Transient Thermal Response Analysis of Al₂O₃-Graphene Hybrid Nanofluid-Enhanced Heat Pipes at Varying Inclination Angles and Heat Loads

A considerable amount of effort in the field of electronic cooling has focused on developing cooling technologies to meet the demands of steady-state operations. Nevertheless, it is a general observation that electronic devices are deployed in time-variant loading conditions. These include microprocessors (especially those deployed in mobile technology), power-electronic devices (such as insulated-gate bipolar transistors, IGBTs), and high-power semiconductor laser diode arrays (LDAs) [1].

The increasing power and heat dissipation rates in electronic devices have significantly increased heat generation, making heat dissipation a design challenge in recent years. Effective heat transfer in the cooling of CPUs, LEDs, Rectifiers, Transistors, travelling-wave receivers, Audio, and Radio Frequency (RF) amplifiers is essential, as the reliability of these devices depends strongly on operating temperature. The cooling systems of these devices must be efficient to achieve high performance. Approximately 50% of failures of these devices are attributable to temperature-related issues. This proves the requirement for compact cooling systems for these devices. Raising the temperature by 10 ℃ will halve the service life of these devices. Lowering the temperature by 10 ℃ can extend their lifespan by a factor of 2. A transient thermal management system must be used in these devices to ensure their performance [2, 3].

Figure 1. Heat pipe

As shown in Figure 1, Heat pipes are passive systems that can transfer heat over long distances without significant temperature loss. Specialists, researchers, and students seeking information on heat pipe science typically spend considerable time browsing archival journals and books on heat pipes. This is among the reasons researchers continue to develop innovative applications of heat pipes [4].

A capillary heat pipe, also referred to as a conventional heat pipe, is a sealed container with a wick structure that lines the inner wall of a tube. The wick is a critical component of the heat pipe, serving as a capillary pump that returns the liquid to the evaporator section. The heat pipe was filled with an appropriate amount of working fluid to saturate the wick. The following describes the operation of a capillary heat pipe: The capillary heat pipe is heated at its evaporator section. The water absorbs heat and evaporates. The vapour then travels to the condenser part due to a higher vapour pressure in the evaporator. The vapour, now hot, condenses to a liquid using the latent heat of vaporisation. The liquid is then sucked by capillary action to the evaporator part of the heat pipe, thus forming a cycle. Capillary heat pipes are most effective due to their two-phase cycle, which enables efficient heat transfer over long distances with minimal temperature drop. They can also maintain a nearly uniform temperature across the surfaces, making them ideal for temperature regulation. However, the critical limitation of these heat pipes is the capillary limit. This occurs when the wick fails to provide sufficient liquid flow to the evaporator, resulting in a markedly elevated, constant rise in evaporator temperature. The conventional capillary heat pipe is widely used in consumer electronics, such as laptops and notebooks, to dissipate heat from processors efficiently. Furthermore, it is used in commercial applications and critical space programs due to its high performance and reliability.

A heat pipe’s thermal characteristics depend on multiple coupled factors, including the working fluid, filling ratio, inclination angle, and heat load. In recent years, nanofluids comprising a specific nanoparticle type and a base working fluid have attracted considerable attention owing to their enhanced thermal conductivity. However, traditional nanofluids have exhibited performance instability, primarily due to nanoparticle agglomeration that settles at the bottom of the heat pipe during operation. To compensate for this drawback, there is a growing interest in hybrid nanofluids that combine two distinct nanoparticle types with an appropriate base working fluid, thereby improving thermal conductivity while maintaining the stability of the working fluid.

This paper examines the transient thermal performance characteristics of a copper heat pipe filled with an Al₂O₃-graphene hybrid nanofluid. Hybrid nanofluids were prepared at volume concentrations of 4%–3%, 3%–2%, and 6%–3% (Al₂O₃-graphene), using water as the base fluid. The thermal performance of a heat pipe was then measured over a fixed 10-minute post-heating period under different heat loads, with the heat pipe inclined at 0°, 60°, and 90°, at 50% fill ratio, and forced convective cooling. The experimental observations revealed that hybrid nanofluids exhibited superior transient thermal performance relative to water during the initial phase.

Despite extensive research on heat pipes using mono- and hybrid nanofluids, a significant limitation in most studies is the availability of steady-state thermal performance evaluation, which overlooks the transient phenomena during which most electronics fail. Also, most current research considers either the nanofluid combination, the angle of inclination, or the heat load, but not the combination of these factors under transient operating conditions. Furthermore, experimental research on the transient performance of Al₂O₃-graphene hybrid nanofluid-based heat pipes at short time scales is minimal. The novelty of the current study relies upon the evaluation of the transient performance (10 minutes) of a heat pipe considering the combination of the concentration of the hybrid nanoparticles, the angle of inclination, and the heat load, considering thermal resistance as the performance criterion, which fetches significant information applicable to practical electronics involving shorter-time heating effects before achieving a steady-state heat dissipation operation.

The remainder of this paper is organised as follows: Section 2 provides a comprehensive review of the literature on heat pipe cooling, including the effects of working fluid, mono- and hybrid nanofluids, inclination angles, and wick design. Section 3 also explains the method used to prepare Al₂O₃-graphene hybrid nanofluids, including the principles underlying the estimation of their thermophysical properties. Section 4 also describes the preparation of the heat pipe and the cooling system setup, including the instrumentation and testing conditions employed to conduct the transient thermal performance analysis of the heat pipe at different inclination angles and heat inputs. Section 5 also explains the principles of the procedure for estimating the performance characteristics and relevant parameters of the heat pipe described above. Section 6 also offers a comprehensive discussion and analysis of the results, including the effects of inclination angles, heat inputs, and the different compositions of the hybrid fluid. Finally, Section 7 presents the concluding remarks and future work.

3.1 Preparation method

Al₂O₃ and Graphene nanoparticles were bought from Shilpent. For the synthesis of the hybrid nanofluid, graphene particles and Al₂O₃ nanopowders are initially blended in a predetermined ratio using a mortar and pestle to achieve a uniform mixture. The powdery mixture is then gradually infused into de-ionised (DI) water using a magnetic stirrer or a glass stirrer to achieve a uniform mixture in about 15–30 minutes. Following stirring, the mixture is placed in an ultrasonic bath to disperse particles uniformly, with a 20-minute on/5-minute off cycle for 1 hour. To prevent overheating, ice packs or chilled water are placed around the beaker to keep the bath temperature below 40 ℃ during sonication. The nanofluid is used immediately after preparation, maintaining stability for approximately 2–4 hours. If slight sedimentation occurs, gentle swirling or brief re-sonication is performed before use. Hybrid nanofluids with 4%–3%, 3%–2%, and 6%–3% (Al₂O₃- Graphene by volume) were prepared using water as the base fluid. The thermophysical properties of Al₂O₃ and graphene nanoparticles used in this study are presented in Table 1. Table 2 shows the thermophysical properties of graphene/water mono-nanofluids at different volume concentrations.

Table 1. Thermophysical properties of nanoparticles

Table 2. Thermophysical properties of mono-nanofluids

Thermophysical Properties of AL203 and Graphene Nanofluid are calculated using the following empirical formulae.

Effective density of nanofluid:

${{\rho }_{eff}}={{\rho }_{b}}\left( 1-{{\varphi }_{np}} \right)+{{\rho }_{np}}{{\varphi }_{np}}$        (1)

where, ${{\rho }_{eff}}~$is the effective density of nanofluid, ${{\varphi }_{np}}$ is the volume percentage of the nanoparticles, and ${{\rho }_{np}}$ is the density of the nanoparticle.

Effective thermal conductivity of nanofluid:

${{\kappa }_{eff}}=\frac{{{\kappa }_{b}}\left[ {{\kappa }_{np}}+2{{\kappa }_{b}}-2{{\varphi }_{np}}\left( {{\kappa }_{b}}-{{\kappa }_{np}} \right) \right]}{{{\kappa }_{np}}+2{{\kappa }_{b}}+{{\varphi }_{np}}\left( {{\kappa }_{b}}-{{\kappa }_{np}} \right)}~~$          (2)

where, ${{\kappa }_{eff}}~$is the thermal conductivity of the nanofluid, ${{\varphi }_{np}}$ is the volume percentage of the nanoparticle, ${{\kappa }_{b}}$ is the thermal conductivity of the base fluid, and ${{\kappa }_{np}}$ is the thermal conductivity of a nanoparticle.

Adequate specific heat of nanofluid:

${{c}_{peff}}=\frac{\left( 1-{{\varphi }_{np}} \right)\times {{\rho }_{b}}{{c}_{pb}}+\left( {{\varphi }_{np}}\times {{\rho }_{np}}{{c}_{pnp}} \right)}{{{\rho }_{eff}}}~$         (3)

where, ${{c}_{peff}}~$is the specific heat of the nanofluid, ${{c}_{pb}}$ is the specific heat of the base fluid, and ${{c}_{pnp}}$ is the specific heat of a nanoparticle.

Effective Viscosity of Nanofluid:

${{\mu }_{eff}}=\left( 1+2.5{{\varphi }_{np}} \right){{\mu }_{b}}$         (4)

where, ${{\mu }_{eff}}~$is the effective viscosity of nanofluid, ${{\varphi }_{np}}$ is the volume percentage of the nanoparticles, and ${{\mu }_{b}}$ is the viscosity of the base fluid. The thermophysical properties of the Al₂O₃/water nanofluid at different volume concentrations are presented in Table 3.

Table 3. Thermophysical properties of AL₂O₃/ water nano-fluid

3.2 Thermophysical properties of Al₂O₃​-nano-fluid

The thermophysical properties, such as density, viscosity, and thermal conductivity, increase with nanoparticle concentration, whereas specific heat decreases. Since the thermal conductivity of nano-sized particles is significantly better than that of the base fluid, the interaction between nanoparticles and the base liquid intensifies at higher concentrations. This interaction helps enhance the thermal conductivity of the hybrid nanofluid (HyNF). Viscosity increases with concentration due to stronger cohesive forces between like and unlike molecules. However, contrary to the previous observations, some studies report a slight increase in specific heat with concentration [1].

3.3 Thermal-physical characteristics of Al₂O₃-graphene/water hybrid-nanofluids

Table 4 summarizes the thermophysical properties of the Al₂O₃–graphene/water hybrid nanofluid used in the present study.

Table 4. Thermophysical properties of Al203-graphene/water hybrid nanofluid

3.4 Thermophysical properties of Al₂O₃-Graphene Nanofluid are calculated using the following empirical formulae

Effective Density of Hybrid Nanofluid:

${{\rho }_{hnf}}={{\phi }_{np1}}{{\rho }_{np1}}+{{\phi }_{np2}}{{\rho }_{np2}}+\left( 1-{{\phi }_{hnp}} \right){{\rho }_{bf}}$            (5)

where, ${{\rho }_{hnf}}~$is the effective density of hybrid nanofluid, ${{\phi }_{np1}}$ is the volume percentage of nano particle 1,$~{{\rho }_{np1}}$ is the density of the nanoparticle 1,$~{{\phi }_{np2}}$ is the volume percentage of the nano particle two and ${{\rho }_{np2}}$ is the density of the nanoparticle 2, ${{\phi }_{hnp}}$ is the volume percentage of the hybrid nanoparticle and ${{\rho }_{bf}}$ is the density of the base fluid.

Effective Volume percentage of Hybrid Nanofluid:

${{\phi }_{hnp}}={{\phi }_{np1}}+{{\phi }_{np2}}$

where, ${{\phi }_{hnp}}$ is the effective volume percentage of hybrid nanofluid, ${{\phi }_{np1}}~$is the volume percentage of the nano particle 1 and$~{{\phi }_{np2}}$ is the volume percentage of the nano particle 2.

Adequate Specific Heat of Hybrid Nanofluid:

$C{{p}_{hnf}}=\frac{\phi {{\rho }_{np1}}C{{p}_{np1}}+\phi {{\rho }_{np2}}C{{p}_{np2}}+\left( 1-{{\phi }_{h}} \right)C{{p}_{bf}}}{{{\rho }_{hnf}}}~~$        (6)

where,$C{{p}_{hnf}}$ is the effective specific heat of the hybrid nanofluid, ${{\phi }_{np1}}$ is the volume percentage of nano particle 1, ${{\phi }_{np1}}$ is the volume percentage of nano particle 1,$~{{\rho }_{np1}}$ is the density of the nanoparticle 1,$~{{\phi }_{np2}}$ is the volume percentage of the nano particle two and ${{\rho }_{np2}}$ is the density of the nanoparticle 2, ${{\rho }_{hnf}}$ is the density of the hybrid nanofluid,$~C{{p}_{bf}}$ is the specific heat of the base fluid.

Effective Thermal Conductivity of Hybrid Nanofluid:

$={{k}_{bf}}\left( \frac{\left( \frac{{{k}_{np1}}{{\phi }_{np1}}+{{k}_{np2}}{{\phi }_{np2}}}{{{\phi }_{np1}}+{{\phi }_{np2}}}+2{{k}_{bf}} \right)-2\left( {{\phi }_{np1}}+{{\phi }_{np2}} \right)\left( {{k}_{bf}}-\frac{{{k}_{np1}}{{\phi }_{np1}}+{{k}_{np2}}{{\phi }_{np2}}}{{{\phi }_{np1}}+{{\phi }_{np2}}} \right)}{\left( \frac{{{k}_{np1}}{{\phi }_{np1}}+{{k}_{np2}}{{\phi }_{np2}}}{{{\phi }_{np1}}+{{\phi }_{np2}}}+2{{k}_{bf}} \right)+\left( {{\phi }_{np1}}+{{\phi }_{np2}} \right)\left( {{k}_{bf}}-\frac{{{k}_{np1}}{{\phi }_{np1}}+{{k}_{np2}}{{\phi }_{np2}}}{{{\phi }_{np1}}+{{\phi }_{np2}}} \right)} \right)$       (7)

where, ${{k}_{hnf}}~$is the thermal conductivity of the hybrid nanofluid, ${{\phi }_{np1}}$ is the volume percentage of nano particle 1,$~{{\rho }_{np1}}$ is the density of the nanoparticle 1,$~{{\phi }_{np2}}$ is the volume percentage of the nano particle two and ${{\rho }_{np2}}$ is the density of the nanoparticle 2, ${{\phi }_{hnp}}$ is the volume percentage of the hybrid nanoparticle and$~{{\kappa }_{bf}}$ is the thermal conductivity of the base fluid.

3.5 Heat pipe details and experimental research

The heat pipe was made of copper, as shown in Figure 2 and Figure 3, with a screen mesh serving as the wick structure. A single 40-mesh layer was used for the screen mesh. Graphene-water nanofluid, Al₂O₃-graphene water nanofluid, and water were used as working fluids in the HP. The evaporator, adiabatic, and condenser sections of the heat pipe each have lengths of 50 mm, 100 mm, and 150 mm, respectively.

For temperature measurement, 4 Thermocouple sensors were mounted on the heat pipe wall surfaces, and two were placed inside the pipe at the evaporator inlet and condenser outlet, respectively. Figure 3 shows the temperature-sensor distribution along the length of the heat pipe. The experimental setup consists of a variac, a digital wattmeter, a mica heater, a temperature scanner data logger, and a cooling fan. Insulation was wrapped around the evaporator and adiabatic portions to reduce the heat leaks from the heat pipe to the ambient.

3.6 Empirical procedure

This study examines the influence of graphene and Al₂O₃ nanofluids on heat pipe performance under varying tilt angles and heat loads, employing forced-convection cooling with a fan. The heat pipe was inclined at three tilt angles: 0° (Horizontal), 60°, and 90° (Vertical). The condenser section was maintained above the HP evaporator for all inclined positions [21, 24]. Al₂O₃ -graphene water nanofluid, and water were used as the working fluids for the heat pipe, in which water readings were considered as the baseline reading for the experiment. The heat flux input was varied from 10 W to 20 W in steps of 5 W. The mica heater's limiting operating temperature (160 ℃) was considered the limiting factor for heat input. A data logger temperature scanner recorded all temperature readings at the 10-minute mark. The detailed specifications of the heat pipe and experimental setup used in this study are summarized in Table 5.

Table 5. Heat pipe specifications

Figure 2. Experimental setup

Figure 3. Schematic diagram of heat pipe

Heat pipe with Al₂O₃-Graphene HNF at 4%–3%, 3%–2%, and 6%–3% volume percentage, and water were investigated over a heat input range from 10 W to 20 W, with a step of 5 W. We have discussed the effect of the inclination angle on the heat-transfer coefficient at varying heat loads on the evaporator temperature, the total thermal resistance, and the percentage decrease in thermal resistance. To evaluate the optimal volume percentage of hybrid nano fluid and inclination angle at various heat loads.

5.1 Effect of inclination angle on the performance of the heat pipe

This preliminary graph illustrates how thermal resistance varies with inclination angle, from 0° to 60° and then to 90° at various heat loads for different hybrid nanofluids. One key observation was made for the 4% Al₂O₃ + 3% Graphene hybrid nanofluid at a heat load of 10 W: as the inclination increased from 0° (horizontal) to 60°, the thermal resistance decreased by approximately 29%. This significant decrement confirms the importance of the inclination angle for heat pipe performance, establishing the fundamental principle that gravity-based heat pipes perform better than those in a horizontal position. An intriguing observation is that as the heat load increased, the decrease in thermal resistance became pronounced. This further confirms that, with a larger inclination angle, such as 60°, the advantages are amplified at high heat loads. In the case of the second hybrid nanofluid consisting of 3% Al₂O₃ and 2% Graphene, the decrement in thermal resistance was 25% at a heat load of 10 W when the position was moved from 0° to 60°. Moreover, for heat loads of 15 W and 20 W, the decrement further decreased to 52%. As before, this confirms that with a high heat load, the advantages of inclination are amplified.

As shown in Figure 4, on the other hand, for both of the previously mentioned hybrid nanofluids-4% Al₂O₃ + 3% Graphene and 3% Al₂O₃ + 2% Graphene, at the inclination of 90°, the thermal resistance reduction was relatively small, with a maximum drop of only about 18%. This indicates that the optimal angle is 60° to enhance performance. At this angle, it achieves an optimal balance between gravitational assistance and capillary action within the wick. However, when investigating the 6% Al₂O₃ + 3% Graphene hybrid nanofluid, we observed minimal reduction in thermal resistance, approximately 5%–9%, even when the inclination was varied from 0° to 60°. This negligible variation indicates that the heat pipe's performance was degraded by agglomeration at a nanoparticle concentration of nearly 10% by volume. This most likely caused clogging within the wick structure and, consequently, degraded the heat pipe's functionality.

Figure 4. Decrease in thermal resistance for different inclination angles

Figure 5. Temperature across the heat pipe 4% Al₂O₃ + 3% graphene hybrid nanofluid heat pipe at 60℃

Figure 6. Temperature across the heat pipe 3% Al₂O₃ + 2% graphene hybrid nanofluid heat pipe at 60℃

Therefore, this data suggests that when there’s little to no change in thermal resistance with an increasing inclination angle, the observed heat transfer improvement is driven by the intrinsic thermal conductivity of the nanofluid itself, rather than any gravitational effects. As shown in Figures 5 and 6, in contrast, the performance gains with the 4% Al₂O₃ + 3% Graphene and 3% Al₂O₃ + 2% Graphene nanofluids were clearly influenced by both enhanced thermal conductivity and favourable orientation, indicating a synergistic effect of the optimized fluid composition and inclination. More interestingly, even water outperformed the 6% Al₂O₃ + 3% Graphene nanofluid in terms of the percentage reduction in thermal resistance across all tested inclination angles. This further supports the conclusion that excessively high nanoparticle concentrations may lead to practical failures in the heat pipe system.

5.2 Effect of inclination angle on evaporator heat transfer coefficient at varying heat loads

With a heat load of 2411.963 W/m², the heat pipe using a 4% Al₂O₃-3% graphene hybrid nanofluid exhibited a heat transfer coefficient of 344.57 W/m²·K at 0° inclination. As the heat pipe was inclined at 60°, the heat transfer coefficient increased to 459.42 W/m²·K, a 33% increase relative to the value at 0°. For 90° inclination, the coefficient marginally reduced to 438.54 W/m²·K, but a 27% increase was still observed compared to the value at 0°. As the heat load was increased to 3617.945 W/m², the heat transfer coefficient at 0° increased to 401.99 W/m²·K. For a 60° inclination, the coefficient again increased to 516.84 W/m²·K, a 28.6% increase relative to 0°. At 90°, the coefficient was 499.03 W/m²·K, a 24% increment relative to the value at 0°. For the highest heat load of 4823.927 W/m², the heat transfer coefficient at 0° increased substantially to 665.37 W/m²·K. At 60°, the coefficient increased slightly to 689.13 W/m²·K, representing a 3.6% increase. At 90°, the coefficient slightly reduced to 669.99 W/m²·K, although a 0.7% increase was observed compared to the value at 0°.

Figure 7. Heat transfer coefficient evaporator vs heat load

As shown in Figure 7, for the 4% Al₂O₃-3% graphene hybrid nanofluid at a heat load of 2411.963 W/m², the increase in the heat transfer coefficient was 33% when the inclination angle was increased from 60° to 90°. However, as the heat load rose to 4823.927 W/m², the increase in the heat transfer coefficient was substantially lower, at only 3.6%. This indicates that, beyond a certain point, the heat-transfer coefficient in the evaporator section is independent of the inclination angles.

For a heat load of 2411.963 W/m², the heat transfer coefficient of the 3% Al₂O₃ and 2% graphene hybrid nanofluid-filled heat pipe with 0° inclination was 332.68 W/m²K. When inclined at 60°, it increased to 401.99 W/m²·K, an increase of approximately 20.8%. At 90°, it decreased slightly to 385.91 W/m²·K, yet it increased by 15.99% relative to 0°. As the heat load was increased to 3617.945 W/m², the heat transfer coefficient at 0° increased to 391.12 W/m²·K. Upon inclining it to 60°, it increased to 482 W/m²·K, indicating a 23.23% improvement. At 90°, it decreased slightly to 452 W/m²·K, yet it was 15.58% higher than at 0°. For the highest possible heat load of 4823.927 W/m², the heat transfer coefficient at 0° increased to 643.19 W/m²·K. When inclined at 60°, it increased slightly to 665 W/m²·K, representing a 3.39% improvement. At 90°, it decreased to 643.19 W/m²·K, indicating no further increase relative to 0°.

The heat pipe with a 6% Al₂O₃- 3% graphene hybrid nanofluid, operating at a heat load of 2411.963 W/m², had a heat-transfer coefficient of 357.32 W/m²·K at a horizontal inclination of 0°. The coefficient increased to 438.54 W/m²·K at an inclination of 60°, representing a 22.7% increase. Subsequently, the inclination was increased to 90°, and the coefficient decreased to 419.47 W/m²·K, although it remained 17.4% higher than at 0°. For a heat load of 3617.945 W/m², the heat transfer coefficient for a 0° inclination was 397.58 W/m²·K. For an inclination of 60°, the coefficient increased to 499.03 W/m²·K, a 25.5% increase. Then, for a 90° inclination, the coefficient decreased to 466.83 W/m²·K, but it was still 17.3% higher. At the highest heat load of 4823.927 W/m², the heat transfer coefficient for a 0° inclination is 660.81 W/m²·K. The heat transfer coefficient at a 60° inclination increased to 684.24 W/m²·K, a 3.6% increase. However, at 90°, the heat transfer coefficient decreased to 622.44 W/m²K, which was still slightly higher than that at 0°, but indicated a reduced influence of inclination angle at higher heat loads.

When comparing 6% Al₂O₃ and 3% graphene hybrid nanofluid with water, the following results are encountered:

Heat load of 2411.963 W/m²: Both the hybrid nanofluid and water experience a rise in the heat transfer coefficient in the evaporator as the angle of inclination rises from 0° to 60°. For the hybrid nanofluid, the increment is 22.7%, whereas for water it is slightly higher at 24.7%. At a higher heat load of 4823.927 W/m², water showed an 11.8% increase in the heat-transfer coefficient as the inclination angle increased from 0° to 60°, whereas the hybrid nanofluid showed only a 3.6% increase.

This suggests that for the hybrid nanofluid, there is a saturation point at a particular heat load, beyond which further increases in heat load do not yield significant improvements in the heat transfer coefficient. At a heat load of 2411.963 W/m², the heat-transfer coefficient at the evaporator for water was 214.97 W/m²·K at a 0° inclination. Increasing the inclination to 60° increased the coefficient to 267.99 W/m²·K, representing approximately a 24.7% increase. At 90°, the coefficient was slightly lower at 260.75 W/m²·K, but still 21.3% higher than at 0°. When the heat load was increased to 3617.945 W/m², the heat transfer coefficient for water at 0° was 237.24 W/m²·K. At 60°, it increased to 278.30 W/m²·K, reflecting a 17.3% improvement. At 90°, the coefficient decreased slightly to 267.99 W/m²·K, remaining approximately 12.9% higher than at 0°. At the highest heat load of 4823.927 W/m², the heat-transfer coefficient at the evaporator for water at 0° was 253.89 W/m²·K. At 60°, the coefficient increased to 283.76 W/m²·K, representing an 11.8% improvement. At 90°, the coefficient decreased slightly to 271.77 W/m²·K but remained 7% higher than at the horizontal position.

5.3 Effect of inclination angle on evaporator temperature at varying heat loads

The lowest evaporator temperature was observed for Al₂O₃-graphene HNF at 4%–3% at a 60-degree inclination angle, whereas the highest temperature was observed for water at a 0-degree inclination angle. At a constant heat input of 10W and a hybrid nanofluid composition of 4% Al₂O₃ + 3% Graphene, we observed that the evaporator temperature of the heat pipe varied significantly with the inclination angle. Figure 8 shows the effect of inclination angle on the evaporator temperature at different heat loads.

Figure 8. Evaporator temperature vs heat load

Figure 9. Evaporator temperature variation for 4% Al₂O₃ + 3% graphene hybrid nanofluid heat pipe

As shown in Figure 9, when the heat pipe was in the horizontal position (0° inclination angle), the evaporator temperature reached 53 ℃. However, when the heat pipe was further inclined to 60°, the evaporator temperature decreased substantially, dropping to 48.75 ℃. This showed an apparent 8.02% decrease in comparison to the horizontal orientation. This improvement is attributed to enhanced gravitational assistance during the condensate's return to the evaporator, thereby improving thermal performance. At a vertical angle of 90°, the evaporator temperature increased slightly to 52 ℃, representing a 6.67% increase relative to the 60° position and a 1.89% decrease relative to the horizontal position. The result obtained by Zhang et al. [15] proves that the effect of gravity exists in the thermal performance, because the processes of evaporation and condensation of the working fluid affect each other, thereby causing a reduction in the rate of heat transfer between the evaporator and the condenser at an inclination angle of 90°. For a heat input of 15 W, the trend reported above for the change in evaporator temperature with the inclination angle was reproduced.

In this case, when the heat pipe was held at a fixed angle of 0°, the evaporator temperature was measured to be 60 ℃. However, when it was raised to an inclined position of 60°, the temperature decreased to 54 ℃, corresponding to a 10% decrease. With successive increments in the inclination angle to 90°, the temperature increased to 58.5 ℃, an 8.33% increase relative to 60°. Notably, this was still lower than the temperature recorded at zero degrees. When the heat load was increased to 20W, this trend continued. The evaporator temperatures were highest at 60 ℃. When the angle was increased to 60°, the temperature decreased to 59 ℃. This was attributed to a 14.49% reduction. However, when this position was raised to 90°, temperatures went higher to 64 ℃. This was attributed to an 8.47% increase. Still, this was lower than the temperature at 0 ℃. The smallest possible temperature difference was observed when the inclination angle increased from 50° to 70°, as reported by Zhang et al. [14].

The optimal inclination angle for Heat Pipes will be further discussed in this study, consistent with prior studies. An interesting trend was identified: as the heat load increases, the percentage difference in thermal resistance becomes larger for the same inclination angle. For example, at an inclination angle of 60°, the thermal resistance decreased by 8.02% at a 10 W heat load; however, as the heat load increased to 20 W, the decrease was 14.49%.

Likewise, for a heat flux of 10W, the evaporator temperature for the 3% Al₂O₃-2% Graphene hybrid nanofluid exhibited a similar trend with the inclination angle. At an angle of 0°, the temperature was measured to be 56.25 ℃. Subsequently, as the incline angle increased to 60°, the temperature decreased to 50.5 ℃, indicating a 10.23% decrease. Furthermore, as the incline angle increased to 90°, the temperature decreased to 49.25 ℃, suggesting a 2.48% reduction relative to the 60° case and a total decrease of 12.46% relative to the 0° case.  

Figure 10. Evaporator temperature variation for 3% Al₂O₃ + 2% graphene hybrid nanofluid heat pipe

For a heat load of 15 W, as shown in Figure 10, the trend was the same for the 3% Al₂O₃-2% Graphene hybrid nanofluid. The evaporator temperature at 0° inclination was 66.25 ℃. When the heat pipe was inclined by 60°, the temperature decreased to 56 ℃, corresponding to a 15.47% reduction. The temperature further elevated to 60.75 ℃ at an inclination of 90°, an increase of 8.48% above the 60° position but an 8.30% reduction relative to the temperature at 0° inclination. However, when the heat load was increased to 20 W, the trend persisted for the 3% Al₂O₃-2% Graphene hybrid nanofluid. The temperature at the evaporator head for the heat pipe at 0° inclination was 72.5 ℃. However, upon inclining the heat pipe by an additional 60°, the temperature decreased to 62.5 ℃, indicating a 13.79% reduction. However, at an additional inclination of 90°, the temperature increased to 69 ℃, an improvement of 10.4% over the temperature at the heat pipe at 60° but a reduction of 4.83% relative to the temperature at the heat pipe at 0° inclination. As observed earlier, the thermal resistance under a 10W heat load decreased by 10.23% at an angle of 60°, and under an additional 20W heat load, the reduction increased to 13.79%.

Figure 11. Evaporator temperature variation for 6% Al₂O₃ + 3% graphene hybrid nanofluid heat pipe

As shown in Figure 11, for the 6% Al₂O₃-3% Graphene hybrid nanofluid at a heat load of 10 W, the evaporator temperature decreases as the inclination angle increases. At 0°, the temperature was 52 ℃. Upon inclining it to 60°, a minute reduction to 51 ℃ was observed, corresponding to a 1.92% decrease. Furthermore, when it was placed vertically at 90°, the temperature decreased to 50.5 ℃, indicating a 0.98% reduction relative to 60° and a cumulative decline of 2.88% relative to 0°. For 15 W, however, it not only became minute but also exhibited a slightly decreasing pattern. As expected, it started at 61.25 ℃ at 0°, then slightly reduced to 60 ℃ at 60°, indicating a 2.04% improvement. As expected, even at 90°, it returned to 61.25 ℃, indicating performance comparable to that at 0°. Thus, it is clear that at a 15 W heat load, optimal performance was achieved at 60°. For 20 W, though, it became even more minute. As expected, at 0° it started at 68.75 ℃, increased to 69 ℃ at 60°, and then decreased slightly to 68.75 ℃ at 90°. As observed, it became flat, implying that at higher heat loads, even minute variations due to angle become irrelevant for the 3% Graphene hybrid nanofluid.

Figure 12. Evaporator temperature variation for water heat pipe

For the water heat pipe, as shown in Figure 12, the evaporator temperature varied with position, particularly at low heating power. At 10 W, the temperature was 63.25 ℃ when the position was maintained at 0°. When the position was changed to 60°, the temperature decreased to 56 ℃, indicating a substantial increase in the heat-transfer rate. Furthermore, when the position was set to 90°, the temperature increased slightly to 57.25 ℃, but it remained much lower than at the 0° position. A similar trend was observed at 15 W, where the temperature began at 74 ℃ at 0°, decreased to 67.25 ℃ at 60°, and then increased slightly to 68 ℃ at 90°. It can thus be inferred that the most favorable position was 60°. At 20 W, the changes were more subtle. The evaporator temperature decreased from 82.75 ℃ at 0° to 79.5 ℃ at 60°, then increased to 80 ℃ at 90° [9].

It can be observed that, unlike the 4% Al₂O₃ + 3% Graphene and 3% Al₂O₃ + 2% Graphene hybrid nanofluids— where a significant reduction in evaporator temperature was seen with increasing inclination angles—the 6% Al₂O₃ + 3% Graphene hybrid nanofluid showed minimal to no change in evaporator temperature across different orientations. This indicates that the beneficial effect of gravity-assisted inclination was not effectively realized in this case. A likely explanation for this behavior is the nanofluid's tendency to agglomerate at such a high concentration. Nanofluid agglomeration occurs due to clumping between particles due to the van der Waals force and weakening of brown motion in a nanofluid. Agglomeration reduces the degree of homogeneity in the nanofluid, causing the particles to settle at the bottom and making the nanofluid appear clear at the top [23]. The dense particle loading may have led to clogging within the wick structure, thereby hindering capillary action, which is essential for effective heat pipe operation. This blockage would disrupt the return flow of the working fluid, weakening the heat pipe effect and resulting in stagnant thermal performance regardless of the inclination angle. However, despite this issue, the evaporator temperatures at all orientations for the 6% Al₂O₃ + 3% Graphene nanofluid were still lower compared to those of the 3% Al₂O₃ + 2% Graphene nanofluid and pure water. This can be attributed to the inherently higher thermal conductivity of the 6% Al₂O₃ + 3% Graphene hybrid nanofluid, which allows better heat absorption and transfer even in the absence of optimal fluid circulation within the pipe.

5.4 Effect of inclination angle on total thermal resistance

As shown in Figure 13, The lowest evaporator thermal resistance was observed for Al₂O₃-Graphene HNF at 4%–3% at a 60-degree inclination angle, whereas the highest thermal resistance was observed for water at a 0-degree inclination angle.

Figure 13. Effective thermal resistance vs heat load

At a constant heat input of 10 W, as shown in Figure 14, and a hybrid nanofluid composition of 4% Al₂O₃ + 3% Graphene, we observed that the heat pipe's evaporator temperature varied significantly with the inclination angle. At a heat load of 10 W, the thermal resistance of the heat pipe using 4% Al₂O₃ + 3% Graphene hybrid nanofluid was measured to be 1.75 C/W at a 0° inclination angle. As the inclination increased to 60°, the thermal resistance decreased to 1.35 C/W, representing a 22.86% decrease. When the angle was increased to 90°, the thermal resistance was 1.6 C/W, representing a minor reduction of approximately 8.57% relative to the 0° position. At a heat input of 15 W, the thermal resistance of the heat pipe using a 4% Al₂O₃-3% Graphene hybrid nanofluid was 1.633 C/W at a 0° inclination angle. By increasing the inclination to 60°, the thermal resistance decreased noticeably to 1.1 C/W, corresponding to a 32.65% reduction. It recorded 1.4833 kW at 90°, with a minor decrease of approximately 9.16% relative to the horizontal position. The measured thermal resistance of the heat pipe filled with a hybrid nanofluid containing 4% Al₂O₃ and 3% Graphene, when positioned horizontally (0° inclination), was 1.625 C/W at a heat load of 20 W. The thermal resistance decreased to 1.0625 C/W as the inclination angle increased to 60°, representing a reduction of approximately 34.62%. At the 90° inclination, the thermal resistance was 1.375 C/W, representing a 15.38% decrease relative to the 0° position.

Figure 14. Thermal resistance variation for 4% Al₂O₃ + 3% graphene hybrid nanofluid heat pipe

A trend was also observed: as the heat load increases, the thermal resistance decreases by a larger percentage for the same inclination angle. As an example, the thermal resistance was reduced by 22.86%. at an inclination of 60° and for a heat load of 10W, which increased to 34.62%.

For a heating power of 10 W, as shown in Figure 15, the thermal resistance of the heat pipe filled with a 3% Al₂O₃-2% Graphene hybrid nanofluid in the horizontal (0°) position was measured to be 2 C/W. However, with an increase in orientation to 60°, the power output decreased to 1.6 kW, a 20% reduction. Further increasing it to 90° slightly increased it to 1.625 C/W, which was still an 18.75% reduction. When the heating power was increased to 15 W, the temperature rise was 1.85 C/W at 0°. This decreased to 1.21 C/W at 60° (34.59% reduction) and to 1.6 C/W at 90° (approximately 13.51% reduction). For an even higher heating power of 20 W, it measured 1.71 C/W at 0°. This further decreased to 1.125 C/W at 60° (34.21% reduction) and to 1.55 C/W at 90° (approximately 9.36% lower than in the horizontal position).

Figure 15. Thermal resistance variation for 3% Al₂O₃ + 2% graphene hybrid nanofluid heat pipe

At a heat load of 10 W, the thermal resistance of the heat pipe was measured to a heat load of 10 W, as shown in Figure 16. The heat pipe with the 6% Al₂O₃-3% Graphene hybrid nanofluid measured 1.8 C/W at 0°, which was progressively lowered at 60° to 1.7 C/W—a steep decrease of 5.56%. However, at 90°, the reading was 1.725 kW, representing a 4.17% decline relative to the previous position. When the heat load was increased to 15 W, the reading at 0° was 1.7166 C/W. This further declined to 1.5667 kW at 60°, representing an 8.73% decrease, whereas at 90° the value was 1.66 kW, 3.3% lower than the initial value. At an even higher heat load of 20 W, the reading at 0° was 1.65 C/W. This decreased at 60° to 1.5 C/W (9.09%), whereas at 90° the reading was 1.5875 C/W (3.78%).

Figure 16. Thermal resistance variation for 6% Al₂O₃ + 3% graphene hybrid nanofluid heat pipe

Figure 17. Thermal resistance variation for water heat pipe

Interestingly, as shown in Figure 17, for 6% Al₂O₃- 3% Graphene hybrid nanofluids, the reduction in thermal resistance percentage with increasing inclination angle was relatively small. At a heat load of 10 W, an increase in the inclination angle from 0° to 60° caused a reduction of 5.56%, whereas an increase from 0° to 90° caused a decrease of 9.09%. In comparison, water exhibited a more significant change under similar conditions—showing a 23.81% reduction in thermal resistance at 10 W when moving from 0° to 60°, and a 10.23% reduction at 20 W for the exact inclination change. This highlights the relatively limited sensitivity of the 6% Al₂O₃ and 3% graphene nanofluids to changes in inclination angle, particularly compared with water.

At a heat load of 10 W, the thermal resistance of the heat pipe with water as the working fluid was 2.65 C/W when horizontally oriented (0° inclination). As the inclination angle increased.