Optimization of Air Conditioning Performance with Al₂O₃-SiO₂/PAG Composite Nanolubricants Using the Response Surface Method

Abstract

A variety of operational parameters can influence the operation of an automobile air-conditioning (AAC) system. This issue is solved by using optimization techniques that can recommend the ideal parameters for the best results. To improve the performance of AAC system usings Al₂O₃-SiO₂/PAG composite nanolubricants, the response surface method (RSM) was employed. RSM was used to design the experimental work, which was based on a face composite design (FCD). The RSM quadratic models were helpful in determining the links between the input parameters and the responses. The addition of composite nanolubricants improved the overall performance of AAC systems. The parameters were optimized using the RSM’s desirability approach, with the goal of increasing cooling capacity and the coefficient of performance (COP), while reducing compressor work and power consumption. The ideal parameters for the AAC system were found to be 900 rpm compressor speed, 155 g refrigerant charge, and 0.019% volume concentration, with a high desirability of 81.60%. Test runs based on the optimum circumstances level were used to estimate and validate cooling capacity, compressor work, COP, and power consumption. Both predicted and measured values were in good agreement with each other. A new RSM model was successfully developed to predict the optimal conditions for AAC system performance.

1. Introduction

Optimization approaches using various methods are useful in determining the optimum parameters to achieve the desired performance. The investigation of the refrigeration system is time-consuming and costly when all experiments must be conducted. Thus, an optimization approach on refrigeration system parameters to find the optimum performance should be evaluated. The most commonly used methods for optimization are the RSM [1,2], Taguchi method [3,4], artificial neutral network (ANN) [5], multi-response optimization method [6], and regression analysis. Recently, improving and optimizing refrigeration system performance using software networks or modeling has begun receiving increasing attention from researchers [7,8]. This is plausible due to improved computer technology, as well as the accessibility of simulation software. RSM is a mathematical and statistical method for improving, enhancing, and optimizing independent parameters in a set of experiments, as well as their interactions with response variables, in a process that allows it to enhance and optimize development [9,10]. RSM is devoted to estimating interactions and quadratic effects, and it is a solution to the multi-variable statistical method problem, providing an idea of the response surface local shape [11]. Likewise, RSM can aid in the quantitative and routine modification of elements that influence the AAC system’s performance. The RSM has an advantage over the complete factorial approach in that it requires fewer tests to construct the experiment and less time to answer the objective problem. Therefore, computing resources are reduced.

Many studies have used the RSM optimization approach to determine the optimum working conditions. The surface roughness of EN31 steel was analyzed by Abhang and Hameedullah [12] using RSM. The feed rate, followed by the cutting speed and depth of the cut, had the greatest impact on surface roughness. During the turning process, RSM was utilized by Makadia and Nanavati [13] to generate a mathematical model for surface roughness. The feed rate had the largest impact on surface roughness, followed by the tool nose radius. The electrical discharge machining (EDM) process was modeled and optimized using RSM [14]. They discovered that RSM could be employed in most optimization-related tasks, and the advantage of RSM-based response parameter analysis was that each working parameter’s effect on the value of the resultant response parameter could be explained individually.

Table 1. Previous studies on optimization method approaches in various applications.

Author (s)	Year	Fields/Applications/Systems	Optimization Methods
Abhang and Hameedullah [12]	2011	EN31 steel turning process	RSM
Barik and Mandel [15]	2012	EN31 steel turning process	RSM
Krishankant et al. [16]	2012	EN34 steel turning process	Taguchi Method
Makadia and Nanavati [13]	2013	EN31 steel turning process	RSM
Rao and Venkatasubbaiah [17]	2016	Surface roughness in CNC turning	Taguchi and ANOVA
Li et al. [18]	2016	CNC machining	Taguchi, RSM, and MOPSO
Costa and Garcia [7]	2016	Refrigeration systems	RSM
Parpas et al. [19]	2017	Refrigeration systems	RSM
Gangil and Pradhan [14]	2017	Electrical discharge machining (EDM) process	RSM
Parpas et al. [19]	2017	Air distribution and refrigeration systems	CFD/EES model
Belman-Flores et al. [20]	2017	Refrigeration systems	ANN
Nataraj et al. [21]	2018	CNC turning	RSM
Ocholi et al. [22]	2018	Sesame biolubricant pilot plant	RSM
Mao et al. [23]	2018	Resident air-conditioning (TAC) systems	RSM
Redhwan et al. [24]	2018	AAC systems	RSM
Qader et al. [25]	2018	Solar air heaters	RSM
Zendehboudi et al. [26]	2019	VCRS	RSM
Canbolat et al. [27]	2019	Absorption refrigeration systems	Taguchi and ANOVA
Zaman [28]	2019	Photonic radiative coolers	Taguchi
Vyas et al. [29]	2019	Capacity of lead acid battery	Taguchi
Huirem and Sahoo [30]	2020	Solar-Assisted Vapor Absorption Refrigeration Systems (SAVARS)	RSM
Ahmed et al. [8]	2021	Refrigeration systems	Multiple Methods
Zawawi et al. [31]	2022	Automotive air-conditioning Systems	Taguchi

provides a list of previous studies using a range of optimization approaches in various applications.

Software solutions for optimization techniques have been used to optimize the properties of nanolubricants [32,33,34], vapor compression refrigeration systems (VCRS) [26,35,36,37,38,39], and AAC systems [40]. Artificial intelligence approaches for modeling and optimizing refrigeration systems were evaluated by Ahmed et al. [8]. They discovered that the COP is the most important cost function to optimize, followed by overall cost, energy consumption, and cooling capacity, according to trend analysis. To date, there are previous studies available which employ RSM approaches in order to optimize refrigeration [7,26,30] and AAC system performance [41]. Costa and Garcia [7] optimized the parameters of the refrigeration system using RSM. Parameters such as the temperature and flow rate of evaporators and condensers were considered. The behavior of R450A in VCRS was investigated by Zendehboudi et al. [26] using modeling and multi-objective optimization. They used RSM’s central composite design (CCD) to calculate the impact of each variable, model the system, and develop cost functions. The compressor’s power consumption was lowered by 18.39%, the discharge temperature was increased by 53.31%, and the refrigerant mass flow rate was increased by 215.57%. Huirem and Sahoo [30] used a combined Box–Behnken statistical design (BBD) and RSM technique to maximize the COP, exergetic COP (ECOP), and total exergy destruction (TED) of a LiBr-H₂O vapor absorption refrigeration system.

A concept of using two or more metal oxide nanoparticles in existing lubricants—known as composite nanolubricants—is adapted due to the limited contribution of single nanolubricants in terms of the stability, compressor operations, wear rates, and performance of AAC system. Nanofluids/nanolubricants have distinct thermal physical and tribological properties, as well as performance, compared to base fluids, according to several investigations [42,43,44,45]. Previous studies on the thermal physical and tribological properties, along with the performance and optimization of AAC using PAG based single-component nanolubricants with SiO₂, Al₂O₃, and TiO₂ metal oxides, are available in the literature [46,47,48,49,50]. Zawawi et al. [51] examined the thermal conductivity of single Al₂O₃, SiO₂, and metal oxide composite nanolubricants. Based on the comparison, metal oxide composite nanolubricants have a substantially higher thermal conductivity than single nanolubricants. Additionally, few studies investigated the performance of single nanolubricants and composite nanolubricants in refrigeration and AAC systems [41,52,53]. Sharif et al. [53] examined the performance of the AAC system employing SiO₂/PAG nanolubricants. They discovered a maximal COP enhancement of up to 24%. In another study, Redhwan et al. [41] claimed that COP and cooling capacity were improved by up to 31% and 32%, respectively, in another experiment. Meanwhile, Zawawi et al. [54] found that Al₂O₃-SiO₂/PAG composite nanolubricants showed greater COP and cooling capacity increases than single nanolubricants, with values of 28.10% and 65.21%, respectively, at 0.015% volume concentration. For the optimization of nanolubricants, Redhwan et al. [24] used the RSM approach to study the AAC system performance using single-component Al₂O₃ nanolubricants in a PAG based nanolubricant in AAC systems. They found that the compressor speed, initial refrigerant charge, and nanolubricant volume concentration all have a significant impact on the AAC system’s efficiency. The literature on the use of composite nanolubricants to improve the performance of AAC systems is scarce [55]. Despite this, no further research into the performance improvement of AAC systems using composite nanolubricants by employing RSM has been done in recent years.

Previous studies have reported on the impact of single-component nanolubricants on refrigeration and AAC system performance; however, more research into the effects of AAC system parameters operating with Al₂O₃-SiO₂/PAG using RSM is still essential. Therefore, in this study, the effects of operational parameters on COP, cooling capacity, compressor work (W_in), and power consumption for Al₂O₃-SiO₂/PAG nanolubricants in AAC systems were explored using RSM. The current study makes use of Design–Expert software, and the experiments are designed employing the FCD procedure. For maximum augmentation in COP and cooling capacity, as well as maximum decrease in W_in and power consumption, optimal operating settings, such as speed, initial refrigerant charge, and composite nanolubricants volume concentration, were determined.

2. Materials and Methods

2.1. Preparation of Al₂O₃-SiO₂ Composite Nanolubricants

In this investigation, Al₂O₃ and SiO₂ nanoparticles in dry powder form, as well as polyalkylene glycol (PAG) 46, were employed.

Table 2. Properties of nanoparticles [46,56].

Properties	Al2O3	SiO2
Molecular mass (g/mol)	101.96	60.08
Average particle diameter (nm)	13	30
Density (kg/m3)	4000	2220
Thermal Conductivity (W/m.k)	36	1.4
Specific heat (J/kg·K)	773	745

lists the features of these nanoparticles [46,56], and

Table 3. Properties of PAG 46 lubricant [57].

Properties	PAG 46
Density, g/cm3 @ 20 °C	0.9954
Flash Point, °C	174
Kinematic viscosity, cSt @ 40 °C	41.4–50.6
Pour point, °C	−51

illustrates the characteristics of PAG 46 lubricant at atmospheric pressure [57]. To confirm the existence of the nanoparticles, a chemical composition test was performed. The chemical composition of both nanoparticles was assessed by EDX analysis, as shown in Figure 1. In Figure 1a,b, the elemental composition of the materials for Al₂O₃ and SiO₂ nanoparticles, respectively, was validated. TEM evaluation was carried out for the composite nanolubricant to observe the colloidal nanoparticle dispersion in nanolubricants. Figure 2 shows TEM imaging of the Al₂O₃-SiO₂/PAG composite nanolubricants. Both nanoparticles were discovered to be spherical. In addition, the graph demonstrates the presence of two groups of nanoparticles with various diameters. Al₂O₃ nanoparticles are represented by the smaller diameter particles, while SiO₂ nanoparticles are represented by the larger diameter particles. The appearance of nanoparticles in grayscale shades may be caused by overlap particles and small aggregation. The formulation and characterization of composite nanolubricants was previously addressed in the literature. Therefore, this study focused on the preparation and formulation procedures for composite nanolubricants.

In this study, the Al₂O₃-SiO₂/PAG composite nanolubricants were made utilizing a two-step procedure, and their stability was then investigated using UV-Vis and zeta potential. Zawawi et al. [51] found that the best combination for both nanolubricants used is a composition ratio of 60:40. The Al₂O₃-SiO₂/PAG composite nanolubricants in a 60:40 ratio, according to the authors, produces better thermal characteristics [58], tribological behavior [59], and AAC system performance [54] compared to other combination ratios. Therefore, the optimum ratio for Al₂O₃-SiO₂/PAG composite nanolubricants is chosen for the current work as a continuation of the prior work. The nanolubricants of Al₂O₃/PAG and SiO₂/PAG were first prepared separately. A total volume of 63 mL of Al₂O₃/PAG nanolubricants was then mixed with 42 mL SiO₂/PAG using a magnetic stirrer. The desired volume concentrations used in this study are 0.005% up to 0.045%. Equation (1) is used to compute the volume concentration of the composite nanolubricants.

$$\mathsf{\varphi }=\frac{{\mathrm{m}}_{\mathrm{p}}/{\mathsf{\rho }}_{\mathrm{p}}}{{\mathrm{m}}_{\mathrm{p}}/{\mathsf{\rho }}_{\mathrm{p}}+{\mathrm{m}}_{\mathrm{L}}/{\mathsf{\rho }}_{\mathrm{L}}}\times 100$$

(1)

where $\mathsf{\varphi }$ is the volume concentration of nanolubricants (%), ${\mathrm{m}}_{\mathrm{p}}$ is the nanoparticle mass (g), ${\mathsf{\rho }}_{\mathrm{p}}$ is the nanoparticle density (kg/m³), ${\mathrm{m}}_{\mathrm{L}}$ is the lubricant mass (g), and ${\mathsf{\rho }}_{\mathrm{p}}$ is the lubricant density (kg/m³). The prepared composite nanolubricants were then sonicated in an ultrasonic bath for 2 h for a uniform dispersion and stable suspension, based on previous works [51,55,58,60,61,62], and shown in the Figure 3. The absorbance ratio of the mixed nanolubricant dispersions, measured at various sonication durations (0 to 2.0 h) up to 700 h, is shown in Figure 3. The graph is used to determine the ideal sonication duration required to preserve the stability of Al₂O₃-SiO₂/PAG composite nanolubricants. With the most stable composite nanolubricants, the absorbance ratio with the highest value indicates the ideal sonication time. According to the graph, two hours of sonication sustained the concentration ratio beyond 90%, even after up to 700 h of sedimentation.

The zeta potential and zeta sizer were used in the study to analyze the zeta potential reading and polydispersity index (PDI) of the composite nanolubricants. The current absolute zeta potential reading for the Al₂O₃-SiO₂/PAG is up to 61.1 mV. The zeta potential for Al₂O₃-SiO₂/PAG was found to be beyond the stable limit, thus proving an excellent stability. The current absolute zeta potential reading for the Al₂O₃-SiO₂/PAG is up to 61.1 mV, whereas other combination of metal oxides, i.e., Al₂O₃-TiO₂/PAG and TiO₂-SiO₂/PAG composite nanolubricants, which were studied prior to this work [51], recorded up to 31.7 mV and 22.7 mV, respectively. Previously, Redhwan et al. [41] reported that the zeta potential for Al₂O₃/PAG single nanolubricants was 37.8 mV. When compared to single-component nanolubricants, the Al₂O₃-SiO₂/PAG composite nanolubricants employed in this study showed improved stability. The present results were compared to the stability classification suggested by Lee et al. [63], as shown in Figure 4. The zeta potential for Al₂O₃-SiO₂/PAG was found to be beyond the stable limit, thus proving an excellent stability. The breadth or spread of the particle size distribution is described by the PDI, which is another crucial metric [64]. The maximum PDI value was found to be 0.86 for the Al₂O₃-TiO₂/PAG composite nanolubricants, while the lowest PDI value was found to be 0.22 for the Al₂O₃-SiO₂/PAG, as can be seen in Figure 4. In light of this, it should be observed that the lowest PDI value is quite comparable to that of the monodisperse state. A suspension will be monodisperse, according to Sadeghi et al. [65], if the PDI value is less than 0.3, and the size distribution curve has a single peak.

2.2. Design of Experiment with RSM

The initial step in RSM is to confirm a range with the optimal condition. Secondly, the relationship model between response and the group of independent factors must be established. The last stage is to optimize the process with the model. A selection of elements in RSM study included batch tests on AAC performance with parameters of composite nanolubricants including volume concentrations, compressor speeds, and refrigerant charges. Meanwhile, cooling capacity, compressor work, COP, and power consumption were selected for the output responses of the experiment. The RSM is used to optimize all AAC system performance responses simultaneously by incorporating them into a single objective function. The objective of RSM in the current study is to examine the effect of the compressor speed, initial refrigerant charge, and volume concentration of composite nanolubricants on the AAC system performance.

The CCD was used to optimize the model, and it worked well for fitting a quadratic surface and for process optimization in general. In this study, FCD is used because there is a common area of interest and operability, and the trials are based on the design matrix. Each parameter includes three levels of variation: (i) high (+1), (ii) low (−1), and (iii) center points (coded as level 0). Six central points, six axial points, and eight factorial points were used in this study, with alpha $\mathsf{\alpha }=1$. The $\mathsf{\alpha }$ value is denoted as the distance between each axial point and the CCD’s center [24]. Multi-objective responses of AAC performance optimization of optimum design, with the highest desirability, are sought. Three AAC system parameters, with their levels according to RSM analysis, were investigated. Twenty experimental runs, including six replicates at the center point, were used in an FCD with three factors and three levels. The factor levels of the independent variables for AAC system performance were previously shown in

Table 4. AAC system design parameter.

Level	A-Volume Concentration, φ (%)	B-Compressor Speed (rpm)	C-Refrigerant Charge (g)
−1	0.005	900	95
0	0.025	1500	125
1	0.045	2100	155

.

Table 5. The design of the experiment (DOE) and the results from the experiments.

φ (%)	Speed (rpm)	Refrigerant Charge (g)	Cooling Capacity (kW)	Compressor Work (kJ/kg)	COP	Power Consumption (kW)
0.005	900	95	0.665	23.10	8.13	0.61
0.045	900	95	0.477	24.80	7.65	0.59
0.005	2100	95	0.860	39.20	4.72	1.07
0.045	2100	95	0.568	43.10	4.31	1.06
0.005	900	155	0.777	19.70	9.16	0.68
0.045	900	155	0.873	20.20	8.66	0.73
0.005	2100	155	1.452	32.20	5.15	1.42
0.045	2100	155	0.954	34.50	4.87	1.34
0.005	1500	125	0.956	32.80	6.06	0.94
0.045	1500	125	0.770	33.30	5.62	0.89
0.025	900	125	0.797	21.90	8.52	0.60
0.025	2100	125	0.891	37.35	4.81	1.08
0.025	1500	95	0.667	33.00	5.49	0.71
0.025	1500	155	1.168	26.60	6.27	0.89
0.025	1500	125	0.832	31.00	5.85	0.85
0.025	1500	125	0.832	31.00	5.85	0.85
0.025	1500	125	0.832	31.00	5.85	0.85
0.025	1500	125	0.832	31.00	5.85	0.85
0.025	1500	125	0.832	31.00	5.85	0.85
0.025	1500	125	0.832	31.00	5.85	0.85

illustrates the complete design matrix for the experiments to be conducted, as well as the collected findings, which were analysed using analysis of variance (ANOVA) by Design–Expert Software (V13, Stat-Ease Inc., Minneapolis, MN, USA).

2.3. Data Analysis Using RSM

The model’s adequacy is further determined using ANOVA. The significance of each term in the model equation is used to calculate the goodness of fit in each case. The data is subjected to regression analysis to obtain the coefficient of the regression equation. Three-dimensional surface plots are then generated from the validated models. The normal plot of the residuals, predicted against the actual plots for all responses, were presented to ensure that the chosen model was suitable for predicting the response variables in the experimental values. Good agreement of both values is important for verification of the model [25]. The distribution of the close points along the straight lines indicates a good agreement between the test values and the calculated response values [22]. The normal probability is plotted to check for the residual range. Response surface plots as a function of two independent variables or factors, with the other parameters held constant, are useful tools for evaluating the interaction and correlation of the variables, as well as comprehending the main and interactive effects [66,67]. These surface plots are used to locate the optimum points of operating parameters to attain maximum performance of the AAC system. The desirability technique of RSM can ultimately be used to find the best combination of speed, refrigerant charge, and volume concentration of composite nanolubricants.

3. Results and Discussion

3.1. ANOVA Analysis

A summary of p-value and model statistics for cooling capacity are shown in

Table 6. P-value and model summary statistics for cooling capacity.

Source	p-Value	Std. Dev	R2	Adj R2 (%)	Pred R2 (%)	Remark
Linear	<0.0001	0.097	0.8075	0.7714	0.5784	suggested
2FI	0.0076	0.069	0.9207	0.8841	0.3576	suggested
Quadratic	0.7544	0.075	0.9293	0.8656	−0.1099	not suggested
Qubic	0.0088	0.035	0.9905	0.9698	−10.7188	aliased

. The CCD module suggested that a linear and 2FI model to be use for analysis. In order to analyse the cooling capability, linear and two-way interaction (2FI) models were both employed. The model has been improved by the addition of linear and interaction components, as shown by the low p-value (Prob > F). The quadratic model is not suggested for this case. The Qubic model was noted as aliased because of the existence of aliased terms. The Qubic model was not suggested, due to the insufficient running of experiments to independently estimate all the terms.

Table 7. ANOVA response for cooling capacity.

Source	Sum of Squares	df	Mean Square	F Value	p-Value
Model	0.70	6	0.17	25.16	<0.0001	significant
A	0.11	1	0.11	23.62	0.0003
B	0.13	1	0.13	26.84	0.0002
C	0.39	1	0.39	81.94	<0.0001
AB	0.061	1	0.061	12.66	0.0035
AC	7.849 × 10−4	1	7.849 × 10−4	0.16	0.6931
BC	0.028	1	0.028	5.7	0.0325
Residual	0.063	13	4.819 × 10−3
Lack of fit	0.063	8	7.830 × 10−3
Pure error	0.000	5	0.000
R2						0.9207
Adj R2						0.8841
Pred R2						0.3576
Adeq Precision						21.986

shows ANOVA analysis for cooling capacity. The model F value is noted at 25.16. This indicates that the proposed model is significant. A 95% significant level was used throughout all response analyses. Model terms with p-values less than 0.05 are considered as significant. The model terms are not significant if the value is larger than 0.10. All terms except AC, which is the combination of volume concentration and refrigerant charge, were significant. The fitness of model equation is validated by referring to the coefficient of regression R². R² = 92.07% for cooling capacity, demonstrating that the model could accurately predict the response. The closer the R² value to 1, the better the models fits the experimental data [68]. Pred R² of 0.3576 showed a great difference to the adj R² of 0.8841. Thus, model reduction was suggested. The signal-to-noise ratio is measured by Adeq precision, and a ratio greater than 4 is desired [22]. The signal was adequate in this case, with a ratio of 21.986.

Table 8. P-value and model summary statistics for compressor work.

Source	p-Value	Std. Dev	R2	Adj R2 (%)	Pred R2 (%)	Remark
Linear	<0.0001	1.47	0.9520	0.9429	0.9133	not suggested
2FI	0.1947	1.37	0.9661	0.9505	0.8683	not suggested
Quadratic	<0.0001	0.39	0.9979	0.9961	0.9852	suggested
Qubic	0.0377	0.24	0.9995	0.9985	0.4299	aliased

represents p-value and model summary statistics for compressor work. The CCD module suggested that a quadratic model be use for analysis. The Qubic model was not suggested for this case. The ANOVA analysis for compressor work was recorded in

Table 9. ANOVA response for compressor work.

Source	Sum of Squares	df	Mean Square	F Value	p-Value
Model	718.55	9	79.84	536.88	<0.0001	significant
A	7.92	1	7.92	53.27	<0.0001
B	587.52	1	587.52	3950.82	<0.0001
C	90.00	1	90.00	605.21	<0.0001
AB	2.00	1	2.00	13.45	0.0043
AC	0.98	1	0.98	6.59	0.0280
BC	7.22	1	7.22	48.55	<0.0001
A2	8.25	1	8.25	55.46	<0.0001
B2	7.88	1	7.88	53.02	<0.0001
C2	6.34	1	6.34	42.62	<0.0001
Residual	1.49	10	0.15
Lack of fit	1.49	5	0.30
Pure error	0.000	5	0.000
R2						0.9979
Adj R2						0.9961
Pred R2						0.9822
Adeq Precision						84.751

. The model F value = 536.88 implicated that the model was significant. All terms were significant. The fitness of the model equation is validated by referring to the coefficient of regression R². For compressor work, with an R² of 99.79%, the model was able to accurately predict the response. The Pred R² of 0.9852 was in reasonable agreement with the adj R² of 0.9961. An adequate signal was confirmed by the Adeq precision of 84.751.

Table 10. P-value and model summary statistics for COP.

Source	p-Value	Std. Dev	R2	Adj R2 (%)	Pred R2 (%)	Remark
Linear	<0.0001	0.43	0.9236	0.9093	0.8706	not suggested
2FI	0.8700	0.46	0.9276	0.8941	0.5939	not suggested
Quadratic	<0.0001	0.030	0.9998	0.9995	0.9974	suggested
Qubic	0.1951	0.025	0.9999	0.9997	0.8774	aliased

represents p-value and model summary statistics for COP. The CCD module suggested that a quadratic model be use for analysis. The Qubic model was not suggested for this case. The ANOVA analysis for COP was recorded in

Table 11. ANOVA response for COP.

Source	Sum of Squares	df	Mean Square	F Value	p-Value
Model	38.21	9	4.25	4604.92	<0.0001	significant
A	0.45	1	0.45	489.34	<0.0001
B	33.40	1	33.40	36228.04	<0.0001
C	1.45	1	1.45	1570.68	<0.0001
AB	0.010	1	0.010	11.22	0.0074
AC	1.886 × 10−3	1	1.886 × 10−3	2.05	0.1831
BC	0.14	1	0.14	149.91	<0.0001
A2	6.006 × 10−3	1	6.006 × 10−3	6.51	0.0288
B2	1.66	1	1.66	1798.26	<0.0001
C2	3.415 × 10−4	1	3.415 × 10−4	0.37	0.5564
Residual	9.220 × 10−3	10	9.220 × 10−4
Lack of fit	9.220 × 10−3	5	1.844 × 10−3
Pure error	0.000	5	0.000
R2						0.9998
Adj R2						0.9995
Pred R2						0.9974
Adeq Precision						225.476

. The model F value = 4604.92 implicated that the model was significant. Only the combination of A (volume concentration), B (compressor speed), C (refrigerant charge), and between the AB, BC, A² and B² terms, were considered significant. Thus, all insignificant terms were eliminated. R² = 99.98% for COP, indicating that the model was capable of accurately predicting the response. The adj R² of 0.9974 and the Pred R² of 0.9995 were in reasonable agreement. A signal with a precision of 225.476 was considered adequate.

The summary of p-value and model statistics for power consumption are shown in

Table 12. P-value and model summary statistics for power consumption.

Source	p-Value	Std. Dev	R2	Adj R2 (%)	Pred R2 (%)	Remark
Linear	<0.0001	0.024	0.9556	0.9473	0.9230	suggested
2FI	0.5746	0.025	0.9617	0.9440	0.8285	not suggested
Quadratic	0.0006	0.012	0.9927	0.9862	0.9181	suggested
Qubic	0.3124	0.011	0.9964	0.9885	−3.4727	aliased

. The CCD module suggested that a linear and quadratic model be used for analysis. Due to their superior accuracy over linear models, quadratic models were chosen. The Qubic model was noted as aliased and was not suggested due to insufficient running experiments to independently estimate all the terms.

Table 13. ANOVA response for power consumption.

Source	Sum of Squares	df	Mean Square	F Value	p-Value
Model	0.21	9	0.023	151.49	<0.0001	significant
A	6.882 × 10−5	1	6.882 × 10−5	0.45	0.005179
B	0.18	1	0.18	1176.19	<0.0001
C	0.021	1	0.021	135.83	<0.0001
AB	2.977 × 10−4	1	2.977 × 10−4	1.94	0.1935
AC	5.249 × 10−5	1	5.249 × 10−5	0.34	0.5713
BC	9.312 × 10−4	1	9.312 × 10−4	6.08	0.0334
A2	5.971 × 10−3	1	5.971 × 10−3	38.97	<0.0001
B2	2.481 × 10−4	1	2.481 × 10−4	1.62	0.2320
C2	5.313 × 10−4	1	5.313 × 10−4	3.47	0.0922
Residual	1.532 × 10−3	10	1.532 × 10−4	1.532 × 10−3
Lack of fit	1.532 × 10−3	5	3.064 × 10−4	1.532 × 10−3
Pure error	0.000	5	0.000	0.000
R2						0.9927
Adj R2						0.9862
Pred R2						0.9181
Adeq precision						41.908

shows the ANOVA analysis for power consumption. The F value for the model is 151.49, implying that the model is adequate. A 95% significant level was used throughout all response analyses. Model terms with p-values less than 0.05 are considered significant. All values greater than 0.10, on the other hand, imply that the model terms are not significant. In this case A, B, C, BC, and A² are significant model terms. The fitness of the model equation is validated by referring to the coefficient of regression R². The model was able to predict the reaction with a high accuracy for power consumption, with R² = 99.27%. Pred R² of 0.9862 showed a great difference compared to the Adj R² of 0.9181. Thus, model reduction was suggested. Adeq presicion was noted at 41.908, which indicated an adequate signal model.

3.2. Regression Analysis

Regression analysis was used to fit the supplied RSM response to a quadratic equation, to analyse the link between the inputs and outputs of the models, and to determine the ideal input parameters [25]. All insignificant terms are deleted to reduce the regression model. For cooling capacity, only A, B, C, and AB are chosen as significant model terms. Meanwhile, for compressor work, all terms are significant model terms. Significant model terms A, B, C, AB, BC, A², and B² were selected for COP, and A, B, C, BC, and A² were chosen for power consumption. The difference between Pred R² and the Adj R² of less than 0.2 was desired [24]. The final equation in terms of coded factors can be completed after removing insignificant terms, as shown in Equations (2)–(5) as follows:

Cooling capacity = 0.84 − 0.11 A + 0.11 B + 0.20 C − 0.087 AB

(2)

$$\mathrm{Compressor}\mathrm{work}=31.13+0.89\mathrm{A}+7.66\mathrm{B}-3.00\mathrm{C}+0.50\mathrm{AB}-0.35\mathrm{AC}-0.95\mathrm{BC}+1.73\mathrm{A}2+1.73{\mathrm{A}}^2-1.69{\mathrm{B}}^2-1.52{\mathrm{C}}^2$$

(3)

$$\mathrm{COP}=5.87-0.21\mathrm{A}-1.83\mathrm{B}+0.38\mathrm{C}+0.036\mathrm{AB}-0.13\mathrm{BC}-0.051{\mathrm{A}}^2+0.77{\mathrm{B}}^2$$

(4)

$$\mathrm{Power}\mathrm{consumption}=0.84-(9.041\times {10}^{-0.03})\mathrm{A}+0.28\mathrm{B}+0.10\mathrm{C}+0.052\mathrm{BC}+0.096{\mathrm{A}}^2$$

(5)

where A is the volume concentration of the composite nanolubricants (%), B is the speed (rpm), and C is the refrigerant charge (g).

3.3. Residual and Response Surface Plots

Figure 5 and Figure 6 depict a normal plot of residuals, as well as the normal plot projected against the actual plots for all responses. To compare the two values and examine the distribution of the residuals, the predicted and actual values of cooling capacity, compressor work, COP, and power consumption were plotted. All residuals in the graphs are located on a straight line, indicating that the errors have a normal distribution. The normal probability plot for any ANOVA should be evaluated for the range of residuals near the mean line, showing that residuals are generally fitted for all responses. Therefore, it can be concluded that the model for predicting AAC performance using RSM’s design factors, when applied to a specific set of parameters, has a high level of accuracy.

Response surface plots as a function of two independent variables or factors, with the other parameters held constant, are useful tools for evaluating the interaction and correlation of the variables, as well as for comprehending their main and interactive effects [66,67]. Figure 7 represents the interaction of volume concentration (0.005 to 0.045%) and speed (900 to 2100 rpm) and its effect on cooling capacity when the refrigerant charge is kept constant at 125 g. Increasing volume concentrations with increment of speed reduced the cooling capacity rate. Compressor speed has a greater effect on cooling capacity, as shown through the comparison of the slope between the volume concentration of composite nanolubricants and speed. Figure 8 shows the variation of the compressor work with speed for different refrigerant charges, while volume concentration is fixed at 0.025%. From the figure, compressor work increases against the increasing speed, but decreases with refrigerant charge. The interaction of volume concentration and speed on COP is shown in Figure 9. Refrigerant charge was fixed at 125 g. It was observed that volume concentration had a greater influence on COP, as increasing volume concentrations increased COP, whereas an increase in speed lowered the COP. Figure 10 shows the variation in the power consumption for different refrigerant charges and speeds, with the volume concentration fixed at 0.025%. An increase in refrigerant charge and speed resulted in significant increments in power consumption.

3.4. Optimization and Validation

A confirmation experiment of the control parameters [69] indicated by the RSM optimization technique is required for confirming the improved conditions [70].

Table 14. Optimum operating condition.

Parameter	Optimum Operating Condition
A—Volume Concentration, φ (%)	0.019
B—Compressor Speed (rpm)	900
C—Initial Refrigerant Charge (g)	155

represents the optimal conditions, with a high desirability of 81.6%. As stated in

Table 15. Validation Results.

No.	Responses
	Cooling Capacity			Compressor Work			COP			Power Consumption
	Pred.	Exp.	%	Pred.	Exp.	%	Pred.	Exp.	%	Pred.	Exp.	%
1	0.935	0.976	4.23	19.23	19.6	1.89	9.05	9.34	3.10	0.621	0.650	4.43
2		0.897	4.23		18.6	3.39		9.87	8.31		0.655	5.23
3		0.868	7.73		19.9	3.37		9.19	1.52		0.656	5.33
4		0.987	5.27		19.3	0.36		9.47	4.44		0.674	7.86
5		0.874	6.93		21.3	9.72		8.55	5.85		0.671	7.38
Avg			5.68			3.74			4.64			6.05

, five trial runs at the optimal level were carried out to test and evaluate the reliability of the constructed regression model against the experimental results. The expected and experimental values in the table are quite close to each other. For valid statistical analysis, error values should be less than 20% [71,72]. For all runs, the computed error values were less than 10% and were within acceptable bounds. The validation results were consistent with the current experimental data, reflecting a successful optimization.

4. Conclusions

The effects of experimental operating conditions, such as by volume concentration of composite nanolubricant, the compressor speed, and refrigerant charge, on cooling capacity, compressor work, COP, and power consumption were assessed. The optimization of operating conditions for an AAC system was performed in the present work using the RSM method. Based on the results of the RSM model, the optimal operation suggested for optimal AAC performance were found at a compressor speed of 900 rpm, refrigerant charge of 155g, and volume concentration of 0.019%; cooling capacity = 0.9346 kW, compressor work = 19.2296 kJ/kg, COP = 9.051, and power consumption = 0.6209 kW. The validation test runs were carried out to validate predicted results against the experimental results. The developed model shows that the predicted results are in excellent agreement with the experimental results, with an error value of less than 10%. Therefore, it was recommended to use Al₂O₃-SiO₂/PAG composite nanolubricants with these operating conditions for optimum performance in the AAC system.