Thermal Performance Evaluation of Plate-Type Heat Exchanger with Alumina–Titania Hybrid Suspensions

Abstract

This paper aims to develop models for the thermal conductivity and viscosity of hybrid nanofluids of aluminium oxide and titanium dioxide (Al₂O₃-TiO₂). The study investigates the impact of fluid temperature (283 K–298 K) on the performance of a plate heat exchanger using Al₂O₃-TiO₂ hybrid nanofluids with different particle volume ratios (0:5, 1:4, 2:3, 3:2, 4:1, and 5:0) prepared with a 0.1% concentration in deionised water. Experimental evaluations were conducted to assess the heat transfer rate, Nusselt number, heat transfer coefficient, Prandtl number, pressure drop, and performance index. Due to the lower thermal conductivity of TiO₂ nanoparticles compared to Al₂O₃, a rise in the TiO₂ ratio decreased the heat transfer coefficient, Nusselt number, and heat transfer rate. Inlet temperature was found to decrease pressure drop and performance index. The Al₂O₃ (5:0) nanofluid demonstrated the maximum enhancement of around 16.9%, 16.9%, 3.44%, and 3.41% for the heat transfer coefficient, Nusselt number, heat transfer rate, and performance index, respectively. Additionally, the TiO₂ (0:5) hybrid nanofluid exhibited enhancements of 0.61% and 2.3% for pressure drop and Prandtl number, respectively. The developed hybrid nanofluids enhanced the performance of the heat exchanger when used as a cold fluid.

1. Introduction

Heat exchangers encounter several heat transfer issues during fluid flows. For this reason, industries have adopted the addition of nanoparticles to the working fluid to improve heat exchanger performance. Additives have been considered to enhance thermal properties [1,2,3]. Nanofluids are colloidal mixtures of base fluids and nano-sized particles (10–100 nm) [4,5]. Combining nanoparticles with base fluids makes it possible to improve thermal conductivity, density, viscosity, and specific heat, leading to enhanced heat transfer [6]. Nanofluids can be synthesised in a single or two-step process [7]. Due to their enhanced thermal conductivity, nanofluids find wide applications in various fields, such as heat exchangers [8], solar energy [9], refrigeration systems [10], and thermo-siphons [11]. The thermal conductivity of nanofluids can be measured using the 3-ω method, temperature oscillation, and transient hot-wire techniques [12,13,14]. The constants in models or empirical relationships utilised to evaluate nanofluids’ thermal conductivity and viscosity are based on experimental data [15,16,17,18,19,20,21,22,23].

Researchers have recently focused on developing hybrid nanofluids to enhance thermal conductivity further [24]. Some studies have explored these hybrid solutions’ preparation, characteristics, and heat transfer performance [25,26]. For instance, Qi et al. [27] studied the stability, thermal properties, and heat transfer behaviour of TiO₂ nanofluids. They found that surfactants are added to prevent the accumulation of nanoparticles in hybrid nanofluids [28]. Alkasmoul et al. [29] used TiO₂ and Al₂O₃-water nanofluids to cool a horizontal tube with constant heat flux, and they observed heat transfer degradation due to a decrease in Reynolds number for the same flow rate. Studies of water-based mono/hybrid nanofluids have shown that they can improve heat transfer characteristics and effectiveness in heat exchangers through energetic and exergetic performance analyses [30,31,32,33,34]. Hamid et al. [35] examined the thermal conductivity of hybrid nanofluids by dispersing TiO₂ and SiO₂ nanoparticles in the base fluid and reported a 16% increase in thermal conductivity. However, they also found that the 5:5 ratios of TiO₂/SiO₂ nanoparticles led to high viscosity. Charab et al. [36] established a nonlinear relation between thermal conductivity and particle concentration for Al2O3-TiO₂ hybrid nanofluids. Garud et al. [37] investigated the influence of different particles on the micro-plate heat exchanger. The oblate spheroid and platelet-shaped nanoparticles show superior and worse first and second law characteristics for Al₂O₃ and Al₂O₃/Cu nanofluids. Elias et al. [38] proposed a correlation for the thermal conductivity of hybrid nanofluids based on their shape function, finding that cylindrical particles outperformed other shapes. Various models have been proposed for hybrid nanofluid thermal conductivity [39,40,41,42,43,44] and a viscosity [19,41,45,46,47,48]. Hybrid nanofluids have also been found to improve the performance of plate heat exchangers (PHE) [49,50]. For instance, Maddah et al. [51] used Al₂O₃-TiO₂ hybrid nanofluids and observed enhanced exergetic efficiency. Hamid et al. [52] achieved heat transfer enhancement of up to 35.32% by mixing a 2:3 ratio of TiO₂/SiO₂ nanoparticles with the base fluid.

Based on previous investigations, limited research is available on evaluating the viscosity and thermal conductivity of Al₂O₃-TiO₂-water nanofluids and the thermal performance of plate heat exchangers (PHE) with hybrid nanofluids. Most studies have focused on the variation of nanoparticle concentration. In this study, the authors developed Al₂O₃-TiO₂ hybrid nanofluids with different particle volume ratios (0:5, 1:4, 2:3, 3:2, 4:1, and 5:0) at a concentration of 0.1% in deionised (DI) water. Experiments were conducted to evaluate the PHE performance with the developed hybrid nanofluids, examining the effects of varying particle volume ratios and fluid temperature (283 K-298 K) on various performance indicators. The authors also developed and verified thermal conductivity and viscosity evaluation models based on experimental data. Performance factors considered include the performance index (PI), heat transfer rate, heat transfer coefficient, Nusselt number, Prandtl number, and pressure drop.

This research aimed to investigate the effect of fluid temperature on the performance of a PHE using Al₂O₃-TiO₂ hybrid nanofluids with distinct particle volume ratios at a concentration of 0.1% in deionised water. To achieve this, suitable empirical relations were identified for the thermal conductivity and viscosity of the hybrid nanofluids. Experimental investigations were conducted on the PHE using the developed nanofluids to assess various performance indicators, including the performance index, heat transfer rate, Nusselt number, heat transfer coefficient, Prandtl number, and pressure drop.

2. Preparation and Characterization of Hybrid Nanofluids

A two-step method was followed for developing TiO₂-Al₂O₃-water hybrid nanofluid. The quantity of Al₂O₃ and TiO₂ nanoparticles was purchased and mixed in DI water. The mean size of Al₂O₃ and TiO₂ nanoparticles were 45 nm and 20 nm, respectively. Surfactant Span−80 was added to avoid particle accumulation in the hybrid solution. Hybrid nanofluid prepared with TiO₂ and Al₂O₃ particles of distinct ratios (0:5, 1:4, 2:3, 3:2, 4:1, and 5:0) with 0.1 v%. Equation (1) depicts the volume fractions of solids in the fluid.

$$\varphi =\left\{{\left(\frac{m}{\rho }\right)}_{p1}+{\left(\frac{m}{\rho }\right)}_{p2}\right\}{\left\{{\left(\frac{m}{\rho }\right)}_{p1}+{\left(\frac{m}{\rho }\right)}_{p2}+{\left(\frac{m}{\rho }\right)}_{bf}\right\}}^{-1}$$

(1)

Here ρ (kg/m³) is the density. ϕ is the solid volume fraction. m (kg) is the mass.

SEM (Scanning electron microscopy) and TEM (Transmission electron microscopy) tests were performed and measured the mean size of Al₂O₃ and TiO₂ nanoparticles by ImageJ software 2.0.0-rc-3 (https://imagej.net/imaging/particle-analysis) (accessed on 27 March 2023) as 45 nm and 20 nm, respectively. The small-size particles in Figure 1 represent TiO₂ nanoparticles, whereas larger ones are the Al₂O₃ nanoparticles. Both types of nanoparticles were found to be spherical, with a shape factor of 1. One of the key challenges in studying nanofluids is ensuring their stability and homogeneity. A stability test involving gravitational settling was performed to address this issue, and images of the test tube were taken at different intervals (Figure 2). The results showed that there was no sedimentation throughout the 7-day investigation.

The Hot Disk Thermal Constants Analyser (Figure 3) used the Transient Plane Source technique to measure the thermal conductivity of the base fluids, mono-nanofluid, and hybrid nanofluid with an accuracy of ±1.5%. The specific heat was also measured using the same device. The fluid density was determined by weighing the mass and volume of the liquid using a digital weighing machine. Repeated measurements were conducted to confirm consistency in the results. The DV1 Brookfield digital viscometer (Figure 4), with an accuracy of ±1.0%, was utilized to measure the viscosity of the base fluids, mono-nanofluid, and hybrid nanofluid. The viscometer operates by driving a plate immersed in the test sample, and the viscous force of the fluid was calculated using the measured spring deflection with 1.0 mL of fluid. The operative mechanism of the viscometer is to drive the plate immersed in the test sample. The viscous force of the fluid was evaluated from the measured spring deflection with the help of 1.0 mL of fluid.

3. Performance of PHE with Hybrid Nanofluid

Experimental investigations were carried out on plate heat exchangers (PHE) using Al₂O₃-TiO₂/Water-based binary nanofluid developed in-house. The performance parameters evaluated in the experiments included the performance index, heat transfer rate, heat transfer coefficient, Prandtl number, Nusselt number, and pressure drop. Figure 5 shows the experimental setup. The red arrow in Figure 5 shows the PHE, whose specifications are well described in earlier research [50].

The investigation employed a commercial PHE manufactured by Alfa Laval India Limited as the test section, which had an effective heat transfer area of 0.3 m², was made of SA 240 GR.316 stainless steel material, and had a plate thickness of 0.5 mm. The experimental setup included separate hot and cold fluid circuits. The hot circuit comprised an insulated tank with an immersion heater to maintain the desired inlet temperature of the hot fluid, a float-type flowmeter, a manometer, and a hot fluid pump. The tank contained DI water, which was heated and then pumped to the heat exchanger through a flowmeter to measure the fluid flow rate. The cold circuit consisted of an isothermal bath, a float flowmeter, a manometer, and a plate heat exchanger. A hybrid nanofluid was stored in the isothermal bath and cooled to maintain a constant inlet temperature of the cold fluid, which was then pumped to the plate heat exchanger via a flowmeter. Thermocouples were placed at the inlet and outlet of both hot and cold fluid streams to measure their temperatures, and a U-tube type differential manometer was used to measure the pressure difference between the inlet and outlet of the fluids. The pipes were insulated to minimise heat exchange with the surroundings. Once the inlet temperatures and flow rates of the hot and cold fluids were set, all the measuring parameters were recorded at the steady state condition.

Experiments considered DI water and hybrid solution as the hot and cold fluids, respectively. Heat transfer between a hot liquid (Q_h) and a cold liquid (Q_c) is evaluated from Equations (2) and (3):

$$Q_h={\dot{m}}_h{C}_{ph}(T_{hi}-T_{ho})$$

(2)

and

$$Q_c={\dot{m}}_{nf}{C}_{pnf}(T_{co}-T_{ci})$$

(3)

Experiments were conducted, keeping the hot inlet temperature $\left(T_{hi}\right)$ at 35 °C, and varying the cold inlet temperature $\left(T_{ci}\right)$ between 10 °C and 25 °C with a 3 lpm mass flow rate of both side fluids. LMTD (logarithmic mean temperature difference) value obtained from the measured temperature at terminal points. The hybrid nanofluid heat transfer coefficient (α_c) was obtained from the overall heat transfer coefficient (U) and hot water heat transfer coefficient (α_h).

$$\frac{1}{U}=\frac{1}{{\alpha }_h}+\frac{1}{{\alpha }_c}+\frac{t}{k_w}=\frac{A}{Q}\times LMTD$$

(4)

Here, kw represents the thermal conductivity of the plate material, and (in W/m-K) is the plate thickness (in mm). Q is the heat transfer rate (in W). A is surface area = 0.3 m².

The hot water heat transfer coefficient (α_h) evaluated from the Nusselt number [53]:

$$Nu=0.2594{\mathrm{Re}}^{0.76}{\mathrm{Pr}}^{0.3}$$

(5)

The Nusselt number (Nu) and the Prandtl number (Pr) for hybrid nanofluids obtained from

$$Nu=\frac{\alpha D_h}{k}$$

(6)

$$\mathrm{Pr}=\frac{\mu c_p}{k}$$

(7)

The pressure drop (Δp) was recorded during experiments. Assuming 80% pump efficiency [54], the performance index (PI) of PHE with hybrid nanofluids obtained from

$$PI=\frac{0.8{\rho }_{nf}Q}{\mathsf{\Delta }{p}_{nf}{m}_{nf}}$$

(8)

4. Uncertainty Study

Different parameters were measured using appropriate instruments during experimentation. The uncertainty in the parameters was estimated using Equation (9) [55].

$$\frac{\delta X}{X}=\sqrt{\left[{\left(\frac{\delta x_1}{x_1}\right)}^2+{\left(\frac{\delta x_2}{x_2}\right)}^2+----+{\left(\frac{\delta x_n}{x_n}\right)}^2\right]}$$

(9)

The estimated uncertainties are discussed in the Results and Discussion section.

5. Results and Discussion

This section describes the measured thermo-physical properties and post processing data based on primary data, empirical formulas to determine a hybrid nanofluid’s thermal conductivity, and viscosity. Moreover, the performance analysis of PHE is also discussed.

Table 1. (a). Thermo-physical properties of DI water. (b). Thermo-physical properties of hybrid nanofluids.

(a)
T (K)	${\mathit{k}}_{\mathit{b}\mathit{f}}$ (W/m-K)		${\mathit{\rho }}_{\mathit{b}\mathit{f}}$ (kg/m3)	${\mathit{\mu }}_{\mathit{b}\mathit{f}}$ (mPa·S)	${\mathit{C}}_{\mathit{P}\mathit{b}\mathit{f}}$ (J/kg·K)	${\mathbf{Pr}}_{\mathit{b}\mathit{f}}$
283	0.5823		997.8	0.9549	4183	6.774
288	0.5896		996.8	0.8706	4183	6.106
293	0.5964		996.0	0.8150	4183	5.668
298	0.6014		994.7	0.7493	4183	5.157
(b)
T (K)	Al2O3–TiO2–WaterNanofluids
	TiO2(0:5)	Hybrid (1:4)	Hybrid (2:3)	Hybrid (3:2)	Hybrid (4:1)	Al2O3(5:0)
	$\mathrm{Thermal}\mathrm{Conductivity},k_{hnf}$ (W/m-K)
283	0.5919	0.5921	0.5921	0.5921	0.5922	0.5922
288	0.5979	0.5993	0.5993	0.5994	0.5994	0.5994
293	0.6036	0.6046	0.6046	0.6047	0.6047	0.6047
298	0.6091	0.6100	0.6101	0.6109	0.6109	0.6109
	$\mathrm{Density},{\rho }_{hnf}$ (kg/m3)
283	1001.0	1000.9	1000.9	1000.8	1000.8	1000.7
288	1000.0	999.7	999.7	999.6	999.6	999.5
293	999.0	998.8	998.7	998.7	998.7	998.6
298	997.9	997.7	997.6	997.4	997.4	997.3
	$\mathrm{Viscosity},{\mu }_{hnf}$ (mPa·S)
283	0.9684	0.9684	0.9684	0.9684	0.9684	0.9684
288	0.8935	0.8786	0.8786	0.8786	0.8786	0.8786
293	0.8275	0.8187	0.8187	0.8187	0.8187	0.8187
298	0.7690	0.7612	0.7612	0.7535	0.7535	0.7535
	$\mathrm{Specific}\mathrm{Heat},C_{Phnf}$ (J/kg·K)
283	4169	4169	4169	4169	4169	4169
288	4169	4169	4169	4169	4169	4170
293	4169	4169	4169	4169	4169	4170
298	4168	4169	4169	4169	4169	4170
	Prandtl Number, Prhnf
283	6821	6819	6819	6819	6817	6817
288	6230	6112	6112	6111	6111	6112
293	5715	5645	5645	5644	5644	5646
298	5262	5202	5202	5142	5142	5143

displays the thermo-physical properties (including thermal conductivity ($k_{bf}$), density (${\rho }_{bf}$), viscosity (${\mu }_{bf}$), specific heat ($C_{Pbf}$), and the Prandtl number (${\mathrm{Pr}}_{bf}$)) measured using instruments with various temperatures (T) for the base fluid (DI Water), nanofluid, and hybrid nanofluid.

5.1. Empirical Relation for Thermal Conductivity

In the first step, the thermal conductivity of the samples was measured through experiments. The adequacy of the Corcione model [19] was then verified by modifying it with the obtained test data. Following this, hybrid nanofluid was prepared by dispersing alumina and titania nanoparticles in the base fluid. Different suspensions of 0.1 v% composition, with varying ratios (5:0, 4:1, 3:2, 2:3, 1:4, and 0:5) of alumina and titania nanoparticles, were tested for the specific temperature range (from 283 K to 298 K). Defining ${\varphi }_1$ and ${\varphi }_2$ are the concentrations of alumina and titania nanoparticles. $\varphi ={\varphi }_1+{\varphi }_2$, is the concentration of the hybrid nanocomposites. The modified Corcione model for thermal conductivity is:

$$k_{hnf}=k_{bf}\left\{1+f_k{\mathrm{Re}}^{0.4}{\mathrm{Pr}}^{0.66}{\left(\frac{T}{T_{fr}}\right)}^{10}{\left(\frac{k_p}{k_{bf}}\right)}^{0.03}{\varphi }^{0.66}\right\}$$

(10)

Corcione [19] suggested the constant, $f_k$ = 4.4, in Equation (10), whereas in the present study, $f_k$ =8.8. The reference temperature, $T_{fr}=$ 284 K. T is the working temperature. Re = $\frac{{\rho }_{bf}{k}_{B}T}{\pi r_p{\mu }_{bf}^2}$, is the Reynolds number. Pr is the Prandtl number. Thermal conductivity of the nanoparticles, $k_p=\frac{\varphi k_{p1}{k}_{p2}}{{\varphi }_1{k}_{p2}+{\varphi }_2{k}_{p1}}$. The equivalent radius of nanoparticles, $r_p={\left(\frac{{\varphi }_1{r}^3{}_1+{\varphi }_2{r}^3{}_2}{{\varphi }_1+{\varphi }_2}\right)}^{\frac{1}{3}}$. Boltzmann constant, $k_B=1.3807\times {10}^{-23}$.

Table 2. Thermal conductivity for Al₂O₃ and TiO₂ nanofluids (0.1 v%) with temperature.

T (K)	Thermal Conductivity (W/m·K)
	Al2O3 Nanofluid			TiO2 Nanofluid
	Test	${\mathit{f}}_{\mathit{k}}$ = 4.4 in Equation (10)	${\mathit{f}}_{\mathit{k}}$ = 8.8 in Equation (10)	Test	${\mathit{f}}_{\mathit{k}}$ = 4.4 in Equation (10)	${\mathit{f}}_{\mathit{k}}$ = 8.8 in Equation (10)
283	0.5922	0.5840	0.5858	0.5919	0.5836	0.5850
288	0.5994	0.5917	0.5939	0.5979	0.5912	0.5929
293	0.6047	0.5990	0.6016	0.6029	0.5983	0.6003
298	0.6109	0.6045	0.6077	0.6089	0.6038	0.6061

displays the experimental thermal conductivity results for 0.1 v% Al₂O₃ and TiO₂ nanofluids with temperature. The modified Corcione model (10) agrees with the experimental data. In a study by Tiwari et al. [55], thermal conductivity data of Al₂O₃ nanofluids at 323 K for different concentrations were generated, and the modified Corcione model (10) was found to be reasonably accurate in predicting the data, as shown in

Table 3. Thermal conductivity data of Al₂O₃ nanofluid at 323 K for different concentrations.

$\mathbf{Concentration}(\mathit{\varphi })$	Thermal Conductivity (W/m·K)		$\mathbf{Concentration}(\mathit{\varphi })$	Thermal Conductivity (W/m·K)
	Test [56]	${\mathit{f}}_{\mathit{k}}$ = 8.8 in Equation (10)		Test [56]	${\mathit{f}}_{\mathit{k}}$ = 8.8 in Equation (10)
0.005	0.6884	0.6953	0.035	0.8400	0.8408
0.010	0.7232	0.7276	0.040	0.8590	0.8593
0.015	0.7484	0.7546	0.045	0.8779	0.8771
0.020	0.7737	0.7787	0.050	0.8969	0.8942
0.025	0.7990	0.8007	0.055	0.9127	0.9107
0.030	0.8179	0.8213	0.060	0.9285	0.9268

. The modified Corcione model (10) predicts thermal conductivity well for low and high concentrations of Al₂O₃ nanofluids. A comparison of estimates with test data of thermal conductivity for the developed hybrid suspensions is shown in

Table 4. Thermal conductivity of hybrid nanofluids at different temperatures and particle ratio.

Fluid	Temperature, T (K)
	283	288	293	298
DI Water	0.5896	0.5964	0.6014	0.6077
TiO2 (0:5)	0.5919	0.5979	0.6029	0.6089
Hybrid (1:4)	0.5920	0.5983	0.6031	0.6094
Hybrid (2:3)	0.5921	0.5985	0.6035	0.6098
Hybrid (3:2)	0.5921	0.5987	0.6039	0.6102
Hybrid (4:1)	0.5922	0.5992	0.6043	0.6106
Al2O3 (5:0)	0.5922	0.5994	0.6047	0.6109

. The hybrid nanofluids exhibit higher thermal conductivity than the base fluid, with slightly lower thermal conductivity for titaniananofluids than for alumina nanofluids. Thus, the thermal conductivity of the solution is enhanced when the alumina contribution is higher in the solution. The thermal conductivity (Figure 6) increases with temperature, which is significant at high temperatures due to the Brownian effect. The experiments were conducted multiple times to ensure the measured data’s repeatability, and the data’s variation at each data point was represented using error bars.

The thermal conductivity of the hybrid nanofluid was modelled using the modified Corcione model (model 2), which considers the temperature, volume fraction, thermal conductivity and size of nanoparticles, and the base fluid thermal conductivity. The comparison between the measured and estimated thermal conductivity for hybrid nanofluid is presented in Figure 7. Based on the superposition principle, the model proposed by Eid and Nafe [57] gave low values for the thermal conductivity of a hybrid nanofluid. On the other hand, the modified Corcione model demonstrated an average deviation of only 0.3% between the test data and estimated values.

5.2. Empirical Relation for Effective Viscosity

The modified Corcione model for effective viscosity (${\mu }_{eff}$) of hybrid nanofluid is:

$${\mu }_{eff}={\mu }_{bf}{\left\{1-27.02{\left(\frac{d_p}{d_{bf}}\right)}^{-0.3}{\varphi }^{1.03}\right\}}^{-1}$$

(11)

Here,

$d_{bf}=\sqrt[3]{\frac{0.006M}{\pi N{\left({\rho }_{bf}\right)}_0}}$, represents the equivalent diameter of a fluid molecule; $M=18.0152891$ moles, represents the molecular weight of the fluid; $N=6.022\times {10}^{23}$, represents the Avogadro number; and ${\left({\rho }_{bf}\right)}_0=998$ kg/m³, describes the mass density of the base fluid at temperature $d_p=2r_p$, represents the particle diameter.

The measured viscosity of alumina (Al₂O₃) nanofluid and titania (TiO₂) nanofluid for different concentrations and temperatures are presented in

Table 5. Effective viscosity (${\mu }_{eff}$) of Al₂O₃ and TiO₂ nanofluids (0.1 v%) with temperature.

Temperature, T (K)	$\mathbf{Effective}\mathbf{Viscosity},{\mathit{\mu }}_{\mathit{e}\mathit{f}\mathit{f}}$ (mPa·s)
	Al2O3 Nanofluid Model 3		TiO2 Nanofluid
	Test	Equation (3)	Test	Equation (3)
283	0.9684	0.9600	0.9684	0.9614
288	0.8786	0.8753	0.8935	0.8766
293	0.8187	0.8194	0.8275	0.8206
298	0.7535	0.7533	0.7690	0.7544

. Estimates from Equation (11) match the test data with a 1.5% deviation. Estimates from Equation (11) and Tiwari et al. [55] test data for different particle concentrations at 323 K in

Table 6. Effective viscosity (${\mu }_{eff}$) of Al₂O₃ nanofluid (0.1 v%) at 323 K varying concentration ($\varphi$).

Concentration, $\mathit{\varphi }$	$\mathbf{Effective}\mathbf{Viscosity},{\mathit{\mu }}_{\mathit{e}\mathit{f}\mathit{f}}$ (mPa·s)
	Test [50,53]	Equation (3)
0.005	0.5467	0.5536
0.010	0.5596	0.5706
0.015	0.5763	0.5891
0.020	0.5973	0.6089
0.025	0.6220	0.6304
0.030	0.6511	0.6536
0.035	0.6839	0.6786
0.040	0.7211	0.7058

have a 2% deviation. The effective viscosity of the hybrid nanofluid (

Table 7. Effective viscosity (${\mu }_{eff}$) of hybrid nanofluid having different particle ratios at a specific temperature.

Fluid	$\mathrm{Effective}\mathrm{Viscosity},{\mu }_{eff}$ (mPa·s)
	Temperature, T (K)
	283	288	293	298
DI Water	0.9549	0.8706	0.8150	0.7493
TiO2 (0:5)	0.9707	0.8850	0.8285	0.7617
Hybrid (1:4)	0.9690	0.8835	0.8271	0.7604
Hybrid (2:3)	0.9683	0.8828	0.8264	0.7598
Hybrid (3:2)	0.9679	0.8824	0.8261	0.7595
Hybrid (4:1)	0.9675	0.8821	0.8258	0.7592
Al2O3 (5:0)	0.9673	0.8819	0.8256	0.7590

) is more than the base fluid. Due to high titania particle viscosity, titania nanofluid is high, and alumina nanofluid is low.

Estimated and measured effective viscosity (${\mu }_{eff}$) for alumina nanofluid and titania nanofluid are in agreement. In the case of a hybrid nanofluid, Equation (11) is used, replacing the particle size with an adequate size of the hybrid nanofluid. Figure 8 illustrates that the estimated viscosity had an average deviation of 0.8% from the measured viscosity. The error bar on the graph depicts the variability and repeatability of the experimental data.

Empirical relations for density and specific heat of hybrid nanofluid are [43]:

$${\rho }_{hnf}={\varphi }_1{\rho }_{p1}+{\varphi }_2{\rho }_{p2}+\left(1-{\varphi }_{}\right){\rho }_{bf}$$

(12)

$${\rho }_{hnf}{C}_{Phnf}={\varphi }_1{\rho }_{p1}{C}_{P1}+{\varphi }_2{\rho }_{p2}{C}_{P2}+\left(1-\varphi \right){\rho }_{bf}{C}_{Pbf}$$

(13)

5.3. Experimental Results

Experiments were conducted on a plate heat exchanger (PHE) with coolant as a hybrid nanofluid and hot fluid as DI water. Hybrid nanofluids were prepared by suspending TiO₂ and Al₂O₃ nanoparticles in ratios, 5:0, 4:1, and so on till 0:5, to a base fluid (DI water) at 0.1 v% for the specific operating temperature (varying from 283 K to 298 K). The hot fluid inlet temperature and flow rate were 35 °C (308 K) and 3 lpm, respectively. Factors determined for performance assessment of PHE were heat transfer rate (Q), heat transfer coefficient (α_nf), Nusselt number (Nu_nf), Prandtl number (Pr_nf), pressure drop (Δp_c), and performance index (PI).

Table 8. Recorded cold and hot fluids outlet temperature keeping the hot inlet temperature $\left(T_{hi}\right)$ at 35 °C and varying the cold inlet temperature $\left(T_{ci}\right)$.

Fluid	Outlet Temperature, Tco (°C) of the Cold Fluid				Outlet Temperature, Tho (°C) of the Hot Fluid
	$\mathbf{Cold}\mathbf{Inlet}\mathbf{Temperature},{\mathit{T}}_{\mathit{c}\mathit{i}}$ (°C)				$\mathbf{Cold}\mathbf{Inlet}\mathbf{Temperature},{\mathit{T}}_{\mathit{c}\mathit{i}}$ (°C)
	10	15	20	25	10	15	20	25
DI water	23.55	26.20	28.85	30.95	21.42	23.81	26.44	28.95
TiO2 (0:5)	23.65	26.32	29.06	31.15	21.40	23.72	26.39	28.91
Hybrid (1:4)	23.68	26.37	29.10	31.28	21.39	23.69	26.37	28.89
Hybrid (2:3)	23.72	26.44	29.18	31.41	21.37	23.66	26.35	28.87
Hybrid (3:2)	23.76	26.53	29.27	31.50	21.35	23.63	26.33	28.85
Hybrid (4:1)	23.79	26.61	29.35	31.59	21.33	23.60	26.31	28.83
Al2O3 (5:0)	23.82	26.69	29.43	31.68	21.31	23.59	26.30	28.82

provides the recorded outlet temperature of cold $\left(T_{co}\right)$ and hot $\left(T_{ho}\right)$ liquids. Thermo-physical properties of fluids at 25 °C are in

Table 9. Thermo-physical properties of fluids at 25 °C.

	Cp (J/kg·K)	k (W/m·K)	ρ (kg/m3)	μ (mPa·s)
DI water	4183	0.6077	994.7	0.7493
TiO2 (0:5)	4169	0.6136	997.9	0.7544
Hybrid (1:4)	4169	0.6120	997.7	0.7538
Hybrid (2:3)	4169	0.6114	997.6	0.7536
Hybrid (3:2)	4169	0.6110	997.4	0.7535
Hybrid (4:1)	4169	0.6108	997.4	0.7534
Al2O3 (5:0)	4170	0.6107	997.3	0.7533

. These recorded data are used for the calculation of heat transfer rate (Q), heat transfer coefficient (αnf), Nusselt number (Nu_nf), Prandtl number (Pr_nf), pressure drop (Δp_c), and performance index (PI).

The uncertainties estimated from equation 9 are 2.1%, 2.0%, 3.9%, 4.5%, 0.1%, and 1.2% in the performance index, heat transfer rate, convective heat transfer coefficient, Nusselt number, pressure drop, and Prandtl number, respectively.

The results of performance parameters with hybrid nanofluids at a constant flowing rate of 3 lpm and varying inlet temperatures (283 K to 298 K) are presented in

Table 10. Performance parameters varying coolant inlet temperature from 283 K to 298 K.

	Heat Transfer Rate, Q (kW)				Pressure Drop, Δpc (Pa)
	283 K	288 K	293 K	298 K	283 K	288 K	293 K	298 K
DI water	2833.983	2342.48	1790.978	1264.443	315.01	310.46	305.5	300.4
TiO2 (0:5)	2845.343	2359.654	1810.557	1281.66	316.25	311.5	307.4	302.6
Hybrid (1:4)	2851.596	2360.077	1812.895	1286.066	316.16	311.31	307.21	302.42
Hybrid (2:3)	2859.934	2372.668	1818.571	1289.165	316	311.09	307.13	302.26
Hybrid (3:2)	2868.272	2378.429	1832.332	1295.925	315.9	310.89	306.78	302.1
Hybrid (4:1)	2869.526	2390.105	1839.008	1301.686	315.76	310.75	306.53	301.84
Al2O3 (5:0)	2870.779	2407.365	1848.155	1307.78	315.64	310.64	306.38	301.61
	Nusselt number, Nunf				Prandtl number, Prnf
DI water	10.116	11.056	12.274	14.353	6775	6106	5645	5143
TiO2 (0:5)	10.192	11.351	12.683	14.997	6821	6158	5715	5262
Hybrid (1:4)	10.248	11.400	12.767	15.112	6819	6116	5669	5244
Hybrid (2:3)	10.333	11.597	12.984	15.368	6819	6115	5665	5225
Hybrid (3:2)	10.418	11.763	13.350	15.760	6818	6114	5661	5204
Hybrid (4:1)	10.455	11.969	13.620	16.169	6817	6113	5658	5182
Al2O3 (5:0)	10.484	12.209	13.898	16.713	6817	6111	5656	5158
	Heat transfer coefficient, αnf (W/m2.K)				Performance Index, PI
DI water	1217.26	1345.69	1506.43	1780.02	549.49	454.39	347.58	245.51
TiO2 (0:5)	1231.13	1385.00	1562.34	1864.27	551.72	457.67	351.31	248.80
Hybrid (1:4)	1238.34	1394.31	1575.24	1881.25	552.84	457.76	351.77	249.66
Hybrid (2:3)	1248.58	1418.40	1602.10	1913.42	554.47	460.22	352.88	250.27
Hybrid (3:2)	1258.94	1438.95	1647.46	1964.82	556.09	461.34	355.56	251.58
Hybrid (4:1)	1263.59	1464.10	1680.88	2015.89	556.34	463.61	356.86	252.71
Al2O3 (5:0)	1267.07	1493.51	1715.09	2083.64	556.59	466.97	358.64	253.90

. As expected, the heat transfer rate decreases with the inlet temperature of the cold fluid, whereas the addition of hybrid nanofluids increases the heat transfer rate. Specifically, the Al₂O₃ and TiO₂ particle combination with a ratio of 5:0 (Al₂O₃ (5:0)) shows an augmentation in the heat transfer rate of 3.44%. This improvement is attributed to the higher thermal conductivity of solid particles compared to the base fluid, resulting in an overall enhancement of the thermal conductivity of the solution. Moreover, since the thermal conductivity of alumina is greater than that of titania nanoparticles, Al₂O₃ (5:0) fluid offers the maximum heat transfer rate.

Furthermore, an investigation was conducted to determine the heat transfer coefficient of the fluid. The results indicate that the combination of Al₂O₃ (5:0) offers the best performance, with an improvement of 16.9% in the heat transfer coefficient. This finding can be attributed to this fluid’s high thermal conductivity and heat transfer rate, leading to an elevated heat transfer coefficient. In addition, the Nusselt number was found to have increased by 16.9% for the Al₂O₃ (5:0) nanofluid. The Nusselt number is directly related to the heat transfer coefficient. Consequently, since the heat transfer coefficient is highest for the Al₂O₃ (5:0) nanofluid and lowest for water, the Nusselt number behaves similarly. Furthermore, the heat transfer coefficient and Nusselt number increase with an increase in the inlet temperature of the fluid.

The decrease in the inlet temperature of the coolant led to a reduction in pressure drop, whereas hybrid nanofluids caused an increase in pressure drop. Among the hybrid nanofluids, TiO₂ (0:5) showed the highest pressure drop with a negligible increase of 0.6%. The addition of nanoparticles increased pressure drop due to the mass-volume ratio. The fluid with the highest mass-volume ratio exhibited the maximum pressure drop.

Using hybrid nanofluids with high heat capacity improved the heat transfer coefficient and heat transfer rate. However, the increase in viscosity resulted in a higher pressure drop. The Performance Index (PI) was utilized as a criterion to compare the enhancement in heat transfer rate and pump work. The results showed that adding nanoparticles to the base fluid increased both factors. The PI, defined as the heat transfer rate and pressure drop ratio, was highest for the Al₂O₃ (5:0) nanofluid, indicating that the heat transfer rate improvement was greater than the pump work increase. The PI increased by 3.41%.

It was observed that the Prandtl number reduces with a rise in the temperature. Furthermore, it was enhanced with the addition of nanoparticles in the primary fluid. It was increased by around 2.3% for the titania nanofluid (TiO₂ (0:5)) case because viscosity is higher and thermal conductivity is less for titania than alumina nanofluid. Moreover, the Prandtl number is a viscosity and thermal conductivity ratio. The improved performance characteristics of hybrid nanofluids make them a superior preference for industrial applications.

6. Conclusions

The heat transfer performance of a plate-type heat exchanger (PHE) primarily depends on thermal properties such as thermal conductivity. To enhance thermal conductivity, nanoparticles are introduced into the base fluid. This study presents empirical models for determining the thermal conductivity and viscosity of TiO₂–Al₂O₃/water hybrid nanofluids by modifying the Corcione empirical relations with measured data. These models can estimate binary and mono nanofluids’ thermal conductivity and viscosity.

Additionally, the heat transfer characteristics of Al₂O₃-TiO₂ hybrid nanofluid were investigated in a plate-type heat exchanger. The experiments were performed at various particle ratios and inlet temperatures, using a 0.1% volume concentration. The results of the investigation are presented below:

• The Al₂O₃-TiO₂/water-based hybrid nanofluids performed better than DI water. However, as the concentration of TiO₂ particles in the solution increased, the heat transfer coefficient and the heat transfer rate decreased. An improvement of 16.9% in heat transfer coefficient, 16.9% in Nusselt number, and 3.44% in heat transfer rate were observed with 0.1% volume concentration of Al₂O₃/water nanofluid;
• Pressure drop reduces with inlet temperature. A total of 0.61% enhancement was observed in the pump work for 0.1 v% TiO₂-water nanofluid;
• The Prandtl number was observed to be highest for TiO₂-water nanofluid with an enhancement of 2.3%;
• An increase in the inlet temperature results in a reduction in the performance index, whereas the use of hybrid nanofluids leads to its improvement. The alumina nanofluid showed an enhancement of 3.41% in the performance index;
• The use of hybrid nanofluids as coolants in plate heat exchangers improved their performance. Among the studied fluids, the alumina nanofluid performed better in most cases.