosity was superior on increasing the pH range from 5 to 9 and processing time from 0.4 to 0.6 hr.Figure 5
(a) pH range of water and processing time on TC; (b) pH range of water and processing time on SHC; (c) pH range of water and processing time on viscosity.
(a)(b)(c)


#### 3.2.4. Contourplots of Sonication Processing Time and Weight Fraction of SiO2 on Thermal Properties

Figure6(a)–6(c) exhibited the contour plots sonication processing with durations and weight fraction on the thermal conductivity, SHC and viscosity, respectively. From the figures, it is understood that the thermal conductivity was improved at high level of processing time (0.6 hr) and weight fraction was increased from low (2.0) to moderate level (3.0). The SHC was enhanced at low level of processing time (0.2) to moderate level (0.4) and weight fraction from (2.0% to 3.0%). Finally, viscosity level was enhanced at low level processing time and low level weight fraction.Figure 6
(a) Processing time and weight fraction of SiO2 on TC; (b) processing time and weight fraction of SiO2 on SHC; (c) processing time and weight fraction of SiO2 on viscosity.
(a)(b)(c)


#### 3.2.5. Contourplots of Desirability on the Thermal Properties of Nanofluid SiO2

In this study, desirability was approached on the thermal properties to find out the optimal process parameters. Before that the input factors were arranged in the Taguchi design with L9 array as per the discussion in Materials and Method section. The main objective of this desirability is to convert the multiresponses into a single response for better understanding. During the desirability, the outcomes like thermal conductivity at maintaining the maximum the better concept, and SHC and viscosity were considered as the smaller the better condition, respectively. Normalized signal to noise ratios of thermal conductivity, SHC, and viscosity values and other related values of desirability coefficient and its composite desirability values are listed in Table3. From Table 3, the ranking methods from the weight of 0.5 values were used to find out the ranking procedures. Experimental runs show that the 9th sample gives a better rank. Optimum process parameters found that weight fraction 4%, 30 nm of particles of SiO2, pH-5 range and 0.4 hr of sonication processing. The ranking graph and its overall processing runs are displayed in Figure 7. The metal oxide of SiO2 achieved better thermal conductivity, SHC, and viscosity as mentioned ranges.Figure 7
Nanofluids SiO2 and DFA rank.Table 3
Desirability values with their input factors and thermal outcomes.
RunSignal to noise ratios—NormalizedDFA-coefficientDFAGradeTCSHCVTCSHCV11.0000−0.5882−1.00000.00001.58822.00000.0000920.7854−1.0000−0.53060.21462.00001.53060.8104430.1820−0.88240.00000.81801.88241.00001.2409240.9598−0.3529−0.71430.04021.35291.71430.3055750.5096−0.0588−0.40820.49041.05881.40820.8551360.7874−0.4118−0.85710.21261.41181.85710.7467570.83910.0000−0.97960.16091.00001.97960.5644680.9655−0.2941−0.87760.03451.29411.87760.2895890.0000−0.4706−0.65311.00001.47061.65311.55921


## 3.1. Desirability Function Analysis on Processed Nanofluid Parameters

Based on the detailed processing procedures, thermophysical properties are obtained with appropriate processing parameters. There is need to validate the processing parameters to enhance the physical properties. Therefore, desirability approaches were used to identify the optimal process parameters. The composed nanofluids contain conditions like maximum thermal conductivity, minimum SHC, and viscosity [28]. The influenced process parameters are weight fraction of SiO2, particle sizes, pH range, and sonication process time, and outcomes are thermal conductivity, SHC, and viscosity. The Taguchi L9 design was utilized to frame the processing levels [29]. The input aspects and its outcomes are displayed in Table 2 as per the L9 Taguchi technique.Table 2
Outcomes of thermal properties with L9 input.
RunsWeight fraction of SiO2SiO2 sizepH range (H2O)Sonication processing time (hr)TC (W/mK)SHC (J/kg K)V (Cp)121050.20.91016860.00145231070.40.92136790.00168341090.60.95286810.00194422090.40.91226900.00159532050.60.93576950.00174642070.20.92126890.00152723070.60.91856960.00146833090.20.91196910.00151943050.40.96236880.00162


## 3.2. Contour-Analysis of Thermal Properties with Input Factors

### 3.2.1. Contourplots of Weight Fraction and SiO2 Particle Size on Thermal Properties

The contourplots of weight fraction of SiO2 and particle size on the thermal conductivity, SHC and viscosity are displayed in Figures 3(a) and 3(b), respectively. From the figures, the thermal conductivity was increased at increasing of weight fraction 3%–4% and sizes of the particles were increased from 20 to 30 nm. Similarly, SHC, was enhanced with increase of weight fraction 3%–4% and low-level particle size 10 nm, and viscosity was improved at low-weight fraction and increase of particle sizes from 10 to 30 nm, respectively.Figure 3
(a) Weight fraction and SiO2 particle size on TC; (b) weight fraction and SiO2 particle size on SHC; (c) weight fraction and SiO2 particle size on viscosity.
(a)(b)(c)


### 3.2.2. Contourplots of Particle Size of SiO2 and pH Range on Thermal Properties

The contourplots of SiO2 particle size and pH range on the thermal conductivity, SHC, and viscosity are displayed in Figures 4(a) and 4(b), respectively. From the figures, increase of particle size of SiO2 and pH range from 7 to 9 improved the thermal conductivity. Meanwhile, decreasing the particle size of SiO2 at 10 nm and raising the pH range from 7 to 9 enhanced the SHC. The viscosity was improved when the particle size was increased from 10–30 nm and pH range from 7 to 9.Figure 4
(a) SiO2 particle sizes and pH range of water on TC; (b) SiO2 particle sizes and pH range of water on SHC; (c) SiO2 particle sizes and pH range of water on viscosity.
(a)(b)(c)


### 3.2.3. Contourplots of pH Range of Water and Sonication Processing Time on Thermal Properties

Figure5(a)–5(c) displays the contourplots pH range of water and processing of sonication on the thermal conductivity, SHC, and viscosity, respectively. From the figures, increase of pH range from 5 to 9 and processing time from low level (0.2) to medium level (0.4) enhanced the thermal conductivity. The SHC was improved on increasing the pH range from 7 to 9 and with low-level processing time. The viscosity was superior on increasing the pH range from 5 to 9 and processing time from 0.4 to 0.6 hr.Figure 5
(a) pH range of water and processing time on TC; (b) pH range of water and processing time on SHC; (c) pH range of water and processing time on viscosity.
(a)(b)(c)


### 3.2.4. Contourplots of Sonication Processing Time and Weight Fraction of SiO2 on Thermal Properties

Figure6(a)–6(c) exhibited the contour plots sonication processing with durations and weight fraction on the thermal conductivity, SHC and viscosity, respectively. From the figures, it is understood that the thermal conductivity was improved at high level of processing time (0.6 hr) and weight fraction was increased from low (2.0) to moderate level (3.0). The SHC was enhanced at low level of processing time (0.2) to moderate level (0.4) and weight fraction from (2.0% to 3.0%). Finally, viscosity level was enhanced at low level processing time and low level weight fraction.Figure 6
(a) Processing time and weight fraction of SiO2 on TC; (b) processing time and weight fraction of SiO2 on SHC; (c) processing time and weight fraction of SiO2 on viscosity.
(a)(b)(c)


### 3.2.5. Contourplots of Desirability on the Thermal Properties of Nanofluid SiO2

In this study, desirability was approached on the thermal properties to find out the optimal process parameters. Before that the input factors were arranged in the Taguchi design with L9 array as per the discussion in Materials and Method section. The main objective of this desirability is to convert the multiresponses into a single response for better understanding. During the desirability, the outcomes like thermal conductivity at maintaining the maximum the better concept, and SHC and viscosity were considered as the smaller the better condition, respectively. Normalized signal to noise ratios of thermal conductivity, SHC, and viscosity values and other related values of desirability coefficient and its composite desirability values are listed in Table3. From Table 3, the ranking methods from the weight of 0.5 values were used to find out the ranking procedures. Experimental runs show that the 9th sample gives a better rank. Optimum process parameters found that weight fraction 4%, 30 nm of particles of SiO2, pH-5 range and 0.4 hr of sonication processing. The ranking graph and its overall processing runs are displayed in Figure 7. The metal oxide of SiO2 achieved better thermal conductivity, SHC, and viscosity as mentioned ranges.Figure 7
Nanofluids SiO2 and DFA rank.Table 3
Desirability values with their input factors and thermal outcomes.
RunSignal to noise ratios—NormalizedDFA-coefficientDFAGradeTCSHCVTCSHCV11.0000−0.5882−1.00000.00001.58822.00000.0000920.7854−1.0000−0.53060.21462.00001.53060.8104430.1820−0.88240.00000.81801.88241.00001.2409240.9598−0.3529−0.71430.04021.35291.71430.3055750.5096−0.0588−0.40820.49041.05881.40820.8551360.7874−0.4118−0.85710.21261.41181.85710.7467570.83910.0000−0.97960.16091.00001.97960.5644680.9655−0.2941−0.87760.03451.29411.87760.2895890.0000−0.4706−0.65311.00001.47061.65311.55921


## 3.2.1. Contourplots of Weight Fraction and SiO2 Particle Size on Thermal Properties

The contourplots of weight fraction of SiO2 and particle size on the thermal conductivity, SHC and viscosity are displayed in Figures 3(a) and 3(b), respectively. From the figures, the thermal conductivity was increased at increasing of weight fraction 3%–4% and sizes of the particles were increased from 20 to 30 nm. Similarly, SHC, was enhanced with increase of weight fraction 3%–4% and low-level particle size 10 nm, and viscosity was improved at low-weight fraction and increase of particle sizes from 10 to 30 nm, respectively.Figure 3
(a) Weight fraction and SiO2 particle size on TC; (b) weight fraction and SiO2 particle size on SHC; (c) weight fraction and SiO2 particle size on viscosity.
(a)(b)(c)


## 3.2.2. Contourplots of Particle Size of SiO2 and pH Range on Thermal Properties

The contourplots of SiO2 particle size and pH range on the thermal conductivity, SHC, and viscosity are displayed in Figures 4(a) and 4(b), respectively. From the figures, increase of particle size of SiO2 and pH range from 7 to 9 improved the thermal conductivity. Meanwhile, decreasing the particle size of SiO2 at 10 nm and raising the pH range from 7 to 9 enhanced the SHC. The viscosity was improved when the particle size was increased from 10–30 nm and pH range from 7 to 9.Figure 4
(a) SiO2 particle sizes and pH range of water on TC; (b) SiO2 particle sizes and pH range of water on SHC; (c) SiO2 particle sizes and pH range of water on viscosity.
(a)(b)(c)


## 3.2.3. Contourplots of pH Range of Water and Sonication Processing Time on Thermal Properties

Figure5(a)–5(c) displays the contourplots pH range of water and processing of sonication on the thermal conductivity, SHC, and viscosity, respectively. From the figures, increase of pH range from 5 to 9 and processing time from low level (0.2) to medium level (0.4) enhanced the thermal conductivity. The SHC was improved on increasing the pH range from 7 to 9 and with low-level processing time. The viscosity was superior on increasing the pH range from 5 to 9 and processing time from 0.4 to 0.6 hr.Figure 5
(a) pH range of water and processing time on TC; (b) pH range of water and processing time on SHC; (c) pH range of water and processing time on viscosity.
(a)(b)(c)


## 3.2.4. Contourplots of Sonication Processing Time and Weight Fraction of SiO2 on Thermal Properties

Figure6(a)–6(c) exhibited the contour plots sonication processing with durations and weight fraction on the thermal conductivity, SHC and viscosity, respectively. From the figures, it is understood that the thermal conductivity was improved at high level of processing time (0.6 hr) and weight fraction was increased from low (2.0) to moderate level (3.0). The SHC was enhanced at low level of processing time (0.2) to moderate level (0.4) and weight fraction from (2.0% to 3.0%). Finally, viscosity level was enhanced at low level processing time and low level weight fraction.Figure 6
(a) Processing time and weight fraction of SiO2 on TC; (b) processing time and weight fraction of SiO2 on SHC; (c) processing time and weight fraction of SiO2 on viscosity.
(a)(b)(c)


## 3.2.5. Contourplots of Desirability on the Thermal Properties of Nanofluid SiO2

In this study, desirability was approached on the thermal properties to find out the optimal process parameters. Before that the input factors were arranged in the Taguchi design with L9 array as per the discussion in Materials and Method section. The main objective of this desirability is to convert the multiresponses into a single response for better understanding. During the desirability, the outcomes like thermal conductivity at maintaining the maximum the better concept, and SHC and viscosity were considered as the smaller the better condition, respectively. Normalized signal to noise ratios of thermal conductivity, SHC, and viscosity values and other related values of desirability coefficient and its composite desirability values are listed in Table3. From Table 3, the ranking methods from the weight of 0.5 values were used to find out the ranking procedures. Experimental runs show that the 9th sample gives a better rank. Optimum process parameters found that weight fraction 4%, 30 nm of particles of SiO2, pH-5 range and 0.4 hr of sonication processing. The ranking graph and its overall processing runs are displayed in Figure 7. The metal oxide of SiO2 achieved better thermal conductivity, SHC, and viscosity as mentioned ranges.Figure 7
Nanofluids SiO2 and DFA rank.Table 3
Desirability values with their input factors and thermal outcomes.
RunSignal to noise ratios—NormalizedDFA-coefficientDFAGradeTCSHCVTCSHCV11.0000−0.5882−1.00000.00001.58822.00000.0000920.7854−1.0000−0.53060.21462.00001.53060.8104430.1820−0.88240.00000.81801.88241.00001.2409240.9598−0.3529−0.71430.04021.35291.71430.3055750.5096−0.0588−0.40820.49041.05881.40820.8551360.7874−0.4118−0.85710.21261.41181.85710.7467570.83910.0000−0.97960.16091.00001.97960.5644680.9655−0.2941−0.87760.03451.29411.87760.2895890.0000−0.4706−0.65311.00001.47061.65311.55921


## 4. Convective Heat Transfer with Prepared Nanofluids through Straight Tube

Based on the L9 array, desirability functions were used to compose better optimal process parameters. Now these parameters were analyzed to carry out the convective heat transfer with straight tube heat transfer section with specialized parameters. The designed heat-transfer system was a loop section which contained nanofluid reservoir, nanofluid pump, flow meter, the chambers having heater, insulator, K-thermocouple, and manometer, and another section contained cooling water reservoir, flow meter, cooling water pump, and heat exchanger.The copper-made tube was used with heat-transfer test chamber with thickness of 2.5 mm, inner diameter of 8.2 mm, and length of 0.873 m, respectively. The thermocouples having K-type design with 0.2°C precisions were maintained with wall temperature. Similarly, the two types of T-thermocouples were maintained at same precision as mentioned in K-type to estimate the bulk temperature on both sides of the sections. Throughout the process, constant heat flux condition was attained with electrically heated transfer condition using power supply. The heat exchanger with plate design was used to locate the inlet temperature in the range of 26+ or −1°C and the volume-flow rate was calculated by the flow meter with 0.02 L/min precision.


### 4.1. Data Processing

As per the required formula, density and specific heat properties were found with help of mixture characteristics of nanofluids, and assuming the thermal equilibrium among the nanoparticle SiO2 and working fluid, the SHC and thermal conductivity were also identified and optimal parameters were pointed out. Next to the total heat flux finding, Q1 and Q2 were found with heat input values.(1)Totalheatfluxq=HeatInputfromheaterQ1+HeatInputtothefluidQ22πDL,(2)Heattransfercoefficienth=Totalheatfluxqaxiallengthwalltemperature−bulktemperature.Similarly, heat transfer coefficient was found in the Equation (1) and by the heat temperatures with wall and fluids bulk temperature and axial length (x) from the inlet of the heat transfer. The Nusselt number was identified from the heat flux, tube diameter from thermal conductivity, and the Reynolds number was employed with velocity, diameter of the pipe, and kinematic viscosity. Equations (3) and (4) exhibit the Nusselt and Reynolds number formulas.(3)Nusseltnumber=hDThermalconductivityK,(4)Reynoldsnumber=Densityofthefluid×fluidvelocity×diameterofpipeViscosityV.From the entire equations, the heat transfer coefficients, and Nusselt and Reynolds numbers were identified with output responses like thermal conductivity and viscosity. These number outcomes and heat-transfer coefficient values were employed with L9 table. Table4 exhibits the heat-transfer coefficients, and Nusselt and Reynolds numbers with convective heat transfer throughout the straight tube with specified conditions.Table 4
Heat transfer coefficient, Nusselt and Reynolds number.
RunsTC (W/mK)SHC (J/kg K)V (Cp)Fluid velocity (m/s)Heat transfer coefficient (W/m2 K)Nusselt numberReynolds number10.91016860.001450.361.450.0130922.03586220.92136790.001680.521.550.0137962.53809530.95286810.001940.811.690.0145453.42371140.91226900.001590.591.850.016633.04276750.93576950.001740.4581.910.0167382.15839160.92126890.001520.2351.440.0128181.26776370.91856960.001460.671.730.0154453.76301480.91196910.001510.2981.570.0141181.61827890.96236880.001620.3691.390.0118451.867778Figures8 and 9 show the various runs of nano-SiC fluids and Nusselt and Reynolds numbers. From the figures, it is clear that the correlations of different process parameters and numbers were clearly noted. From the Reynolds number, the attained values are <2,000 ranges so that the flows are related with laminar flow. From the figures, it is implicit that the fifth and seventh runs attained highest values.Figure 8
Various runs of nanofluids and Nusselt number.Figure 9
Various runs of nanofluids and Reynolds number.


## 4.1. Data Processing

As per the required formula, density and specific heat properties were found with help of mixture characteristics of nanofluids, and assuming the thermal equilibrium among the nanoparticle SiO2 and working fluid, the SHC and thermal conductivity were also identified and optimal parameters were pointed out. Next to the total heat flux finding, Q1 and Q2 were found with heat input values.(1)Totalheatfluxq=HeatInputfromheaterQ1+HeatInputtothefluidQ22πDL,(2)Heattransfercoefficienth=Totalheatfluxqaxiallengthwalltemperature−bulktemperature.Similarly, heat transfer coefficient was found in the Equation (1) and by the heat temperatures with wall and fluids bulk temperature and axial length (x) from the inlet of the heat transfer. The Nusselt number was identified from the heat flux, tube diameter from thermal conductivity, and the Reynolds number was employed with velocity, diameter of the pipe, and kinematic viscosity. Equations (3) and (4) exhibit the Nusselt and Reynolds number formulas.(3)Nusseltnumber=hDThermalconductivityK,(4)Reynoldsnumber=Densityofthefluid×fluidvelocity×diameterofpipeViscosityV.From the entire equations, the heat transfer coefficients, and Nusselt and Reynolds numbers were identified with output responses like thermal conductivity and viscosity. These number outcomes and heat-transfer coefficient values were employed with L9 table. Table4 exhibits the heat-transfer coefficients, and Nusselt and Reynolds numbers with convective heat transfer throughout the straight tube with specified conditions.Table 4
Heat transfer coefficient, Nusselt and Reynolds number.
RunsTC (W/mK)SHC (J/kg K)V (Cp)Fluid velocity (m/s)Heat transfer coefficient (W/m2 K)Nusselt numberReynolds number10.91016860.001450.361.450.0130922.03586220.92136790.001680.521.550.0137962.53809530.95286810.001940.811.690.0145453.42371140.91226900.001590.591.850.016633.04276750.93576950.001740.4581.910.0167382.15839160.92126890.001520.2351.440.0128181.26776370.91856960.001460.671.730.0154453.76301480.91196910.001510.2981.570.0141181.61827890.96236880.001620.3691.390.0118451.867778Figures8 and 9 show the various runs of nano-SiC fluids and Nusselt and Reynolds numbers. From the figures, it is clear that the correlations of different process parameters and numbers were clearly noted. From the Reynolds number, the attained values are <2,000 ranges so that the flows are related with laminar flow. From the figures, it is implicit that the fifth and seventh runs attained highest values.Figure 8
Various runs of nanofluids and Nusselt number.Figure 9
Various runs of nanofluids and Reynolds number.


## 5. Conclusion

(1)
In this investigation, preparation of SiO2 nanofluids were successfully carried with two-step technique.(2)
The desirability function was approached effectively to improve the efficiency of thermal properties with appropriate process parameters.(3)
The weight fraction of SiO2, particle sizes, pH range of water, and sonication processing durations were most influenced input parameters to thermal properties.(4)
The contour analysis between the input parameters of two-step method and their outcomes like thermal conductivity, SFC, and viscosity was detailed in analysis.(5)
The superior thermal physical properties are 0.9623 W/mK for thermal conductivity, 688 J/kg K for SHC, and 0.00162 for viscosity, respectively.(6)
The heat-transfer coefficient was successfully identified with total heat flux and axial dimensions. The designed heat-transfer system was effectively employed with selected design parameters and heat-transfer coefficient.(7)
The heat-transfer section will be expanded and more thermocouples will be added in the planned design and implement in the further studies.



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*Source: 1008046-2023-01-27.xml*