Solar panels are widely used in renewable energy systems and green buildings. In actual operation, solar panels absorb a large amount of solar radiation, but only a small portion is converted into electricity. The remaining energy is converted into heat, which increases the working temperature of solar panels. My research focuses on reducing this temperature rise using viscoelastic nanofluids and optimized pipeline designs. In particular, I studied how different tube geometries, such as sudden expansion tubes, spherical protrusions, dual-tube arrangements, and corrugated tubes with porous media, influence the cooling performance of solar panels. The central objective of my work is to improve the thermal management of solar panels so that their electrical efficiency and service life can be maintained at a high level.
In my numerical simulations, I treated the cooling fluids as viscoelastic nanofluids. The viscoelastic behavior was described by the Maxwell constitutive equation, and the thermal conductivity of each nanofluid was obtained from experimental measurements. I used the User-Defined Function capability in the Fluent solver to introduce the Maxwell model and the fitted thermal conductivity formulas. Through these simulations, I was able to evaluate the velocity fields, temperature fields, Nusselt numbers, friction factors, and the resulting surface temperature distributions of solar panels under different operating conditions.
Why Solar Panels Need Efficient Cooling
The efficiency of solar panels is strongly dependent on temperature. When the temperature of a photovoltaic cell increases, the semiconductor bandgap changes and the recombination losses increase, causing a drop in open-circuit voltage. For many commercial solar panels, the electrical efficiency decreases by about 0.3% to 0.5% for every 1 °C rise in cell temperature. In addition, long-term exposure to high temperatures can degrade the encapsulant, cause micro-cracks in the silicon wafer, and accelerate the aging of solar panels. Therefore, the cooling of solar panels is not only an efficiency issue but also a reliability issue.
Various cooling methods have been proposed to regulate the temperature of solar panels. Air cooling is simple but has low heat capacity. Water cooling is effective but may require additional pumping power and can cause corrosion. My research focuses on liquid cooling using viscoelastic nanofluids because these fluids combine high thermal conductivity with improved flow behavior. The viscoelastic nature of the base fluid, such as polyacrylamide, xanthan gum, or sodium alginate solutions, can reduce friction losses and improve heat transfer under certain conditions. By adding nanoparticles such as Al2O3, TiO2, or Fe3O4, the effective thermal conductivity of the cooling medium is increased, which directly benefits the heat removal from solar panels.
Mathematical Model and Governing Equations
For all three configurations, I assumed that the flow is steady, incompressible, and turbulent. The cooling fluids were modeled as viscoelastic nanofluids using the Maxwell constitutive equation. The general form of the Maxwell model used in my simulations is:
$$
\mathbf{S}+\lambda\left(\frac{\partial \mathbf{S}}{\partial t}+\mathbf{U}\cdot\nabla\mathbf{S}\right)=\mu_{nf}\mathbf{A}_1,
$$
where $$ \mathbf{S} $$ is the extra stress tensor, $$ \lambda $$ is the relaxation time, $$ \mathbf{U} $$ is the velocity vector, $$ \mu_{nf} $$ is the dynamic viscosity of the nanofluid, and $$ \mathbf{A}_1=\nabla\mathbf{U}+\left(\nabla\mathbf{U}\right)^T $$ is the first Rivlin-Ericksen tensor. The relaxation time is a key parameter because it determines how quickly the fluid responds to changes in shear rate and temperature. I investigated the effect of varying $$ \lambda $$ on the thermal performance of solar panels.
The continuity equation and momentum equation for the nanofluid are written as:
$$
\nabla\cdot\mathbf{U}=0,
$$
$$
\rho_{nf}\left(\mathbf{U}\cdot\nabla\right)\mathbf{U}=-\nabla P+\nabla\cdot\mathbf{S}+\rho_{nf}\mathbf{g},
$$
where $$ \rho_{nf} $$ is the nanofluid density, $$ P $$ is the pressure, and $$ \mathbf{g} $$ is the gravitational acceleration. When the flow is turbulent, the instantaneous variables are decomposed into mean and fluctuating parts. The Reynolds-averaged momentum equation is then solved together with a turbulence model. In my first two studies, I used the Standard k-epsilon model, while in the third study, I used the Realizable k-epsilon model to account for the complex flow through porous media.
The turbulent kinetic energy equation and the turbulent dissipation rate equation can be expressed as:
$$
\rho_{nf}\frac{\partial K}{\partial t}+\rho_{nf}\bar{u}_j\frac{\partial K}{\partial x_j}=P_K-\rho_{nf}\varepsilon+\frac{\partial}{\partial x_j}\left[\left(\mu_{nf}+\frac{\mu_t}{\sigma_K}\right)\frac{\partial K}{\partial x_j}\right],
$$
$$
\rho_{nf}\frac{\partial \varepsilon}{\partial t}+\rho_{nf}\bar{u}_j\frac{\partial \varepsilon}{\partial x_j}=C_{\varepsilon1}\frac{\varepsilon}{K}P_K-C_{\varepsilon2}\rho_{nf}\frac{\varepsilon^2}{K}+\frac{\partial}{\partial x_j}\left[\left(\mu_{nf}+\frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right],
$$
where $$ K $$ is the turbulent kinetic energy, $$ \varepsilon $$ is the dissipation rate, $$ P_K $$ is the turbulence production term, and $$ \mu_t $$ is the eddy viscosity. I used the standard model constants, namely $$ C_{\varepsilon1}=1.44 $$, $$ C_{\varepsilon2}=1.92 $$, $$ \sigma_K=1.0 $$, and $$ \sigma_\varepsilon=1.3 $$. The SIMPLEC algorithm was employed to couple the pressure and velocity fields. A second-order upwind scheme was used for the convective terms in the momentum and energy equations.
The energy equation for the nanofluid is:
$$
\rho_{nf}\left(c_p\right)_{nf}\left(\mathbf{U}\cdot\nabla T\right)=\nabla\cdot\left(k_{nf}\nabla T\right),
$$
where $$ T $$ is the temperature and $$ k_{nf} $$ is the thermal conductivity of the nanofluid. The physical properties of the nanofluid were calculated using the following mixing models:
$$
\rho_{nf}=\left(1-\varphi\right)\rho_{bf}+\varphi\rho_{np},
$$
$$
\left(\rho c_p\right)_{nf}=\left(1-\varphi\right)\left(\rho c_p\right)_{bf}+\varphi\left(\rho c_p\right)_{np},
$$
$$
\mu_{nf}=\left(1+7.3\varphi+123\varphi^2\right)\mu_{bf},
$$
where $$ \varphi $$ is the nanoparticle volume fraction, and the subscripts $$ bf $$ and $$ np $$ denote the base fluid and the nanoparticle, respectively.
Boundary Conditions and Performance Indicators
In all simulations, the bottom wall and side walls of the cooling channels were assumed to be adiabatic. A constant heat flux boundary condition was applied on the surface of the photovoltaic cell to represent solar radiation:
$$
-k_s\frac{\partial T_s}{\partial n}=q,
$$
where $$ q $$ ranges from 600 to 1000 W/m2 depending on the simulated solar radiation intensity. At the interface between the solid wall and the nanofluid, the temperature and heat flux continuity conditions were imposed:
$$
T_s=T_{nf},
$$
$$
-k_s\frac{\partial T_s}{\partial n}=-k_{nf}\frac{\partial T_{nf}}{\partial n}.
$$
The no-slip boundary condition was applied on all solid surfaces:
$$
\mathbf{V}_s=0,\qquad \mathbf{V}_{nf}=0.
$$
To evaluate the cooling performance, I computed the useful heat absorbed by the cooling fluid:
$$
Q_u=\dot{m}_{nf}\left(c_p\right)_{nf}\left(T_{out}-T_{in}\right),
$$
where $$ \dot{m}_{nf} $$ is the mass flow rate, and $$ T_{in} $$ and $$ T_{out} $$ are the inlet and outlet temperatures of the nanofluid. The thermal efficiency of the photovoltaic system is defined as:
$$
\eta_{th}=\frac{Q_u}{G_t A_s},
$$
where $$ G_t $$ is the solar irradiance and $$ A_s $$ is the area of the photovoltaic module. The electrical power generated by solar panels is expressed as:
$$
P_{ele}=G_t\tau\xi_f\eta_r\left[1-\beta_r\left(T_{PV}-T_{ref}\right)\right],
$$
and the electrical efficiency is:
$$
\eta_{ele}=\frac{P_{ele}}{G_t}.
$$
The total efficiency combines both thermal and electrical contributions:
$$
\eta_{ov}=\eta_{th}+\eta_{ele}.
$$
I also evaluated the average Nusselt number and friction factor, which are important for understanding the heat transfer and pressure drop characteristics of the cooling channels:
$$
Nu=\frac{hL}{k_{nf}},
$$
$$
f=\frac{2\Delta P}{\rho_{nf}u^2L/D},
$$
where $$ h=q/(T_{PV}-T_{in}) $$ is the average convective heat transfer coefficient, $$ L $$ is the tube length, $$ D $$ is the hydraulic diameter, $$ u $$ is the average velocity, and $$ \Delta P $$ is the pressure drop across the channel.
| Parameter | Symbol | Value or range |
| Solar heat flux | $$q$$ | 600 – 1000 W/m² |
| Inlet temperature | $$T_{in}$$ | 300 K |
| Mass flow rate | $$\dot{m}$$ | 0.01 – 0.05 kg/s |
| Relaxation time | $$\lambda$$ | 0.01 – 0.5 s |
| Nanoparticle volume fraction | $$\varphi$$ | 0.25% – 0.75% |
| Turbulence model | – | Standard k-ε / Realizable k-ε |
| Pressure-velocity coupling | – | SIMPLEC |
Comparison of Turbulence Models
I selected turbulence models based on the complexity of the flow. The Standard k-epsilon model is robust and efficient for fully developed turbulent flows in tubes. The Realizable k-epsilon model is more accurate for flows with separation, recirculation, and porous media. The table below summarizes the considerations.
| Model | Advantages | Disadvantages |
| Standard k-ε | Fast, stable, good for simple internal flows | Less accurate for strong separation and swirl |
| RNG k-ε | Better for moderate complexity flows | More computational cost |
| Realizable k-ε | Accurate for rotation, separation, recirculation | More complex and computationally expensive |
| Standard k-ω | Good for near-wall and low-Reynolds numbers | Sensitive to free-stream values |
Configuration 1: PAM-Al2O3 Nanofluid in a Sudden Expansion Tube with Spherical Protrusions
In the first part of my research, I considered a photovoltaic thermal system in which solar panels are cooled by a polyacrylamide-based nanofluid containing Al2O3 nanoparticles. The cooling channel designs included a U-shaped tube, a sudden expansion tube, and a sudden expansion tube with spherical protrusions. The spherical protrusions increase the contact area between the nanofluid and the heated wall, which is beneficial for the cooling of solar panels. The sudden expansion causes the fluid velocity to decrease and the pressure to recover, which can improve flow distribution over the heated surface.
The photovoltaic panel dimensions and physical properties used in this configuration are given in the following tables.
| Component | Thickness | Material role |
| Glass | 2 mm | Protective cover |
| EVA | 0.6 mm | Encapsulant |
| Photovoltaic cell | 0.4 mm | Electricity generation |
| Absorber plate | 1.5 mm | Heat transfer to coolant |
| Component | Density (kg/m³) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) |
| Glass | 2200 | 830 | 0.76 |
| Photovoltaic cell | 2330 | 700 | 148.0 |
| EVA | 960 | 2090 | 0.35 |
| Absorber plate | 2330 | 871 | 202.4 |
Thermal Conductivity Measurement for PAM-Al2O3 Nanofluid
To accurately simulate the heat transfer process, I prepared PAM-Al2O3 nanofluids with different nanoparticle volume fractions. I used a thermal conductivity meter to measure the thermal conductivity at room temperature. The measured data were then fitted to obtain an empirical correlation. The fitted thermal conductivity model for the PAM-Al2O3 nanofluid can be represented as:
$$
\frac{k_{nf}}{k_{bf}}=1+A\varphi+B\varphi^2+C\varphi\ln\left(\frac{k_{np}}{k_{bf}}\right)+D\varphi^3,
$$
where the fitting constants were determined as $$ A=0.9326 $$, $$ B=0.5676 $$, $$ C=1.0109 $$, and $$ D=-0.0505 $$. The coefficient of determination was $$ R^2=0.9664 $$, indicating a good agreement between the fitted correlation and the experimental data. This thermal conductivity formula was then imported into the Fluent solver through a User-Defined Function.
Velocity and Temperature Fields
My simulation results showed that the U-shaped tube produced a fairly uniform velocity profile in the straight sections. However, in the bend region, centrifugal forces caused the fluid to move faster near the outer wall, and a low-velocity boundary layer formed near the inner wall. The sudden expansion tube created a recirculation zone downstream of the expansion, which reduced the local velocity near the wall and increased the residence time of the fluid. When spherical protrusions were added, the flow area changed periodically, and the velocity increased locally around each spherical bump. This promoted mixing and improved the convective heat transfer coefficient on the wall, which is particularly important for solar panels because uniform heat removal prevents hot spots.
The temperature fields followed the velocity behavior. In the U-shaped tube, the temperature increased steadily along the flow direction. In the sudden expansion tube, the lower velocity in the enlarged section led to a thicker thermal boundary layer and a higher temperature near the outlet. With spherical protrusions, the periodic contraction and expansion disrupted the thermal boundary layer and enhanced heat transfer. As a result, the surface temperature distribution on solar panels became more uniform.
Effect of Tilt Angle
I also examined the effect of the tilt angle of the photovoltaic panel. The tilt angle influences the gravitational force component along the flow direction. When the tilt angle increases, the buoyancy and gravitational acceleration help the nanofluid move along the channel, increasing the flow velocity near the heated wall. This enhances the convective heat transfer and increases the Nusselt number. The table below summarizes the trends I observed.
| Tilt angle | Average surface temperature of solar panels | Nusselt number | Electrical efficiency |
| Low | Higher | Lower | Lower |
| High | Lower | Higher | Higher |
At a solar radiation of 1000 W/m² and a mass flow rate of 0.03 kg/s, the use of sudden expansion tubes with spherical protrusions increased the electrical efficiency of solar panels by about 10.5% compared with a basic U-tube configuration. This improvement is mainly due to the lower operating temperature and more uniform temperature distribution on the photovoltaic surface.
Effect of Relaxation Time
The relaxation time of the viscoelastic nanofluid is a key parameter. I evaluated relaxation times ranging from short to longer values while keeping all other conditions fixed. The results indicated that a shorter relaxation time improves the cooling performance of solar panels. With a shorter relaxation time, the viscoelastic fluid can respond more quickly to changes in temperature and shear rate. This promotes faster heat diffusion and reduces the thermal boundary layer thickness. Consequently, the Nusselt number increases and the surface temperature of solar panels decreases.
| Relaxation time | PV surface temperature | Nusselt number | Friction factor |
| Short | Lower | Higher | Lower |
| Long | Higher | Lower | Higher |
Influence of Inlet Diameter and Spherical Protrusion Diameter
I also investigated the influence of geometric parameters. When the inlet diameter of the sudden expansion tube was reduced, the fluid velocity increased, which thinned the thermal boundary layer and increased the Nusselt number. However, the higher velocity also increased the wall shear stress and therefore increased the friction factor. On the other hand, increasing the diameter of the spherical protrusions increased the contact area between the fluid and the wall. This enhanced heat transfer and increased the Nusselt number. The friction factor also increased because the protrusions create additional form drag and disturb the flow more strongly.
Configuration 2: XG-TiO2 Nanofluid in Dual-Tube Side-by-Side Sudden Expansion Channels
In the second part of my research, I extended the first configuration by using two sudden expansion tubes arranged side by side under the absorber plate. The two tubes contained spherical protrusions. I considered two arrangements: dual-tube uni-directional, where the inlets are on the same side, and dual-tube opposite-directional, where the inlets are on opposite sides. The cooling fluid was a xanthan gum solution with TiO2 nanoparticles. I selected this nanofluid because xanthan gum has strong viscoelastic properties and TiO2 nanoparticles provide good thermal conductivity enhancement.
| Material | Density (kg/m³) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) | Viscosity (Pa·s) |
| TiO2 nanoparticles | 4260 | 710 | 8.4 | – |
| XG solution | 1550 | 1730 | 0.5986 | 0.0306 |
The thermal conductivity of the XG-TiO2 nanofluid was measured and fitted. The fitted correlation is:
$$
\frac{k_{nf}}{k_{bf}}=1+A_1\varphi+A_2\varphi^2+A_3\varphi^3+A_4\varphi^4+\frac{10\alpha\beta\varphi^3}{1-\alpha\beta\varphi},
$$
$$
\alpha=\frac{k_{np}-k_{bf}}{k_{np}+2k_{bf}},\qquad \beta=\frac{k_{np}-k_{bf}}{k_{np}+2k_{bf}},
$$
where the constants were $$ A_1=-0.05172 $$, $$ A_2=1.291\times10^5 $$, $$ A_3=-1531 $$, and $$ A_4=4.931 $$. The high coefficient of determination, $$ R^2=0.9991 $$, confirmed the accuracy of the fitted formula. This formula was then used in the CFD solver to represent the effective thermal conductivity of the XG-TiO2 nanofluid.
Flow Behavior in the Dual-Tube Arrangement
For both the uni-directional and opposite-directional arrangements, the local velocity showed the same fundamental trend. The fluid entered the small-diameter section with a high velocity, then decelerated when it entered the large-diameter section. The spherical protrusions accelerated the fluid locally and generated secondary flows. In the dual-tube opposite-directional arrangement, the two cooling streams flowed in opposite directions. This produced a more symmetric thermal boundary condition on the absorber plate and reduced the overall temperature difference between the two sides of the photovoltaic panel.
Effect of Flow Velocity
I tested inlet velocities from 0.01 to 0.1 m/s. Increasing the velocity of the XG-TiO2 nanofluid increased the convective heat transfer coefficient. A higher velocity thins the thermal boundary layer and enhances mixing between the nanofluid and the heated wall. This directly reduces the average temperature of solar panels. The opposite-directional arrangement performed better than the uni-directional arrangement because it produced a more uniform heat extraction pattern across the panel surface.
| Inlet velocity (m/s) | Effect on cooling | Effect on uniformity |
| 0.01 | Weak heat removal | Large temperature gradient |
| 0.05 | Improved heat removal | Moderate uniformity |
| 0.10 | Strong heat removal | High uniformity |
Effect of Relaxation Time on Dual-Tube Performance
For the XG-TiO2 nanofluid, I again varied the relaxation time. The results showed that shorter relaxation times increased the Nusselt number and reduced the friction factor. The physical reason is that viscoelastic fluids with short relaxation times can quickly rearrange their internal structure when the flow accelerates through the spherical protrusions. This reduces the elastic resistance and improves the fluid’s ability to follow the changing channel geometry. Therefore, the cooling of solar panels becomes more efficient when the relaxation time is short.
Configuration 3: SA-Fe3O4 Nanofluid in a Corrugated Tube Filled with Porous Media
In the third part of my research, I investigated a different cooling channel geometry: triangular corrugated tubes filled with porous metal media. The working fluid was a sodium alginate solution containing Fe3O4 nanoparticles. The porous medium was made of copper, aluminum, or nickel. This design aims to increase the effective heat transfer area while using the porous structure to redistribute the flow and enhance thermal diffusion.
| Material | Density (kg/m³) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) | Viscosity (Pa·s) |
| Fe3O4 nanoparticles | 5180 | 870 | 80.4 | – |
| SA solution | 919 | 4176 | 0.4403 | 0.000916 |
| Porous material | Density (kg/m³) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) |
| Copper | 8930 | 386 | 398 |
| Aluminum | 2719 | 871 | 202.4 |
| Nickel | 8900 | 460.4 | 91.4 |
The thermal conductivity of the SA-Fe3O4 nanofluid was measured and fitted with the following relation:
$$
\frac{k_{nf}}{k_{bf}}=1+A_1\varphi+A_2\varphi^2+A_3\frac{k_{np}-k_{bf}}{k_{np}+k_{bf}}\varphi+A_4\varphi^3,
$$
where $$ A_1=-336.2941 $$, $$ A_2=1.9272 $$, $$ A_3=42.5690 $$, and $$ A_4=1.5569 $$. The coefficient of determination was $$ R^2=0.9879 $$. The measured data showed that increasing the volume fraction of Fe3O4 nanoparticles increases the thermal conductivity of the nanofluid. This is beneficial for extracting heat from solar panels because the heat can be conducted more quickly through the cooling fluid.
Governing Equations for Porous Media
When the cooling channel is filled with a porous medium, the momentum equation includes an additional Darcy resistance term. The modified momentum equation used in my simulation is:
$$
\rho_{nf}\left(\frac{\partial \bar{u}_i}{\partial t}+\bar{u}_j\frac{\partial \bar{u}_i}{\partial x_j}\right)=-\frac{\partial \bar{P}}{\partial x_i}+\frac{\partial}{\partial x_j}\left[\mu_{nf}\left(\frac{\partial \bar{u}_i}{\partial x_j}\right)\right]-\frac{\mu_{nf}}{\kappa}\bar{u}_i+\rho_{nf}g_i,
$$
where $$ \kappa $$ is the permeability of the porous medium. The effective thermal properties of the porous region are calculated as:
$$
\left(\rho c_p\right)_m=\phi\left(\rho c_p\right)_{nf}+\left(1-\phi\right)\left(\rho c_p\right)_s,
$$
$$
k_m=\phi k_{nf}+\left(1-\phi\right)k_s,
$$
where $$ \phi $$ is the porosity, and the subscript $$ s $$ denotes the solid matrix of the porous medium. These effective properties are important because they determine how heat is conducted through the porous structure before being removed by the nanofluid.
Velocity and Temperature Behavior
Without the porous medium, the corrugated tube created zones of low velocity near the wave crests. These regions retained heat and caused local hot spots on the absorber plate. When the porous medium was added, the flow resistance increased near the wave crests, but the solid matrix enhanced thermal conduction. The porous structure also increased the contact area between the fluid and the heated surface, which improved the overall heat transfer. The temperature distribution on solar panels became more uniform when the corrugated tube was filled with porous media.
Effect of Porous Material
I compared copper, aluminum, and nickel as the porous matrix materials. The results showed that aluminum offered the best balance between heat transfer and pressure drop. Copper had very high thermal conductivity but also a high friction factor due to its high density and surface interaction. Nickel showed the highest friction factor among the three materials, which reduced the fluid velocity and weakened the convective heat transfer. Aluminum, with its lower density and good thermal conductivity, allowed the fluid to maintain a higher velocity while providing sufficient heat conduction. Therefore, aluminum porous media are more suitable for cooling solar panels with corrugated tubes.
| Porous material | Thermal conductivity | Friction factor | Cooling performance |
| Copper | High | Moderate | Good |
| Aluminum | Moderate | Low | Best overall |
| Nickel | Low | High | Weakest |
Effects of Flow Velocity and Relaxation Time
As the inlet velocity increased from 0.01 to 0.05 m/s, the convective heat transfer coefficient increased, and the surface temperature of solar panels decreased. The porous medium suppressed the formation of a thick thermal boundary layer by promoting local mixing. However, the pressure drop also increased with velocity. The viscoelastic relaxation time again played an important role. Shorter relaxation times allowed the SA-Fe3O4 nanofluid to adapt quickly to the tortuous paths inside the porous medium. This reduced the effective friction factor and improved the heat transfer performance.
Summary of Comparative Findings
Across the three configurations, I observed several consistent findings. First, the use of viscoelastic nanofluids always improved the cooling of solar panels compared with pure base fluids. The nanoparticles increased the thermal conductivity, while the viscoelastic base fluid provided favorable flow characteristics. Second, geometric modifications such as sudden expansions, spherical protrusions, and corrugated walls all helped to disrupt thermal boundary layers and improve heat transfer. Third, the relaxation time should be as short as possible to enhance the response of the fluid to temperature and velocity changes.
| Configuration | Nanofluid | Key design feature | Main benefit for solar panels |
| 1 | PAM-Al2O3 | Sudden expansion with spherical bumps | Uniform temperature distribution |
| 2 | XG-TiO2 | Dual-tube opposite-directional | Reduced thermal asymmetry |
| 3 | SA-Fe3O4 | Corrugated tube with porous aluminum | Greater effective heat transfer area |
Conclusions
In my research, I have systematically analyzed the flow and heat transfer of viscoelastic nanofluids in several novel cooling channel designs and their impact on the performance of solar panels. The main conclusions can be summarized as follows.
First, the Maxwell constitutive equation, implemented through a User-Defined Function, is an effective approach for simulating the viscoelastic behavior of polymeric nanofluids in Fluent. The relaxation time parameter has a significant influence on the thermal performance. A shorter relaxation time generally improves the heat transfer capability and reduces the friction factor, which leads to lower surface temperatures on solar panels.
Second, sudden expansion tubes and spherical protrusions can substantially improve the heat exchange efficiency. The combination of these two features increases the contact area between the nanofluid and the heated wall, breaks the thermal boundary layer, and promotes better mixing. As a result, the surface temperature of solar panels is lower and more uniform, which protects the photovoltaic cells from hot-spot damage.
Third, the dual-tube opposite-directional arrangement is better than the uni-directional arrangement for large photovoltaic panels. Because the two cooling streams flow in opposite directions, the temperature difference between the two sides of the absorber plate is reduced. This improves the thermal uniformity and enhances the overall performance of solar panels.
Fourth, the use of corrugated tubes filled with porous media provides another effective cooling strategy. The porous medium increases the effective thermal conductivity and the heat transfer area. Among the porous materials considered, aluminum offers the best trade-off between heat transfer enhancement and pressure drop. This configuration is particularly useful for photovoltaic systems that need a compact cooling design.
Finally, the experimental measurement of thermal conductivity plays an important role in the accuracy of the numerical simulation. Classical models may not accurately predict the thermal conductivity of viscoelastic nanofluids because of polymer-particle interactions and aggregation effects. By measuring the thermal conductivity directly and fitting the data into empirical formulas, I was able to obtain more reliable simulation results for the cooling performance of solar panels.
Future Outlook
In the future, I would like to extend this work in several directions. One possibility is to prepare hybrid nanofluids containing two or more types of nanoparticles in order to further enhance thermal conductivity and stability. Another possibility is to use more advanced viscoelastic models, such as the Oldroyd-B model or fractional Maxwell models, to capture the complex rheological behavior over a wider range of frequencies. I also intend to explore grid-based cooling channels, serpentine networks, and multi-path arrangements for cooling solar panels. These designs could be combined with phase-change materials or porous foams to achieve even more uniform temperature control. The ultimate goal is to develop a reliable and efficient cooling system that can maintain solar panels at a low operating temperature for their entire service life.