Thermal and Exergetic Performance Analyses of a Heat Pipe Heat Exchanger Using CMC/Co₃O₄-Based Non-Newtonian Nanofluids

Abstract

This study presents an experimental evaluation of the thermal and exergetic performance of an air-to-air heat pipe heat exchanger using a cobalt oxide (Co₃O₄)-based non-Newtonian nanofluid, with the additional incorporation of carbon black (CB). Nanofluids were synthesized via a two-step method and tested under turbulent flow conditions across varying Reynolds numbers. The results demonstrated that increasing the Co₃O₄ nanoparticle concentration and adding CB substantially improved both the thermal and exergetic performance compared to deionized water. Specifically, maximum thermal efficiency improvements of 62.7% and 75.4% were recorded for nanofluids containing 1% and 2% Co₃O₄, respectively. The addition of CB further enhanced the thermal efficiency, achieving a maximum improvement of 79.2%. Furthermore, the maximum reduction in thermal resistance reached 61.4% with CB incorporation, while the 2% Co₃O₄ nanofluid achieved a maximum decrease of 50.2%. The use of nanofluids led to a significant reduction in exergy loss, with exergy-saving efficiencies reaching up to 33.6%. These findings highlight the considerable potential of Co₃O₄- and CB-based hybrid nanofluids in advancing waste heat recovery technologies and enhancing the thermodynamic performance of air-to-air heat pipe heat exchanger systems.

1. Introduction

Increasing global energy demand and growing environmental concerns have underscored the critical importance of energy efficiency in industrial processes and HVAC (heating, ventilation, and air conditioning) applications. A significant amount of the energy utilized in these systems is released as waste heat. If properly recovered, this waste energy can significantly enhance overall system efficiency and support broader sustainability goals. Heat recovery systems are developed to capture and utilize waste heat, thereby reducing operational costs and improving thermal performance [1,2,3,4,5]. Among various technologies developed for this aim, air-to-air heat pipe heat exchangers (HPHEs) have gained prominence due to their passive operation, high reliability, and capability to transfer thermal energy between two separate air streams without direct mixing [6,7]. This characteristic makes HPHEs particularly advantageous for applications such as ventilation systems and industrial processes, where maintaining strict air purity and preventing cross-contamination between air streams are essential [8]. The application areas of air-to-air HPHEs are illustrated in Figure 1. In addition, the use of air-to-air HPHEs can allow for a more compact design of heating and cooling systems in newly constructed buildings [9].

Heat pipes, the core components of HPHE systems, rely on phase-change principles to transport heat efficiently over considerable distances with minimal temperature loss. A typical heat pipe comprises three primary sections: an evaporator, where the operating fluid takes in thermal energy and undergoes evaporation; an adiabatic section, through which vapor moves without significant heat loss; and a condenser, where the vapor emits its latent energy and transitions into a liquid phase [10]. The condensed working fluid flows back to the evaporator either through capillary forces or under the influence of gravity [11,12]. The thermal performance of heat pipes is strongly influenced by the thermophysical properties of their working fluids, thus making fluid selection crucial for enhancing overall heat exchanger efficiency [13,14,15,16].

Recent advancements in nanotechnology have enabled the development of nanofluids, which are fluids containing uniformly dispersed nanoparticles that exhibit superior thermal properties compared to conventional working fluids. Various studies have demonstrated that incorporating nanoparticles into working fluids improves thermal conductivity, increases convective heat transfer coefficients, and reduces viscosity, thereby enhancing overall heat transfer performance [17,18,19]. By reducing the thermal resistance of the heat pipe and increasing the evaporation–condensation cycle’s effectiveness, nanofluids offer a promising approach for optimizing the performance of HPHEs. Among the different types of nanoparticles used in heat transfer applications, Co₃O₄ nanoparticles stand out due to their excellent thermal stability, high surface area, and superior heat transfer properties [20,21]. Co₃O₄ has been observed to enhance heat transfer rates by increasing the effective thermal conductivity of the fluid [22]. By integrating Co₃O₄-based nanofluids into heat pipe systems, it becomes possible to extend the operating temperature range of heat exchangers and improve their overall effectiveness in capturing low-grade waste heat. Furthermore, carbon-based materials have recently attracted considerable attention for their ability to enhance the thermal properties of fluids. In particular, nanofluids consisting of Co₃O₄ nanoparticles combined with carbon-based additives have been investigated due to their potential to further enhance heat transfer performance [23,24,25,26,27]. Among carbon-based materials, CB has attracted considerable attention in thermal system applications due to its strong light absorption capacity, high surface area, cost-effectiveness, and favorable dispersion characteristics. CB contributes to increased heat transfer efficiency, particularly in systems involving turbulent flow, heat exchangers, or energy-harvesting technologies. Sarafraz et al. reported a 44% enhancement in the heat transfer coefficient when employing carbon–water nanofluids in double-pipe heat exchangers, accompanied by a 42.2% improvement in thermal–hydraulic performance at a Reynolds number of 10,200 [28]. Similarly, Shiravi et al. reported a 40.7% enhancement in convective heat transfer using CB–water nanofluids in helical-coil heat exchangers [29]. Firoozzadeh et al. used CB nanofluid as a coolant for photovoltaic modules. They reported that the highest overall efficiency was achieved at a concentration of 0.21 wt [30]. Gimeno-Furio et al. investigated the use of CB nanoparticles in thermal oil for solar thermal applications. Their findings demonstrated that CB-enhanced nanofluids maintain high thermal and optical stability under elevated temperatures, making them promising candidates for direct-absorption solar collectors [31].

Despite their promising thermal properties, nanofluids often encounter stability challenges caused by nanoparticle aggregation and sedimentation. To mitigate these issues, stabilizing agents, such as carboxymethyl cellulose (CMC), are employed. CMC is an anionic polysaccharide, produced from natural cellulose by carboxymethylation, and is readily soluble in water. It is widely utilized as a stabilizing, thickening, and dispersing agent in food, pharmaceutical, and industrial applications. In nanofluid formulations, CMC plays a crucial role as a surfactant and rheological modifier, improving the dispersion stability of nanoparticles by preventing agglomeration and sedimentation. Its polymeric structure provides steric hindrance and enhances colloidal stability over extended periods. Owing to its biodegradability, non-toxicity, and environmental compatibility, CMC is considered a green additive for nanofluid systems. CMC solutions also exhibit shear-thinning (pseudo-plastic) rheological behavior [32,33,34,35]. Zainith and Mishra experimentally investigated nanofluids prepared with 0.4 wt% CMC and three different metal oxide nanoparticles (CuO, Al₂O₃, and TiO₂) and reported shear-thinning (non-Newtonian) behavior based on power-law fitting, along with enhanced colloidal stability demonstrated by extended sedimentation times up to 30 days [36]. Within this context, evaluating the thermal performance of CMC-stabilized Co₃O₄ nanofluids in heat transfer systems is highly relevant for advancing energy recovery technologies and enhancing system-level efficiency.

Numerous experimental studies have explored the thermal performance of HPHEs using various nanofluids, aiming to enhance heat transfer efficiency and reduce thermal resistance under different operating conditions. These studies have employed a wide range of nanoparticle types, base fluids, and stabilizing agents to improve the thermophysical properties of working fluids and system effectiveness.

Table 1. Summary of recent experimental studies on nanofluid-enhanced HPHEs.

Nanofluid	Concentration	Results	Ref.
CuO/water	1–5% w/w	The results showed that increasing both the inlet air temperature and CuO nanoparticle concentration enhanced the HPHE effectiveness and heat recovery capacity. The highest effectiveness (0.59346) was achieved at 55 °C inlet air temperature with 5 wt% CuO concentration.	[37]
Graphene oxide/water	0.1% w/w	The GO nanofluid significantly reduced thermal resistance (up to 67%) at low heat input rates compared to DI water, while both fluids performed similarly at higher heat inputs.	[38]
Ag/water	1% v/v	The study demonstrated that using a 1% silver nanofluid significantly enhanced HPHE performance, achieving up to 10% higher heat recovery, a maximum effectiveness of 39.25%, and a 15% reduction in thermal resistance under optimal thermal load and flow conditions.	[39]
ZnO/water	0–2% w/w	ZnO nanofluids enhanced thermal performance by increasing heat transfer coefficients and reducing thermal resistance, achieving a maximum effectiveness of 0.271 at 2% nanofluid concentration and up to 17.2% improvement under optimal conditions.	[40]
Fe2O3/water	0.5–2% w/w	Magnetic nanofluids enhanced the thermal performance of an air-to-air HPHE, increasing thermal efficiency to a maximum of 35.3% and reducing thermal resistance by as much as 71.6% at 2.0% nanoparticle concentration.	[41]
CuO-Fe/water	%2 w/w	The maximum efficiency value of 25.8% was achieved using a CuO-Fe hybrid nanofluid based on pure water.	[42]
Al2O3-TiO2/EG	-	The use of Al2O3-TiO2/EG (50:50) hybrid nanofluids improved thermal performance, achieving a maximum efficiency of 82% and reducing thermal resistance by up to 53.71%.	[43]
Co3O4	1–2% w/w	Co3O4 nanofluids significantly enhanced thermal performance, with up to 75.4% efficiency improvement and 29.3% exergy-saving efficiency at 2% concentration.	This work
Co3O4/CB	2%/0.4% w/w	CB incorporation into 2% Co3O4 nanofluid further boosted thermal efficiency to 79.2% and reduced thermal resistance by up to 61.4% compared to deionized water.	This work

presents a comparative summary of recent experimental research on nanofluid-enhanced HPHE systems, highlighting their working fluids, nanoparticle concentrations, and thermal performance outcomes. The main objective of this study is to enhance the thermal and exergetic performance of air-to-air HPHEs by utilizing Co₃O₄-based non-Newtonian nanofluids stabilized with CMC while specifically investigating the additional improvements provided by CB incorporation. Through a systematic comparison of deionized water, Co₃O₄/CMC nanofluid, and Co₃O₄/CB/CMC hybrid nanofluid under a range of Reynolds number conditions, the study comprehensively assesses key thermal and exergetic parameters, including thermal efficiency, thermal resistance, the heat transfer coefficient, effectiveness, exergy loss, and exergy-saving efficiency. Notably, to the best of the author’s knowledge, no previous study has experimentally examined the effect of Co₃O₄ nanofluid and CB addition on the thermal and exergy behavior of nanofluids in air-to-air HPHEs. This study aims to offer useful insights for developing efficient, sustainable thermal management systems for industrial waste heat recovery and HVAC applications.

2. Materials and Methods

2.1. Preparation of Nanofluid

Nanofluids were systematically synthesized using a two-step method, with deionized water as the base fluid. CMC (0.4 wt.%) was first dissolved under continuous magnetic stirring to provide the desired rheological behavior and enhance dispersion stability. Co₃O₄ nanoparticles (Sigma-Aldrich, St. Louis, MO, USA; 99.5% purity, <50 nm particle size) were added to the base fluid at final concentrations of 1.0 wt.% and 2.0 wt.% to prepare the nanofluids. The pH of the dispersion was determined to be approximately 6.5. No visible sedimentation was observed after 24 h. The XRD pattern of the Co₃O₄ nanoparticles is presented in Figure 2. The diffraction peaks observed at approximately 2θ = 31.3°, 36.8°, 44.8°, 59.3°, and 65.2° correspond to the (220), (311), (400), (511), and (440) planes, respectively. These reflections are in good agreement with the standard spinel Co₃O₄ phase (JCPDS No. 42-1467). The sharp and intense diffraction peaks also suggest a high degree of crystallinity in the nanoparticle samples. To further investigate the effect of carbon-based additives on thermal performance, a hybrid nanofluid was prepared by adding 0.4 wt.% CB (Merck, Rahway, NJ, USA, <100 μm) to the Co₃O₄/CMC–deionized water mixture containing 2.0 wt.% Co₃O₄ nanoparticles. Figure 3 shows the particle size distribution by number for the nanofluid sample, as obtained through Dynamic Light Scattering (DLS) analysis. The figure demonstrates a unimodal and sharply defined peak, indicating that the nanoparticles exhibit a relatively narrow size distribution. This suggests that the particles are well-dispersed within the medium, with minimal aggregation. The CB particles were ground using a Spex-type ball mill (Spex Industries, Inc., Edison, NJ, USA) for three hours before use to obtain nanosized particles [44]. Ball milling is one of the most widely employed top–down techniques for reducing particle size and achieving uniform nanoparticle dispersion and is frequently preferred in the production of nanoparticles used in nanofluids designed for heat transfer applications [45,46,47,48]. All formulations were then subjected to ultrasonic treatment in a water bath (ISOLAB Laborgeräte GmbH, Eschau, Germany) at 120 W for 3 h to ensure uniform particle dispersion and enhance stability (Figure 4).

2.2. Description of the Experimental System

The performance of the nanofluid was tested in an air-to-air HPHE, which consists of two air ducts and five copper heat pipes. The ducts are aligned parallel to each other with a 15 cm gap in between. Each duct is 130 cm long on either side of the heat pipes. Conical inlet sections are positioned at the ends of the ducts in opposite directions, with fan motors installed at their entrances to provide different air velocities. In the lower duct, just before the conical section, four electric heating resistances (each rated at 1000 W) are placed to heat the incoming air (Figure 5b). This setup allows for the utilization of different waste heat temperatures by heating the incoming air to various levels. Each heat pipe is constructed from copper with an inner diameter of 23.4 mm, an outer diameter of 25.4 mm, and a total length of 1 m (Figure 5a). The physical characteristics of the heat pipes are given in

Table 2. Physical characteristics of the heat pipes.

Heat Pipe Material	Copper
Total length of the heat pipe	1 m
Evaporator section length	450 mm
Condenser section length	400 mm
Adiabatic section length	150 mm
Inclination angle	90°
Number of heat pipes	5 units
Outer diameter of the heat pipe	25.4 mm
Inner diameter of the heat pipe	23.4 mm
Wall thickness	1 mm

.

During the experiment, ambient air is directed over the heating elements via a fan, where it is heated before entering the evaporator section of the heat exchanger. The heat causes the working fluid in the evaporator region to evaporate and travel to the condenser section. Simultaneously, cool air is drawn through the upper duct and passes over the condenser section, leading to the condensation of the working fluid. The condensed fluid then returns to the evaporator section by gravity.

Temperature measurements were performed using 14 K-type thermocouples. Five thermocouples were placed in the evaporator section and five in the condenser section of the heat pipes. Two thermocouples measured the inlet and outlet temperatures of the hot air, and two more measured those of the cold air. A schematic and general view of the experimental setup is shown in Figure 6 and Figure 7, respectively. Each heat pipe was vacuum-sealed, and the vacuum level in the pipes was monitored using the manometers mounted on them. Each heat pipe was charged with 65 mL of the prepared nanofluid, corresponding to approximately one-third of the evaporator section volume. The experiments were conducted under eight different conditions, varying the heating power (1000 W and 2000 W), cold air flow rate, and hot air flow rate. The velocity of the air circulating through the ducts was determined using an anemometer. In the hot air duct, the recorded air velocities were 0.555 m·s⁻¹ and 0.985 m·s⁻¹, while the corresponding values in the cold air duct were 0.437 m·s⁻¹ and 0.751 m·s⁻¹. All experimental operating parameters are detailed in

Table 3. Operating conditions for all experiments.

Test Case No.	Heating Power (W)	Hot Air Velocity (m/s)	Cold Air Velocity (m/s)
1	1000	0.555	0.437
2	1000	0.555	0.751
3	1000	0.985	0.437
4	1000	0.985	0.751
5	2000	0.555	0.437
6	2000	0.555	0.751
7	2000	0.985	0.437
8	2000	0.985	0.751

.

3. Data Processing and Uncertainty Analysis

3.1. Data Processing

The efficiency, thermal resistance, effectiveness, and heat transfer coefficient (h) were calculated, and the results were compared to evaluate performance improvements.

Air flow rates were utilized to determine the heat transfer within the ducts. The air mass flow rate ($\dot{m}$) was calculated using Equation (1):

$$\dot{m}=\rho ·V_{avg}·A$$

(1)

where $\rho$ is density (kg⋅m⁻³), $V_{avg}$ is the average air velocity (m·s⁻¹), and $A$ is the cross-sectional area of the duct (m²). $\rho$ and dynamic viscosity ($\mu$) (kg·m⁻¹·s⁻¹) are calculated using Equations (2) and (3) [49]:

$$\rho =351.99 T^{-1}+344.84 T^{-2}$$

(2)

$$\mu ={\displaystyle \frac{\left(1.459\times {10}^{-6}{T}^{1.5}\right)}{\left(110.77+T\right)}}$$

(3)

The nanofluid utilized in this study exhibits pseudo-plastic behavior due to the inclusion of CMC in the base fluid, which alters its rheological characteristics [36,50,51]. Therefore, the apparent viscosity (η) of the CMC/water solution is determined using the power-law model expressed as [33]:

$$\eta =m{\dot{\gamma }}^{n-1}$$

(4)

where $\dot{\gamma }$ is the shear rate, m is the consistency index, and n is the power-law index. The apparent viscosity was estimated using the power-law model parameters reported in the literature for similar CMC-based nanofluids with metal oxide nanoparticles [33]. In the power-law model, a value of n = 1 corresponds to a Newtonian fluid, while 0 < n < 1 is a shear-thinning (pseudo-plastic) fluid, and n > 1 represents a shear-thickening (dilatant) fluid. Experimental studies show that a CMC–water solution with a concentration of 0.0–0.4% can be approximated as a pseudo-plastic fluid for power-law index 0 < n < 1. In this study, CMC–water with a concentration of 0.4% was selected as the base fluid. This solution exhibits non-Newtonian pseudo-plastic behavior with a flow behavior index of n = 0.76 and m = 0.0785 [52]. This concentration level has been widely used in the literature to induce non-Newtonian behavior in nanofluid systems [36,50].

To estimate the viscosity of nanofluids, the Brinkman model provides a widely accepted extension of the classical Einstein equation. According to Brinkman’s formulation, the effective viscosity of a nanofluid (μ_nf) is related to the viscosity of the base fluid (μ_f) and the particle volume fraction ($\varnothing$) as follows [53]:

$${\mu }_{nf}={\mu }_f .{\displaystyle \frac{1}{{(1-\varnothing )}^{2.5}}}$$

(5)

The thermal conductivity of the nanofluid ($k_{nf}$) is calculated using Equation (6) [52].

$$k_{nf}=k_f· \left[{\displaystyle \frac{k_{p }+2 k_f+2\varnothing (k_{p }-k_f)}{k_p+2k_f-\varnothing (k_{p }-k_f)}}\right]$$

(6)

where $k_f$ and $k_p$ are the thermal conductivities of the base fluid and nanoparticles, respectively. The CMC–water solution with 0.4% CMC concentration was considered to have a thermal conductivity of $k_f$ = 0.613 W/mK [52].

The amount of heat transferred from the hot air to the working fluid is determined using Equation (7):

$$Q_e={\dot{m}}_h{· c}_p· \left(T_{in, h}-T_{out, h}\right)$$

(7)

where $c_p$ is the specific heat of air (kJ·kg⁻¹·K⁻¹).

The amount of heat transferred from the working fluid to the cold air stream is calculated using Equation (8).

$$Q_c={\dot{m}}_c{· c}_p· \left(T_{out, c}-T_{in,c}\right)$$

(8)

The heat capacity rates for the evaporator $\left(C_h\right)$ and condenser sections $\left(C_c\right)$ are calculated by Equations (9) and (10):

$$C_{h=}{\dot{m}}_h{· c}_{p,h}$$

(9)

$$C_{c=} {\dot{m}}_c{· c}_{p,c}$$

(10)

The thermal efficiency of the heat exchanger is calculated as the ratio of the energy absorbed by the cold air to the energy supplied by the hot air, as shown in Equation (11):

$$\eta ={\displaystyle \frac{Q_c}{Q_e}}$$

(11)

Thermal resistance is calculated using Equation (12) by dividing the temperature difference between the evaporator and condenser sections by the heat input to the evaporator:

$$R={\displaystyle \frac{T_{evap}-T_{cond}}{Q_e}}$$

(12)

The Reynolds number (Re) was calculated using Equation (13) to characterize the air flow regime in the hot and cold air channels.

$$Re={\displaystyle \frac{\rho \cdot V_{avg}\cdot D_h}{\mu }}$$

(13)

where D_h is the hydraulic diameter (m) of the rectangular duct, which was calculated using the standard expression D_h = 4A/P, where A is the cross-sectional area and P is the wetted perimeter of the duct. The heat transfer coefficient (h) was determined from the cold side using Equation (14):

$$h={\displaystyle \frac{Q}{A·{ ∆T}_{lm}}}$$

(14)

where $A$ denotes the heat transfer surface area (m²) and $\Delta T_{lm}$ is the log mean temperature difference, calculated as follows:

$$\Delta T_{lm}={\displaystyle \frac{(T_{h,in}-T_{c,out})-(T_{h,out}-T_{c,in})}{\ln \left(\frac{T_{h,in}-T_{c,out}}{T_{h,out}-T_{c,in}}\right)}}$$

(15)

The effectiveness (ε), which indicates the ratio of the actual heat transferred to the maximum possible, is a key performance indicator in heat exchanger systems, and it is calculated by Equation (16):

$$\epsilon ={\displaystyle \frac{Q_c}{C_{min}\cdot (T_{h,in}-T_{c,in})}}$$

(16)

$C_{min}=\min (\dot{m}\cdot c_p)$ is the smaller heat capacity rate between hot and cold air streams.

The performance improvement rate was calculated by comparing nanofluids to deionized water using Equation (17):

$$\%Improvement Rate={\displaystyle \frac{{\eta }_{nanofluid}-{\eta }_{deionized water}}{{\eta }_{deionized water}}} \times 100$$

(17)

The exergy balance for a steady-state control volume is expressed as follows:

$$\sum E_{\left(in\right)}=\sum E_{\left(out\right)}+\sum E_{\left(loss\right)}$$

(18)

The total exergy loss (E) in a steady-state system can be determined as follows:

$$E=E_h+E_c$$

(19)

where $E_h$ is the exergy change in the hot fluid, and $E_c$ is the exergy change in the cold fluid. Each of these can be expressed in two different forms [54]:

$$E_h=T_e\left[m_h\left(S_{h,out}-S_{h,in}\right)\right] or{ E}_h=T_e\left[C_{h}In\left( {\displaystyle \frac{T_{h,out}}{T_{h,in}}} \right)\right]$$

(20)

$$E_h=T_e\left[m_c\left(S_{c,out}-S_{c,in}\right)\right] or E_h=T_e\left[C_{c}In\left( {\displaystyle \frac{T_{c,out}}{T_{c,in}}} \right)\right]$$

(21)

$T_e$, the environmental reference temperature, is taken as 25 °C (298.15 K) in this study. The total exergy loss of the heat exchanger can be rewritten as follows:

$$E=T_e\left[C_h ln\left( {\displaystyle \frac{T_{h,out}}{T_{h,in}}}\right)+C_c ln\left({\displaystyle \frac{T_{c,out}}{T_{c,in}}} \right)\right]$$

(22)

The exergy-saving efficiency (%) is calculated as follows:

$$Exergy-Saving Efficiency\% =\left(1-{\displaystyle \frac{E_{nanofluid loss}}{E_{water loss}}}\right)\times 100$$

(23)

3.2. Uncertainty Analysis

In order to describe and quantify uncertainties in the experimental data obtained across multiple tests, uncertainty analysis is conducted. Measurement uncertainties can arise from a range of factors, including experimental conditions, measurement procedures, instrument types, data reading, and connection points of the gauge probes. Typically, the result R is expressed as a function of independent variables $x_1$, $x_2$,…, $x_n$. The uncertainty in the outcome, $W_R$, is a combination of the uncertainties in each independent variable, denoted by $w_1$,$w_2$,…,$w_n$.

The total uncertainty in the calculated quantity can therefore be estimated using the general partial derivative method expressed as follows [55]:

$$W_R={\left[{\left( {\displaystyle \frac{\partial R}{{\partial x}_1}}{w}_1\right)}^2+{ \left({\displaystyle \frac{\partial R}{{\partial x}_2}}{w}_2 \right)}^2+\dots +{ \left({\displaystyle \frac{\partial R}{{\partial x}_n}}{w}_n\right)}^2\right]}^{1/2}$$

(24)

In the present study, all fluid temperatures in the experimental setup were measured using K-type thermocouples with an accuracy of ±0.5 °C. Data were collected via a datalogger with a reading accuracy of ±0.20 °C. To ensure steady-state conditions, all temperature measurements were repeated three times, and the average values were recorded to minimize random errors and enhance the reliability of the data. The standard deviations were calculated using the sample-based formula, which estimates variability by computing the square root of the variance divided by n − 1, where n is the number of replicate measurements. The total uncertainty in the temperature measurement $W_T$ may stem from various sources of error, including the accuracy of the thermocouples ($w_{thermocouple accuracy}$), the connections of each thermocouple ($w_{thermocouple attachment}$), and the data reading from the measurement equipment ($w_{reading}$). The combined uncertainty in temperature measurements $W_T$ is calculated as ±1.27 °C. The air flow rates were calculated using the air velocity, air density, and duct cross-sectional area. The air velocity was measured using an anemometer with a sensitivity of ±0.01 m·s⁻¹, while the duct dimensions were measured with a tape measure with ±0.001 m precision. Additionally, the location of the anemometer within the duct introduced further uncertainty due to spatial variability in velocity distribution, estimated at ±0.5%. As a result, the combined uncertainty in mass flow rate measurement was computed as ±0.5%.

While the system was insulated to minimize thermal losses using vacuum layers and operated under steady-state conditions, slight efficiency deviations may still occur due to unavoidable heat dissipation. These were not directly quantified; however, the uniformity of test conditions across all experiments ensures that the comparative analysis between different fluids remains valid. The calculated values confirm that the uncertainties in both the temperature and mass flow rate measurements remain within acceptable limits, ensuring the reliability and accuracy of the experimental results presented in this study.

4. Results

The performance of the air-to-air HPHE was experimentally evaluated under different conditions. All tested conditions were within the turbulent flow regime, as confirmed by the calculated Reynolds numbers for both the hot and cold air streams.

Figure 8 shows the variation in the convective heat transfer coefficient concerning different heat capacity rate ratios for deionized water and 1% and 2% Co₃O₄ nanofluids. The heat transfer coefficient is a key indicator of convective heat transfer performance and depends on both the thermophysical properties of the working fluid and the flow dynamics. According to Figure 8, when the hot-side air velocity increases, the heat transfer coefficient enhances. This enhancement results from intensified convective heat transfer in the evaporator section. Higher hot air velocity increases the Reynolds number, reduces thermal boundary layer thickness, and results in more effective heat absorption by the working fluid inside the heat pipes. In addition to velocity, air temperature also affects the Reynolds number by altering air properties. Specifically, increasing temperature leads to a rise in dynamic viscosity and a simultaneous decrease in density, both of which contribute to a reduction in the Reynolds number. Therefore, the combined effect of air temperature and velocity governs the overall flow regime. Moreover, the use of nanofluids significantly improves the heat transfer coefficient compared to deionized water. At all velocity ratios, both 1% and 2% Co₃O₄ nanofluids demonstrate superior thermal performance. The 2% Co₃O₄ nanofluid consistently yielded the highest heat transfer coefficient values, validating its effectiveness in promoting convective heat transfer within the heat pipe system.

Under all test conditions, the hot and cold air channels exhibited turbulent flow, ensuring stable external convective heat transfer. This consistent air flow regime provides a reliable thermal boundary for evaluating the relative performance of different nanofluid working fluids inside the heat pipe. Figure 9 illustrates the variation in thermal efficiency and improvement rates for deionized water and nanofluids containing 1% and 2% Co₃O₄ under different Reynolds number conditions. As shown in Figure 9, the highest efficiency was obtained at a hot-side Reynolds number of 13,500 and a cold-side Reynolds number of 6000 for all tested fluids. Under these conditions, the thermal efficiency reached 21.0% for the 1.0% Co₃O₄ nanofluid and 24.2% for the 2% Co₃O₄ nanofluid, while deionized water exhibited a lower efficiency of 14.8%. The highest improvement rates were recorded at Re = 14,200 (hot side) and 10,400 (cold side), reaching 62.7% for the 1% Co₃O₄ nanofluid and 75.4% for the 2% Co₃O₄ nanofluid, compared to deionized water. This condition corresponds to a favorable flow ratio, allowing for effective heat absorption in the evaporator and sufficient residence time in the condenser, thus facilitating optimal heat transfer. The trend in the figure demonstrates that increasing the Reynolds number in the hot channel, when combined with a relatively lower Reynolds number in the cold channel, promotes higher efficiency by enhancing the temperature gradient across the heat exchanger. Additionally, the higher nanoparticle concentration further amplifies this effect by increasing thermal conductivity and disrupting thermal boundary layers, thereby improving heat absorption and dissipation throughout the heat exchanger. The effective thermal conductivities of the nanofluids containing 1% and 2% w/w Co₃O₄ in a 0.4% CMC–water base fluid were calculated as approximately 0.616 W/m·K and 0.619 W/m·K, respectively, while their viscosities at a shear rate of 10 s⁻¹ were estimated as 0.0454 mPa·s and 0.0456 mPa·s. These results indicate that increasing the nanoparticle concentration slightly enhances both the thermal conductivity and viscosity, which reflects the typical trade-off between improved heat transfer performance and increased flow resistance.

Some parameters affect the effectiveness of the HPHE. Higher air inlet temperatures improve the effectiveness [56,57]. This trend aligns with findings of the study, which reported that the effectiveness of the evaporator and condenser sections is enhanced by increasing the hot-side air inlet temperature. It was also observed that increasing the air flow rate on the hot side positively influenced the effectiveness on the evaporator side [58]. Figure 10 illustrates the variation in the thermal effectiveness (ε) with the average evaporator wall temperature for deionized water and Co₃O₄-based nanofluids. An increase in the average evaporator wall temperature tends to enhance the system’s effectiveness, as higher wall temperatures generally facilitate improved heat transfer rates. However, when compared at similar operating conditions, nanofluids exhibit superior effectiveness values even at lower evaporator wall temperatures relative to deionized water. The addition of nanofluids enables the achievement of higher thermal performance despite lower wall temperature levels. Figure 10 also shows that the use of nanofluids leads to a reduction in wall temperatures within the evaporator section. This decrease in the wall temperature indicates that the evaporation process occurs more efficiently at lower temperatures when Co₃O₄ nanofluids are used compared to deionized water. The enhanced thermal performance of the nanofluids results from their superior thermal conductivity and improved convective heat transfer characteristics. These properties allow for more effective heat absorption from the surrounding air, resulting in lower surface temperatures during evaporation. This behavior demonstrates the ability of nanofluids to recover heat from lower temperature sources, making them highly beneficial for increasing the thermal performance of heat-pipe-based heat exchangers. An enhanced particle concentration appears to promote greater disruption of the thermal boundary layer, further supporting effective energy exchange. The results confirm that the inclusion of Co₃O₄ nanoparticles significantly improves thermal effectiveness, with the 2% concentration consistently yielding the best performance.

Figure 11 presents the variation in thermal resistance and corresponding improvement rates for deionized water, 1% Co₃O₄ nanofluid, and 2% Co₃O₄ nanofluid across different Reynolds number combinations. The thermal resistance is a critical parameter that inversely correlates with heat transfer performance, and lower values indicate more efficient heat transfer. As shown in the figure, the thermal resistance of the heat pipe system decreases significantly when nanofluids are used instead of deionized water. The lowest thermal resistance values for all working fluids were recorded at a hot-side Reynolds number of 14200 and a cold-side Reynolds number of 10400. Under this condition, the thermal resistance dropped significantly to its minimum, and the corresponding improvement rates were calculated as 36.8% for the 1% Co₃O₄ nanofluid and 50.2% for the 2% Co₃O₄ nanofluid, relative to deionized water. This enhancement in performance can be attributed to the improved thermal conductivity and convective heat transfer behavior of the nanofluids. The nanoparticles disrupt the thermal boundary layer and enhance energy transport mechanisms within the fluid, resulting in more efficient heat removal and a significant reduction in thermal resistance. Additionally, higher Reynolds numbers are typically associated with increased turbulence, which reduces the thermal boundary layer thickness and enhances convective heat transfer. Sözen et al. reported a maximum 52.3% reduction in thermal resistance using graphene nanofluid at Re = 11,700 (cold) and 11,000 (hot) in an HPHE [59]. Similarly, Babat et al. observed a maximum 71.6% reduction in thermal resistance when magnetic nanofluid was used under Re = 11,450 conditions in the cold duct [41]. These examples align with the trends observed in the current study, further confirming the effectiveness of nanofluids under turbulent flow regimes.

Figure 12 illustrates the variation in exergy loss with respect to the heat capacity rate ratio (C_h/C_c) for deionized water, 1% Co₃O₄ nanofluid, and 2% Co₃O₄ nanofluid. As can be seen, the exergy loss consistently increases with a rising C_h/C_c across all tested fluids. Exergy loss reflects the irreversibilities arising from heat transfer across finite temperature gradients and viscous dissipation during air flow through the heat exchanger. Although exergy loss to the environment was not explicitly isolated, its contribution is assumed to be implicitly reflected in the total entropy generation observed under steady-state and well-insulated operating conditions. The experimental setup was thermally insulated to minimize external losses, and all measurements were obtained after thermal stabilization. The observed reduction in exergy loss when using nanofluids can be attributed to improved thermal transport mechanisms and more uniform flow behavior, which collectively reduce temperature gradients and entropy generation throughout the system. Among the working fluids, deionized water exhibited the highest exergy loss, while the 2% Co₃O₄ nanofluid demonstrated the lowest exergy loss across the entire range.

Figure 13 presents the exergy-saving efficiency, which quantifies the percentage reduction in exergy loss relative to deionized water, as a function of the C_h/C_c. As the heat capacity rate ratio increases, the exergy-saving efficiency also improves for both the 1% and 2% Co₃O₄ nanofluids. At a C_h/C_c of 3, the use of 2% and 1% Co₃O₄ nanofluids instead of deionized water resulted in exergy loss reductions of 29.3% and 21.5%, respectively. The 2% Co₃O₄ nanofluid consistently outperformed the 1% concentration, highlighting the beneficial effect of higher nanoparticle loading. This improvement is due to enhanced convective heat transfer and more effective thermal energy utilization, reducing system irreversibility compared to the base fluid. The results indicate that increasing the nanofluid concentration and the hot-side flow rate enhances the system’s capability to recover and utilize thermal energy more efficiently, supporting the potential of nanoparticle-enhanced working fluids for improving the thermodynamic performance of air-to-air HPHEs. The use of nanofluids, such as graphene oxide-based formulations, has been shown to significantly reduce exergy losses compared to distilled water in shell-and-tube heat exchangers. This improvement is attributed to enhanced thermal conductivity and reduced entropy generation resulting from the presence of nanoparticles [60]. Similarly, in pulsating heat pipe systems designed for chimney heat recovery, the incorporation of silver nanofluids has been found to reduce exergy destruction and slightly improve exergy efficiency compared to conventional working fluids, such as ethanol [61]. Nanoparticle-enhanced fluids improve heat transfer characteristics and reduce irreversibilities, thereby substantially enhancing the thermodynamic performance of heat exchanger systems.

The influence of CB addition on the thermal efficiency of the nanofluid is presented in Figure 14. The Co₃O₄/CB nanofluid showed higher thermal efficiency than both deionized water and the base Co₃O₄ nanofluid under nearly all tested conditions. The highest efficiency was achieved at a hot-side Reynolds number of 13,500 and a cold-side Reynolds number of 6000 for all tested fluids. Under this condition, the thermal efficiency reached 24.2% for the 2.0% Co₃O₄ nanofluid and 25.4% for the Co₃O₄/CB nanofluid, whereas the deionized water demonstrated a lower efficiency of 14.8%. The maximum improvement rate of 79.2% was achieved using Co₃O₄/CB nanofluid compared to deionized water when the Reynolds number was equal to 14,200 on the hot side and 10,400 on the cold side. The highest improvement was observed, with the thermal efficiency of the Co₃O₄/CB nanofluid exceeding that of the Co₃O₄ nanofluid by 14.6%, when the Reynolds number was 14,950 on the hot side and 6650 on the cold side. This enhancement indicates that CB contributes positively to the overall energy transfer performance of the heat exchanger system. Enhanced Brownian motion and localized thermal fluctuations introduced by the nanoparticles improve the rate of energy exchange between the fluid and the suspended particles.

Figure 15 highlights the impact of CB incorporation on thermal resistance across varying Reynolds numbers. The Co₃O₄/CB nanofluid exhibited consistently lower thermal resistance values compared to both deionized water and the base Co₃O₄ nanofluid across all tested Reynolds number conditions. The reduction in thermal resistance when using Co₃O₄/CB relative to the Co₃O₄ nanofluid ranged from 8.7% to 22.8%, demonstrating the enhancing role of CB in thermal transport performance. The highest overall improvement for Co₃O₄/CB was observed at a hot-side Reynolds number of 14,200 and a cold-side Reynolds number of 10,400, where the thermal resistance decreased by 61.4% compared to deionized water. CB possesses a high surface area and complex porous structure, which likely improves thermal interaction between fluid layers and the pipe wall. Its presence also enhances uniform thermal energy transport throughout the system. The introduction of CB may increase localized fluid agitation, reinforcing convective heat transfer processes and contributing to the overall reduction in thermal resistance. These effects may contribute to a notable reduction in thermal resistance when CB is introduced into the nanofluid formulation.

Figure 16 shows the variation in exergy loss concerning the C_h/C_c, specifically emphasizing the effect of CB incorporation into the Co₃O₄ nanofluid. While previous evaluations already established the improvement of nanofluids over deionized water, the addition of CB further reduces exergy losses across all tested conditions. Figure 17 presents the corresponding exergy-saving efficiency for the 2% Co₃O₄ nanofluid and the Co₃O₄/CB hybrid nanofluid. At every heat capacity rate ratio, the Co₃O₄/CB nanofluid consistently exhibited lower exergy loss values compared to the 2% Co₃O₄ nanofluid without CB. The Co₃O₄/CB hybrid nanofluid outperformed the 2% Co₃O₄ nanofluid in all tested conditions. At a C_h/C_c of 3, the use of Co₃O₄/CB nanofluid instead of deionized water resulted in exergy loss reductions of 33.6%. This improvement can be attributed to the enhanced thermal energy transport pathways and more uniform internal flow characteristics introduced by the addition of CB particles. These effects reduce temperature gradients and local flow resistance within the heat exchanger, which in turn suppresses entropy generation and minimizes overall exergy destruction under steady-state operation. The results demonstrate that the synergistic interaction between Co₃O₄ nanoparticles and CB significantly improves exergetic performance beyond that achievable with Co₃O₄ nanoparticles alone, making hybrid nanofluids a promising approach for advanced thermal management applications.

5. Conclusions

In this experimental study, the thermal and exergetic performances of an air-to-air HPHE were evaluated using Co₃O₄ nanoparticles dispersed in CMC-stabilized aqueous solutions, with and without CB addition. The key conclusions are summarized as follows:

• Turbulent flow regimes in the hot and cold air channels were confirmed under all tested conditions, ensuring consistent external convective heat transfer. This stable boundary condition enables a reliable evaluation of the relative thermal performance improvements achieved by nanoparticle-enhanced fluids within the heat pipe.
• The use of Co₃O₄ nanofluids substantially improved the thermal efficiency, heat transfer coefficient, and thermal effectiveness compared to deionized water. The highest thermal efficiency improvements were recorded as 62.7% and 75.4% for the 1% and 2% Co₃O₄ nanofluids, respectively. CB incorporation further enhanced the thermal efficiency of the 2% Co₃O₄ nanofluid, achieving a maximum improvement of 79.2%.
• Thermal resistance values significantly decreased with nanoparticle addition, and further reductions were obtained by introducing CB. The highest thermal resistance reduction observed was 61.4% relative to deionized water, highlighting the effective role of CB in facilitating heat transfer processes.
• Exergy loss decreased with the use of nanofluids, and the exergy-saving efficiency reached up to 29.3% and 33.6% with the 2% Co₃O₄ nanofluid and Co₃O₄/CB nanofluid, respectively. CB contributed to further reducing exergy losses by improving thermal dispersion and minimizing system irreversibility.

These results demonstrate the significant potential of hybrid Co₃O₄- and CB-based nanofluids for improving the thermal and exergetic performance of heat recovery systems, offering valuable opportunities for advancing energy-efficient, sustainable technologies in industrial and building applications.