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

: This paper aims to develop models for the thermal conductivity and viscosity of hybrid nanoﬂuids of aluminium oxide and titanium dioxide (Al 2 O 3 -TiO 2 ). The study investigates the impact of ﬂuid temperature (283 K–298 K) on the performance of a plate heat exchanger using Al 2 O 3 -TiO 2 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 TiO 2 nanoparticles compared to Al 2 O 3 , a rise in the TiO 2 ratio decreased the heat transfer coefﬁcient, Nusselt number, and heat transfer rate. Inlet temperature was found to decrease pressure drop and performance index. The Al 2 O 3 (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 TiO 2 (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.


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].
Here ρ (kg/m 3 ) 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 Al 2 O 3 and TiO 2 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 TiO 2 nanoparticles, whereas larger ones are the Al 2 O 3 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.
Fluids 2023, 8, x FOR PEER REVIEW 3 of 17 Here ρ (kg/m 3 ) 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.
Here ρ (kg/m 3 ) 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, mononanofluid, 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. 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, mononanofluid, 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.

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 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, mononanofluid, 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.

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].

Performance of PHE with Hybrid Nanofluid
Experimental investigations were carried out on plate heat exchangers (PHE) using Al 2 O 3 -TiO 2 /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 m 2 , 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 (Qh) and a cold liquid (Qc) is evaluated from Equations (2)   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 m 2 , 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): and Experiments were conducted, keeping the hot inlet temperature (T hi ) at 35 • C, and varying the cold inlet temperature (T ci ) 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 ).
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 m 2 .
The hot water heat transfer coefficient (α h ) evaluated from the Nusselt number [53]: The Nusselt number (Nu) and the Prandtl number (Pr) for hybrid nanofluids obtained from The pressure drop (∆p) was recorded during experiments. Assuming 80% pump efficiency [54], the performance index (PI) of PHE with hybrid nanofluids obtained from

Uncertainty Study
Different parameters were measured using appropriate instruments during experimentation. The uncertainty in the parameters was estimated using Equation (9) [55].
The estimated uncertainties are discussed in the Results and Discussion section.

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 displays the thermo-physical properties (including thermal conductivity (k b f ), density (ρ b f ), viscosity (µ b f ), specific heat (C Pb f ), and the Prandtl number (Pr b f )) measured using instruments with various temperatures (T) for the base fluid (DI Water), nanofluid, and hybrid nanofluid.

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 φ 1 and φ 2 are the concentrations of alumina and titania nanoparticles. φ = φ 1 + φ 2 , is the concentration of the hybrid nanocomposites. The modified Corcione model for thermal conductivity is: 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 f r = 284 K. T is the working temperature.    (10) agrees with the experimental data. In a study by Tiwari et al. [55], thermal conductivity data of Al 2 O 3 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. The modified Corcione model (10) predicts thermal conductivity well for low and high concentrations of Al 2 O 3 nanofluids. A comparison of estimates with test data of thermal conductivity for the developed hybrid suspensions is shown in Table 4. 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. 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.

Empirical Relation for Effective Viscosity
The modified Corcione model for effective viscosity ( eff  ) of hybrid nanofluid is:

Empirical Relation for Effective Viscosity
The modified Corcione model for effective viscosity (µ e f f ) of hybrid nanofluid is: Here, , represents the equivalent diameter of a fluid molecule; M = 18.0152891 moles, represents the molecular weight of the fluid; N = 6.022 × 10 23 , represents the Avo-gadro number; and ρ b f 0 = 998 kg/m 3 , describes the mass density of the base fluid at temperature d p = 2r p , represents the particle diameter.
The measured viscosity of alumina (Al 2 O 3 ) nanofluid and titania (TiO 2 ) nanofluid for different concentrations and temperatures are presented in Table 5. 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 have a 2% deviation. The effective viscosity of the hybrid nanofluid (Table 7) 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 (µ e f f ) 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.
Estimated and measured effective viscosity ( 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]:

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 TiO 2 and Al 2 O 3 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 (∆p c ), and performance index (PI). Table 8 provides the recorded outlet temperature of cold (T co ) and hot (T ho ) liquids. Thermo-physical properties of fluids at 25 • C are in Table 9. 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 (∆p c ), and performance index (PI).  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. 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 Al 2 O 3 and TiO 2 particle combination with a ratio of 5:0 (Al 2 O 3 (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, Al 2 O 3 (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 Al 2 O 3 (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 Al 2 O 3 (5:0) nanofluid. The Nusselt number is directly related to the heat transfer coefficient. Consequently, since the heat transfer coefficient is highest for the Al 2 O 3 (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, TiO 2 (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 Al 2 O 3 (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 (TiO 2 (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.

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 TiO 2 -Al 2 O 3 /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 Al 2 O 3 -TiO 2 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 Al 2 O 3 -TiO 2 /water-based hybrid nanofluids performed better than DI water. However, as the concentration of TiO 2 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 Al 2 O 3 /water nanofluid; • Pressure drop reduces with inlet temperature. A total of 0.61% enhancement was observed in the pump work for 0.1 v% TiO 2 -water nanofluid; • The Prandtl number was observed to be highest for TiO 2 -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.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.