The mono GNP and GNP-alumina hybrid nanofluids used in this study were prepared using a two-step technique. The GNP (15 nm thickness and 50–80 m²/g specific surface area) and gamma-alumina (20–30 nm diameter, 180 m²/g specific surface area) were purchased from Sigma Aldrich (Germany) and Nanostructured and Amorphous Materials Inc. (United States), respectively. Sodium dodecyl sulfate obtained from Sigma Aldrich (Germany) was used as surfactants to suspend the nanomaterials in distilled water stably. The hybrid nanofluids with a volume concentration of 0.1 vol% were prepared with different GNP and alumina (Al₂O₃) mixing ratios (25:75, 50:50, and 75:25). The weight of the nanomaterials was calculated using Eq. 1 φ =   ω GNP ( m ρ ) GNP + ω A l 2 O 3 ( m ρ ) A l 2 O 3   ω GNP ( m ρ ) GNP +   ω A l 2 O 3 ( m ρ ) A l 2 O 3 +   ( m ρ ) water   (1)

All measurements were done using Radwag AS 220. R2 digital weighing balance (±0.01 g accuracy, Poland). The sodium dodecyl sulfate surfactant at a nanomaterial-surfactant ratio of 1:1 was first added to the distilled water, and the mixture was agitated using a magnetic stirrer for 5 min. The mono or hybrid nanomaterial was then added, followed by further agitation for 10 min. Finally, the agitated nanofluid mixture was further sonicated for 45 min using a Q-700 Qsonica ultrasonicator (700 W, 20 kHz). To prevent overheating and evaporation of the nanofluid during sonication, the temperature of the nanofluid was maintained at a constant temperature of 20°C using a LAUDA ECO RE1225 water bath.

Different instruments were used to measure the thermophysical properties of the prepared nanofluids at different temperatures. The temperature of the nanofluids was controlled using the LAUDA ECO RE1225 water bath. All the instruments were first calibrated before the collection of data. The electrical conductivity of the nanofluids was measured using CON700 EUTECH electrical conductivity meter (±1% accuracy). The pH of the nanofluids was obtained using Jenway 3510 pH meter (±0.003 accuracy). SV-10 Vibro-viscometer (A and D, Japan; ±3% accuracy) was employed to determine the viscosity of the nanofluids. Finally, the thermal conductivity of the nanofluids was obtained using the DECAGON KD2 Pro thermal meter (±5% accuracy) with the aid of a KS-1 hot wire needle sensor.

The free convection heat transfer of GNP-alumina hybrid nanofluids was studied in a 99.7 mm × 113.2 mm × 120.8 mm rectangular cavity at different temperature gradients (20°C, 25°C, 30°C, and 35°C). The set-up for the study is presented in Figure 1. The set-up includes two PR20R Polyscience digital-controlled water baths (0.005°C accuracy) and isothermal shell and tube heat exchangers to achieve the cavity’s differential heating by maintaining the temperature of the cold and hot walls. In addition, Burkert 8,081 flow meter (accuracy ±0.01%) was employed to obtain the flow rate of water flowing through the heat exchangers. The temperatures in the cavity were measured using T-type thermocouples (Omega Engineering, United States, accuracy of 0.1°C) connected to Data Logger (SCXI-1303 National instrument).

The experimental data for the natural convection were collected after the nanofluids prepared were charged into the cavity and allowed to reach a steady-state after 1 h at different temperature gradients.

The average heat transfer rate, average heat transfer coefficient, Rayleigh number, and Nusselt number were calculated by measuring the flow rates, internal and external temperatures of the cavity. The model for the experimental values of the viscosity and thermal conductivity for the examined nanofluids were used in the calculations. The density, specific heat capacity, and coefficient of thermal expansion of the different nanofluid samples were estimated using Eqs 2, 3, 4. The thermophysical properties of the base fluid and nanomaterials are presented in Table 1. ρ NF = φ GNP ρ GNP + φ A l 2 O 3 ρ A l 2 O 3 + ( 1 − φ HNF ) ρ water (2) ρ NF C p , NF = φ GNP ρ GNP C p , GNP + φ A l 2 O 3 ρ A l 2 O 3 C p , A l 2 O 3 + ( 1 − φ HNF ) ρ water C p , water (3) ρ NF β NF = φ GNP ρ GNP β GNP + φ A l 2 O 3 ρ A l 2 O 3 β A l 2 O 3 + ( 1 − φ HNF ) ρ water β water (4)

The Rayleigh number, Ra, was estimated using Eq. 5 Ra =   gβ ( T h −   T c ) ρ 2 C p L 3 μ λ (5)

After that, the average heat transfer rate, Q, and average convection heat transfer coefficient, h, was calculated using Eqs 6, 7, respectively. Q = m ˙ C p Δ T (6) h =   Q A ( T h −   T c ) (7) Where   m ˙   is the mass flow rate,   T h   is the temperature of the hot wall, T c is the cold wall temperature, and A is the heat transfer area of the cavity.

The average Nusselt number, Nu, was evaluated using Eq. 8. Nu= hL λ (8)

The experimental result was validated by examining the Nu of distilled water in the cavity as a function of Ra at different temperature gradients of 20°C, 25°C, 30°C, and 35°C. Furthermore, the results obtained were compared with that of the model proposed by Berkovsky and Polevikov (1977) and Leong et al. (1998). The Berkovsky model and Leong model are presented in Eqs. 9, 10. Nu ¯ = 0.18 ( Pr 0.2 + Pr Ra ) 0.29 ( 1 ≤ H / L ≤ 2 , Ra ≤ 10 10 ) (9) Where Prandtl number, Pr = μ C p λ . N u ¯ = 0.145 × R a 0.292 ( 3.7 x 10 8 ≤ R a ≤ 7 × 10 9 ) (10)

Uncertainty analysis of Q, h, and Nu was done to quantify the data’s reliability due to the inputs’ variability. The inputs, which are a source of error, include temperature and flow rates. The values of uncertainty were obtained using Eqs. 11, 12, 13 (Giwa et al., 2020a). δ Q ˙ = ( ∂ Q ˙ ∂ m ˙ δ m ˙ ) 2 + ( ∂ Q ˙ ∂ Δ T δ Δ T ) 2 (11) δ h = ( ∂ h ∂ Q ˙ δ Q ˙ ) 2 + ( ∂ h ∂ A δ A ) 2 + ( ∂ h ∂ T h δ T h ) 2 + ( ∂ h ∂ T c δ T c ) 2 (12) δ N u =   ( ∂ N u ∂ h δ h ) 2 + ( ∂ N u ∂ L c δ L c ) 2 + ( ∂ N u ∂ λ δ λ ) 2 (13)

The maximum uncertainty for Q, h, and Nu are 5.96, 6.03, and 6.33%, respectively.

The stability of the nanofluid samples used for this study was studied using a transmission electron microscope, viscosity measurement, and visual technique. The transmission electron microscope images of the mono-GNP nanofluid and hybrid GNP-alumina (50:50) nanofluid are presented in Figure 2. The alumina particles can be observed on the surface of the GNP, which indicates the stability of the hybrid nanofluid. The stability of the nanofluids was further analyzed by taking the viscosity of the nanofluids over 24 h, which is more than the total time taken to carry out the experiments. The viscosity of all the nanofluids as a function of time is illustrated in Figure 3. The almost linear measurements of all the nanofluids indicate that the nanofluids remain relatively stable for at least 24 h. Also, the visual analysis displayed in Figure 4 shows that the nanofluids are stable for at least 3 weeks without any visible sedimentation.

The effects of temperature on the electrical conductivity ( σ N F ) of the hybrid nanofluids are depicted in Figure 5A. The σ N F of all the nanofluids and distilled water was found to increase as the temperature increases. This is in concordance with numerous studies (Mehrali et al., 2014; Giwa et al., 2020a). This can be attributed to the enhancement in the random movement of liquid molecules at elevated temperatures. Also, the σ N F all the nanofluids is higher than that of water, which shows the addition of GNP and alumina tends to improve the electrical conductivity of water. Further observation shows that nanofluids with a higher ratio of alumina tend to have higher σ N F . This indicates that alumina contributes the most to the σ N F of the hybrid nanofluids. This is clearly evident in the plot of σ r e l a t i v e as a function of temperature illustrated in Figure 5B. The σ r e l a t i v e is an indicator of the increase in electrical conductivity of nanofluid in relation to that of water. σ r e l a t i v e   is a ratio of σ N F to that of σ w a t e r . From Figure 5B, GNP-alumina (25:75) has a higher σ r e l a t i v e , followed by GNP-alumina (50:50) and GNP-alumina (75:25), while mono GNP nanofluid has the least increase. The σ w a t e r increased by 123.69–135.74%, 102.08–116.79%, 78.30–94.77%, and 61.89–79.06% with the addition of GNP-alumina (25:75), GNP-alumina (50:50), GNP-alumina (75:25) and GNP, respectively at the examined temperature. These enhancement results agree with previous studies on the electrical conductivity of mono or hybrid nanofluids. Giwa et al. (2020a) observed a σ N F enhancement of 134.12–255.34% with the addition of hybrid alumina-MWCNT (80:20) nanomaterials in water. Mehrali et al. (2014) reported an increase of 950% with the addition of GNP in base fluid.

The measured pH of water, mono-GNP nanofluid, GNP-alumina nanofluids with mixing ratios of 75:25, 50:50, and 25:75 were observed to range from 7.69–7.46, 8.06–7.01, 7.10–5.95, 8.19–6.87, and 8.25–7.41, respectively as the temperatures increase 15 °C–55 °C. This indicates that the pH of all the samples reduces at elevated temperatures. Further observation revealed that the hybrid GNP-alumina nanofluids have a lesser pH than mono GNP nanofluids. This shows that the addition of alumina causes a reduction in the H⁺ concentration of the GNP nanofluids.

The effects of temperature on the viscosity ( μ N F ) of the hybrid nanofluids are depicted in Figure 6A. The μ N F of all the nanofluids and distilled water was found to decrease as the temperature is elevated. This is in concordance with numerous studies (Said et al., 2015; Taherian et al., 2018). This temperature-induced diminution of nanofluid’s viscosity can be attributed to the reduction in the particle-particle and particle-molecules forces due to Brownian motion, which consequently lessens the resistance to flow. The μ N F of all the nanofluids are higher than that of water, which shows that the addition of GNP and alumina tends to increase the viscosity of water. The study further shows that GNP nanofluid has a higher viscosity than that of the hybrid nanofluids. Also, it can be observed that the increase in the mixing ratio of GNP produces an increase in the viscosity of the hybrid nanofluids. This can be confirmed in Figure 6B, which presents the relative viscosity ( μ r e l a t i v e ) of the nanofluids at different temperature. μ r e l a t i v e , which is the ratio of μ N F to that of μ w a t e r , indicates the increase in μ w a t e r   with the addition of mono or hybrid nanomaterials. From Figure 6B, it can be observed that the nanofluids with higher ratio of GNP tend to have a higher μ N F . Mono-GNP nanofluid has the highest μ r e l a t i v e , followed by GNP-alumina (75:25) and GNP-alumina (50:50) nanofluid, while GNP-alumina (25:75) nanofluid has the least μ r e l a t i v e . The μ w a t e r increased by 5.31–10.53%, 7.08–12.28%, 7.96–15.79%, and 9.73–17.54% with the addition of GNP-alumina (25:75), GNP-alumina (50:50), GNP-alumina (75:25) and mono-GNP, respectively at the examined temperature. The higher viscosity of mono-GNP nanofluid compared to that of its hybrid nanofluids is similar to the observation made Kumar and Sarkar (2020) in a study on another carbon-based hybrid nanofluids. They investigated the effect of particle ratio on the thermophysical properties of alumina-MWCNT hybrid nanofluids. They found that an increase in the MWCNT fraction increases the viscosity of the hybrid nanofluids. However, this disagrees with the study by Giwa et al. (2020a), as they observed a reduction in the viscosity of the alumina-MWCNT hybrid nanofluids as the MWCNT fraction increases. Also, the result of this present study agrees with the observation by Dezfulizadeh et al. (2021) that the addition of metal oxides in hybrid nanofluids prevent an increase in viscosity and also controls the viscosity at low pressure. The higher viscosity associated with a high ratio of GNP could be attributed to the higher intra-molecular force of GNP and the tendency of its particles to clump together. This clumpiness consequently increases the resistance of the layers of fluid to flow. It can be assumed that this flow resistance is improved due to Brownian motion at elevated temperatures, which results in a reduction in viscosity.

The effects of temperature on the thermal conductivity ( λ N F ) of the hybrid nanofluids are illustrated in Figure 7. An augmentation in the λ N F of all the nanofluids and distilled water was observed as the temperature is elevated. This observation agrees with numerous studies (Said et al., 2015; Taherian et al., 2018). The temperature-induced intensification of λ N F can be ascribed to the enhancement in Brownian motion of particles, which then causes more collision between molecules, thus transferring energy. The λ N F all the nanofluids is higher than that of water, which shows that the addition of GNP and alumina tends to increase the thermal conductivity of water ( λ w a t e r ) . Furthermore, the study shows that mono-GNP nanofluid has a higher thermal conductivity than that of the hybrid nanofluids. Also, it can be observed that the increase in the mixing ratio of GNP produces an increase in the thermal conductivity of the hybrid nanofluids. Thus, it is noteworthy to state that mono-GNP has the highest thermal conductivity enhancement, followed by GNP-alumina (50:50) and GNP-alumina (75:25), while GNP-alumina (25:75) has the least enhancement. The λ w a t e r increased by 1.66–3.09%, 1.99–4.23%, 1.83–3.42%, and 4.48–5.62% with the addition of GNP-alumina (25:75), GNP-alumina (50:50), GNP-alumina (75:25) and GNP, respectively at the examined temperatures. The higher λ N F of mono nanofluid agrees with the study by Kumar and Sarkar (2020) and Wang et al. (2021).

A new correlation for the electrical conductivity ( σ H N F ), viscosity ( μ H N F ) , and thermal conductivity ( λ H N F ) of the hybrid nanofluids was developed based on the experimental data (φ = 0.1 vol%). The developed correlation with a coefficient of determination (R ²) of 98.86, 97.68, and 94.31% is presented, respectively, in Eqs 14, 15, 16 as a function of temperature (T) and hybrid mixing ratio (R). σ H N F = 1229.50 + 3.307 T − 443.70 R (14) μ H N F = 1.3569 − 0.014025 T + 0.0528 R (15) λ H N F = 0.55675 + 0.002005 T + 0.018327 R (16) Where R, which is the ratio of the weight of GNP to the total weight of GNP-alumina, ranges from 0.25 to 1. Figures 8A–C shows that the developed correlation for the predicted values of σ H N F , μ H N F , and λ H N F highly corresponds with their experimental values. The developed correlation for σ H N F and μ H N F was observed to predict the experimental values with a margin of error which ranges from -2.79 to 2.63% and -5.93–5.28%, respectively. The margin of deviation between the predicted values and the experimental values of λ H N F lies between 1.24 and 0.78%.

Natural thermo-convection are employed for numerous applications where heat transfer without forced or external motion is required. This section focused on the experimental results of the study on the natural convection of GNP-based nanofluids in a cavity.

In order to assess the forced convective heat transfer performance of the nanofluids in a thermal system, Mouromtseff Number (Mo) was employed. Mo is an indicator of the efficacy of a thermo-fluid in a thermal system. It is noteworthy to state that higher Mo values indicate higher thermal performance. The Mo of the samples was estimated using Eq. 18 (Minea and Moldoveanu, 2017). M o =   ρ a C p b λ c μ d (18) Where the constants a = 0.8, b = 0.33, c = 0.67 and d = 0.47 for the nanofluids’ turbulent flow regime, while a = 0.8, b = 0.33, c = 0.8 and d = 0.47 for that of water (Huminic and Huminic, 2018; Leena and Srinivasan, 2018; Kumar et al., 2021).

Figure 14A shows Mo for the different hybrid nanofluids at different temperatures. All the nanofluids were found to display better heat transfer efficiency than water as the Mo of all the nanofluids is greater than water. It is noteworthy to state that all the GNP-alumina hybrid nanofluids exhibit better performance than the single GNP nanofluid. Also, the Mo results show that the nanofluid’s viscosity greatly influences the efficiency of a thermal system. This is evident as the hybrid nanofluids with the lowest viscosity exhibit the best performance. GNP-alumina (25:75) nanofluid displayed the best performance, followed by GNP-alumina (50:50) and GNP-alumina (75:25).

It is important to note that viscosity significantly influences the pumping power of a thermal system. A higher viscosity is expected to increase the pumping power. Thus, the pumping power for the turbulent flow will be evaluated using Eq. 19 (Huminic and Huminic, 2018). W N F W w a t e r = ( μ N F μ w a t e r ) 0.25 ( ρ w a t e r ρ N F ) 2 (19)

The pumping power ratio, W N F W w a t e r   is a measure of the heat transfer usefulness of a thermo-fluid. If the W N F W w a t e r   is less than 1, then the nanofluid is deemed to be suitable for heat transfer application. The pumping power ratio of the nanofluids at different temperatures is illustrated in Figure 14B. All the nanofluids were found to have a pumping power ratio of less than 1, which indicates that they are all useful for heat transfer applications. It can also be seen that GNP-alumina (25:75) nanofluids have the lowest power ratio, followed by GNP-alumina (50:50) and GNP- GNP-alumina (75:25) nanofluids, with GNP nanofluid having the higher pumping power ratio. The forced convection and the natural convection results show that the hybrid nanofluids offer more beneficial thermal performance than mono GNP nanofluids and water.