Performance Optimization of a Thermoelectric Device by Using a Shear Thinning Nanofluid and Rotating Cylinder in a Cavity with Ventilation Ports

Abstract

The combined effects of using a rotating cylinder and shear thinning nanofluid on the performance improvements of a thermoelectric generator (TEG)-installed cavity with multiple ventilation ports are numerically assessed. An optimization algorithm is used to find the best location, rotational speed and size of the cylinder to deliver the highest power generation of the TEG. The power generation features with varying Rew are different for the first nanofluid (NF1) when compared to the second one (NF2). The power rises with higher Rew when NF1 is used, and up to 49% enhancement is obtained. The output power variation between nanofluids NF1 and NF2 is the highest at Rew = 0, which is obtained as 68.5%. When the cylinder location is varied, the change in the output power becomes 61% when NF2 is used. The optimum case has 11.5%- and 161%-higher generated power when compared with the no-object case with NF1 and NF2. The computational effort of using the high-fidelity coupled system is reduced when optimization is considered.

1. Introduction

Convective heat transfer (HT) in cavities with ports is relevant in many different engineering systems, including building ventilation, convective drying, electronic cooling, solar power applications, thermal energy storage and many others. The inclusion of multiple vented ports in cavities results in complex flow regimes, and many re-circulations are established [1,2]. Many studies have considered the convective HT performance for vented cavities. The location of the ports and Reynolds number (Re) were found to be effective regarding the flow and HT characteristics [3,4,5].

Many different enhancement techniques have been offered for convective HT in ventilated cavities, including the use of fins [6], flexible walls [7], magnetic fields [8,9] and flow pulsation [10,11,12]. In one of the methods, rotating cylinders have been used in channels/cavities for convective HT control [13,14,15,16]. The location, size, conductivity ratio and rotational speed have been considered as the most influential parameters that affect the HT [17,18,19,20,21,22].

There are a few studies that considered the impacts of rotating cylinders in 3D cavity configurations [23,24,25,26]. Another method that can be used to control the convection for ventilated cavities is the utilization of nanofluids. The theory and applications of nanofluids in thermal engineering systems have been reviewed in many studies [27,28,29,30,31,32,33,34,35]. The accurate modeling of nanofluid behavior requires good representation of the thermophysical properties and simulation tools. Non-Newtonian behavior of nanofluids in different thermal systems has been considered in various studies [36,37,38,39,40,41,42,43].

Currently, the need for alternative energy sources is growing due to energy costs and environmental side impacts. Thermoelectric generators (TEGs) are considered as one of the alternatives for thermoelectric energy conversion. They offer many advantages, such as having no moving parts, being compact and working quietly [44,45]. They have been used in many energy system applications, including military, solar and refrigeration [46]. They can also be used as control elements for thermal management in various systems.

Performance improvements for renewable energy systems may be enhanced by using TE devices [47,48,49]. The power generation characteristics of these devices depend on many factors, including the material properties and operating conditions of the installed system [50,51,52,53,54]. Applications of nanofluids with TEG-integrated systems have been considered in various studies, while the potential of using nanofluids has been explored [55,56,57,58]. Simulation studies of TEG-installed systems with computational fluid dynamics (CFD) are used to analyze the system performance and to determine the influencing parameters of interest.

The computations may be expansive due to the coupled physics of systems with different-length scales in 3D where TEG is considered as a sub-system. Therefore, methods are needed to increase the computational efficiency and performance estimation of TEG-integrated systems. Artificial neural networks and other soft computing techniques may be considered as one of the available options that are widely used in energy system technologies [59,60,61,62,63,64,65]. In CFD applications, parametric variations of the variables on the performance features are explored.

The optimum conditions for the operating parameters of interest may not be obtained when using only parametric CFD. Optimization routines should be used with CFD. As the computational cost of coupled multi-physics systems involving multiple time and length scales is expensive, the importance of optimization routines in CFD becomes apparent in order to achieve the best system performance. In a recent study, optimization was integrated for CFD simulation of convective drying [66]. Machine-learning methods have been used in TEG-integrated systems [67,68,69,70,71,72,73].

The present study aims to analyze the performance characteristics of TEG-integrated cavities with multiple vented ports in 3D using CFD. A rotating cylinder is placed within the vented cavity, and optimization-based analysis is performed to find the best operating parameters in order to achieve the highest power generation from the system. Comparisons are made with the parametric CFD and with the case of no-object configuration. A shear thinning nanofluid is used as the HT fluid, while the rheological properties of nanofluids are taken from an experimental study. The coupled multi-physics system of the TEG-installed system is analyzed using the finite element method and COBYLA optimization algorithm, and two different shear thinning nanofluids are utilized.

As many different applications of vented cavity configurations are available in various energy system technologies as mentioned before, a practical application of power generation with TEG installation is proposed, while performance improvement is further enhanced by using nanofluids and rotating cylinders. In the literature, the utilization of nanoparticle loading in the base fluid has been considered for thermo-electric conversion in vented cavities, and other methods of performance improvement have been used; however, the non-Newtonian aspects of nanofluids have never been considered with optimization.

The best cylinder location, size and rotational speed are found by using the optimization to deliver the highest power generation. The proposed method of CFD-based optimization is also novel in order to increase the computational efficiency of high-fidelity CFD for TEG-installed systems and to find the optimum parameters for the best performance.

2. Mathematical Modeling

2.1. System Configuration

The combined impacts of using a rotating cylinder and shear thinning nanofluid on the performance characteristics of TEG-mounted cavities with multiple ventilation ports are numerically assessed. One inlet port and two outlet ports are considered, and the port sizes are termed di and do for the inlet and outlets as shown in Figure 1. The sizes of the cavity are termed Hm and Lm. The cylinder has a radius of R and is rotating with a speed of $\mathrm{\Omega }$. The center location is (yc, zc). Hot fluid with a temperature of Th and a velocity of uh enters the ventilated cavity (VC), while a TEG device is mounted on the bottom surface of the VC.

The fluid exhibits non-Newtonian behavior (shear thinning), and the experimental data is utilized for the parameters for the rheological behavior (m—consistency index and n—power law index). Two different nanofluids with a solid volume fraction of 0.05 (NF1) and 0.45 (NF2) are used. The TEG module has legs with dimensions of 2 × 2 × 2 mm for the width, length and height. The conductor length, thickness and width are 2, 0.2 and 4.5 mm, while the thickness of the ceramic is 0.3 mm.

2.2. Vented Cavity Equations

For the shear thinning nanofluid flow in the VC, the governing equations (mass, momentum and energy) are stated as in the following:

$$\nabla ·\left(\rho \mathbf{u}\right)=0$$

(1)

$$\frac{\partial \rho \mathbf{u}}{\partial t}+\nabla ·\left(\rho \mathbf{u}\mathbf{u}\right)=-\nabla P+\nabla ·\tau$$

(2)

$$\frac{\partial T}{\partial t}+\nabla ·\left(\mathbf{u}T\right)=\alpha {\nabla }^{2}T$$

(3)

where $\tau$ is the shear stress, which is defined as:

$$\tau =\mu \left(\nabla \mathbf{u}+{\left(\nabla \mathbf{u}\right)}^T\right),$$

(4)

where $\mu$ is the dynamic viscosity. In the above given equations, the impacts of free convection and viscous dissipation are not taken into account, and the single phase approach of the nanofluid is adopted. For the shear stress and shear rate relations, the Ostwald-de Waele model is used:

$$\tau =m{\left|\dot{\gamma }\right|}^{n-1}\dot{\gamma },$$

(5)

where the two constants m and n are experimentally obtained in Ref. [74] for Al₂O₃-water nanofluid. The nanofluid shows shear thinning fluid behavior, and the power law index (n) takes the values of 0.88 and 0.5 for solid volume fractions of 0.005 and 0.045.

The model by Chon et al. [75] is used for the nanofluid thermal conductivity:

$$\frac{k_{nf}}{k_f}=1+64.7{\varphi }^{0.7640}{\left(\frac{d_f}{d_p}\right)}^{0.3690}{\left(\frac{k_f}{k_p}\right)}^{0.7476}{\mathrm{Pr}}^{0.9955}{\mathrm{Re}}_p^{1.2321}$$

(6)

where Pr and ${\mathrm{Re}}_p$ are given as:

$$\mathrm{Pr}=\frac{{\mu }_f}{{\rho }_f{\alpha }_f},{\mathrm{Re}}_p=\frac{{\rho }_f{k}_{b}T}{3\pi {{\mu }_f}^2{l}_f}.$$

(7)

where $k_b$ is the Boltzmann constant with a value of $1.3807\times {10}^{-23}$ J/K and $l_f$ is the mean path of a fluid particle.

The non-dimensional numbers are the Prandtl number (Pr), Reynolds number (Re) and rotational Re number (Rew), which are given as:

$$\mathrm{Pr}=\frac{c_{p}m}{k}{\left(\frac{uh}{H}\right)}^{n-1},\mathrm{Re}=\frac{\rho H^n{\left(uh\right)}^{2-n}}{m}and\mathrm{Rew}=\frac{\rho H^n{\left(\mathrm{\Omega }R\right)}^{2-n}}{m}$$

(8)

2.3. TEG Domain Equations

In the TEG domain, the coupled electric field and thermal field equations are used, and they are given as:

$$\nabla ·J=0,E=\rho J+\alpha \nabla T,q=\mathrm{\Pi }J-k\nabla T.$$

(9)

where the current density, Peltier coefficient and heat flux are denoted by the terms $J,\mathrm{\Pi }$ and q. In addition to that, the following relations are given as:

$$\mathrm{\Pi }=\alpha T,J=\sigma \left(E-\alpha \nabla T\right),E=-\nabla V.$$

(10)

In the solid domain, the energy equations is given as [76]:

$$\nabla \left(k\nabla T\right)+\frac{J^2}{\sigma }-TJ·\nabla \alpha =0$$

(11)

Thermal energy conversion into electrical energy is achieved the TEG device, and the Seebeck coefficient ($\alpha$) and figure of merit (ZT) are described as:

$$\alpha =-\frac{\Delta V}{\Delta T}\left(\mathrm{V}/\mathrm{K}\right),\mathrm{ZT}=\frac{{\alpha }^2\sigma }{k}T.$$

(12)

where k and $\sigma$ are the thermal conductivity and electrical conductivity. The TEG device has 80 legs, and the material properties are given in Ref. [54].

2.4. Boundary Conditions

At the inlet of the VC, the velocity and temperature are uniform with values of uh and Th. The walls of the VC are are adiabatic ($\frac{\partial T}{\partial n}=0$). The cylinder is rotating with a speed of $\mathrm{\Omega }$. On the walls of the cylinder, the y and z velocity components are $v=-\mathrm{\Omega }(z-zc)$ and $w=\mathrm{\Omega }(y-yc)$. Electrical insulation ($n·J=0$) is used at the surfaces of solid parts (except for the ceramics). Zero electrical potential ($V=0$) is utilized at the ground, while, at the terminal, the current is zero. The external surfaces of the TEG device are exposed to convection at the ambient temperature.

2.5. Optimization

The optimization procedure is used to find the optimal location and size of the cylinder to achieve the highest generated power from the TEG device.

The analyzed system is parametrized while control variables are used, and function of the PDE solution is attained in the PDE constraint optimization. The objective function is the generated output power from the device. In the general optimization, the PDE problem is considered as an equality constraint by using the control variables ($\psi$) and constraints (G) as [77,78]:

$$\begin{array}{cccc}\hfill & \underset{\psi }{\mathrm{minimize}}\hfill & \hfill & \mathrm{f}\left(\mathrm{\Phi }\right(\psi ),\psi )\hfill \\ \hfill & \mathrm{subject}\mathrm{to}\hfill & \hfill & \zeta \left(\mathrm{\Phi }\right(\psi ),\psi ))=0,\hfill \\ \hfill & \hfill & & lb\le G\left(\mathrm{\Phi }\right(\psi ),\psi ))\le ub\hfill \end{array}$$

(13)

where $\mathrm{\Phi }$ denotes the PDE solutions, and the bounds (lower and upper) are denoted by $lb$ and $ub$. The COBYLA (Constrained Optimization BY Linear Approximations) optimization procedure is used, which is a gradient-free method that performs better with lower numbers of variables. Interpolation at the vertices of a simplex is performed inside a trust region. More details about the optimization procedure can be found in Ref. [77]. The lower and upper bounds are given as $-3000\le \mathrm{Rew}\le 3000$, $0.06\mathrm{Hm}\le R\le 0.18\mathrm{Hm}$, $0.35\le Yp\le 0.65$ and $0.35\le Zp\le 0.65$. The optimum conditions are searched for NF1 and NF2 for the highest power generation of the TEG.

2.6. Solver

The Galerkin-weighted residual finite element method (FEM) is used. The foundations and basic procedures of FEM formulation for heat transfer and fluid flow problems are given the references [79,80,81,82]. The FEM applications of TEG-integrated systems have been considered in various studies [83,84,85,86]. In the formulation, approximated field variables ($\mathrm{\Gamma }$) are given as:

$$\mathrm{\Gamma }=\sum _{m=1}^{N^s}{\mathrm{\Phi }}_m^s{\gamma }_m$$

(14)

where ${\mathrm{\Phi }}^s$ and $\gamma$ are the shape function and nodal value, while $N^s$ denotes the number of modes. The Lagrange FEM of various orders is considered. When they are used in the governing equations, a residual is formed, and the weighted average of it is forced to zero. To handle the local numerical instabilities, the SUPG (streamline upwind Petrov–Galerkin) method is used, and the BICGStab (biconjugate gradient stabilized method) is considered for the fluid flow and HT modules of the solver. Convergence of the solution is achieved for the convergence criterion of ${10}^{-7}$.

2.7. Grid Independence and Code Validation

Tests for grid independence of the solution are conducted. Figure 2a shows the test results for the generated power (PW with units in W) at two different Rew when using NF1 considering different grid sizes. A grid system gr-5 with a 3980431 number of elements is selected. The grid distribution of gr-5 system is shown in Figure 2b, and the grid is fine near the walls and at the interfaces.

Two different validation test cases are considered. In the first work, the numerical results of Khandelwal et al. [87] were used. In the study, the flow separation characteristics of a T channel were explored using shear thinning fluid. In Ref. [87], the authors developed a correlation for the dimensionless recirculation length with respect to changes in the Reynolds number and power-law index, and an exponential form of the correlation was used.

Figure 3 shows the comparison results of the normalized reattachment length for different power law indices at Re = 100. The maximum difference between the results was obtained as $5\%$ for n = 0.2. The second validation test case was performed for the convective HT in a cavity with ventilation ports, while the results of Saeidi and Khodadadi [1] were used. The configuration corresponds to case where the outlet port is located at the middle of the bottom wall, and the port size is taken as W = 0.25 (non-dimensionalized using the cavity height).

Figure 4 shows the variation of average Nu versus Re comparisons. The overall agreement between the results is adequate, and the highest deviation below 3% is obtained.

3. Results and Discussion

Performance optimization a TEG device using shear thinning nanofluid and a rotating cylinder in a vented cavity is performed. A rotating circular cylinder is located in the vented cavity, and a rotational Re number (Rew) is considered between −3000 and 3000. Two different fluids (shear thinning nanofluids-NF1 and NF2) are considered, and the solid volume faction and power law index of NF1 are (0.005, 0.88) and (0.045, 0.5) for NF2.

The size of the rotating object (R) is taken between 0.06 and 0.18 Hm, while locations of the object (Yp, Zp) are considered between (0.35, 0.35) and (0.65, 0.65). First, parametric CFD is used to see the trends in power characteristics of TEG with varying parameters. Then, the optimization algorithm is invoked to find the best location and size of the rotating object to deliver the highest power. The cases are also compared with a no-object configuration.

Figure 5 shows the impacts of the rotational Re number (Rew) on the flow pattern variations in the mid-plane of the 3D cavity when NF1 Figure 5a–c and NF2 Figure 5d–f are used. In the case of stationary object with NF1, a vortex is seen in the left upper part of the cylinder. When rotations are activated, at Rew = −3000 (CCW rotations), the upper vortex moves toward the right, while vortices appear near the lower part of the cylinder.

For CW rotation at Rew = 3000, the fluid is accelerated near the cylinder, and the vortices established in the previous cases disappeared. When NF2 is used, at Rew = 0, the main flow stream is directed toward the exit of the second port on the right. In this case, the fluid velocity is lower at the same Re value for NF2 and the cylinder acts as a barrier for the second flow stream to the first exit on the left. For CW directional rotation with NF2, the fluid stream from the inlet is directed toward the first and second exit ports under the cylinder with rotations since the fluid velocity is lower.

The variations in the FP distributions near the TEG device with cylinder rotations have influences on the variations of interface temperatures (ITs) in the x and y directions as shown in Figure 6. Compared to the motionless object case (Rew = 0), the temperature is higher in both directions at Rew = 3000 when the cylinder is rotating in the CCW direction. In this case, the hot fluid stream has more contact with the interface of the TEG, and the fluid velocity is higher. However, significant reductions in the IT are seen when the cylinder is rotating in the CW direction at the highest speed. This is due to the counter effects of rotation on the fluid stream movement toward the interface.

Generated power features versus the rotational Re number for different sizes and different shear thinning nanofluids are shown in Figure 7. As compared to the case with a cylinder size of R = 0.06 Hm, the configuration with a size of R = 0.18 Hm is significant regarding the power generation features when using NF1 and NF2. When NF1 is used, the generated power rises with higher values of Rew in the CCW direction (positive Rew), and the trend is the opposite for negative values of Rew. There is a 49% increase in the TEG power when the cases of lowest and highest rotational Re numbers are compared for NF1.

The amount of power reduction is obtained as 30% when a case for CW rotation at the highest speed is compared with the motionless cylinder configuration. A cylinder with a smaller size of R = 0.06 Hm has slight impacts of the power generation. The power characteristics are different with varying rotational velocity when NF2 is considered. In this case, since the fluid velocity is lower when rotations are activated, the impacts of rotation on the fluid stream movement toward the interface become important. Depending upon the rotational direction, the fluid stream goes from the bottom and top part of the cylinder to the exit and is spread over the TEG interface, which results in enhanced powers.

Even though the generated powers are lower in the case of NF1, the rise in the power becomes 76.3% and 103.2% when the motionless cylinder case is compared with activated rotation cases at Rew = −3000 and Rew = 3000 with using NF2. A comparison between the power features using NF1 and NF2 with varying Rew is considered in Figure 7c. The power is higher when using NF1 due to the increased fluid stream velocity and enhanced thermal transport.

The discrepancy between the generated powers of different nanofluids becomes the highest when the cylinder is not rotating, which is obtained as 68.5%. It is the lowest for CW rotation at Rew = −3000, which is calculated as 19%. This is attributed to the lower powers for NF1 and higher power features with NF2 with negative values of Rew. For CCW rotation at Rew = 3000, the amount of variation becomes 39%.

The locations of the object on the FP distribution in the mid-axis are shown in Figure 8 for NF1 at Rew = −3000 Figure 8a–c, for NF1 at Rew = 0 Figure 8d–f, for NF2 at Rew = −3000 Figure 8g–i and for NF2 at Rew = 0 Figure 8j–l. The position of the cylinder within the cavity is highly influential on the flow pattern variations. When rotations are not active for NF1, the vortex is formed on the upper part of the cylinder at (0.35, 0.35), while the fluid stream toward the left exit port is largely blocked at the location of (0.65, 0.65). When CCW rotations are activated for NF1, vortex formation appears near the right and upper part of the cylinder for the locations (0.35, 0.35) and (0.5, 0.5).

The fluid velocity is lower for NF2, while the partition of the main fluid stream for NF2 is apparent with the rotation of the cylinder. Figure 9 shows the generated power characteristics with different locations of the cylinder and rotational speeds for NF1 and NF2. When NF1 is considered, the highest powers are achieved at the locations (0.35, 0.35), (0.5, 0.5) and (0.5, 0.65) for rotational Re numbers of −3000, 0 and 3000, respectively.

However, the variations in the generated power with varying locations of the cylinder become 44.3%, 41.6% and 19% for these rotational speeds. When NF2 is used, the characteristics become different when compared to using NF1. The highest power is achieved at locations (0.65, 0.65) and (0.5, 0.65) for Rew = −3000 and Rew = 3000. Up to 61% variation in the generated power is obtained with a varying cylinder location when NF2 is utilized.

As seen, the generated power features with varying parameters of interest show non-monotonic behavior, and obtaining the best configuration in terms of higher power generation cannot be realized with parametric CFD. Therefore, optimization is needed to find the best location, size and rotational speed combination in order to have the maximum power from the device. Optimization studies are performed for configurations where NF 1and NF2 are used as the HT fluid.

Figure 10 shows the search for the maximum of the power with varying parameters obtained by utilizing the COBYLA algorithm. The optimum cases are obtained as (Rew, R, Yp, Zp) = (3000, 0.3 Hm, 0.479, 0.65) and (Rew, R, Yp, Zp) = (3000, 0.3 Hm, 0.49, 0.65) for NF1 and NF2, and the generated powers at those cases are calculated as 0.3328 and 0.2488. Figure 11 shows the comparison results of the flow pattern distributions between the optimum case and no-object case when NF1 and NF2 are used. The presence of the cylinder in the cavity at the optimum case affects the flow pattern variations in the cavity and near the TEG device when compared to the no-object case.

A vortex near the left corner is established for the case without a cylinder with NF2, and the rotations of the cylinder become effective in distributing the hot fluid stream over the TEG interface at the optimum. The flow features show similar trends except for the location of the rotating cylinder when NF1 is used. However, the acceleration of the fluid stream toward the interface with rotation is apparent for NF1. Figure 12 shows the variations of the IT between the optimum and no-object case in the y and z directions.

The trends in the curves are similar. The optimum case delivers higher temperatures, and the power generation will be higher. The amounts of the power increase at the optimum when compared to the no-object configuration become 11.5% and 161% for the NF1 and NF2 cases. Particularly for NF2, the amount of increment is substantial, while the flow directional movement is best accomplished using the rotating cylinder at the optimum configuration.

The advantage of using optimization for obtaining the best TEG performance is also compared with the parametric CFD simulation results. Figure 13 shows the comparison results for the enhancement (Enh) of the generated power in percentage when the no-object case is considered when NF1 and NF2 are used. For NF1, by installing a cylinder with CCW rotation (positive Rew), enhancements up to 4.5% are achieved with parametric CFD at the highest speed. However, when optimum solutions are used, the value is 6.5% higher with the parametric CFD value at this speed, which gives a 10.9% rise of the power with installed CFD when compared to the no-cylinder configuration.

In the case of CW rotation (negative values of Rew), installation of the cylinder is not advantageous, and the generated power reduces by about 46.6% at Rew = −3000 when the no-object case is compared. When the optimum case is considered using NF1, the power rises by about 11.5% when compared to the no-object case. Both CW and CCW rotations of the cylinder produce higher power outputs when NF2 is used. However, the optimum conditions produce more TEG power when compared to the parametric CFD, which are 41% and 18.5% at Rew = −3000 and Rew = 3000. Figure 14 shows the power generation enhancements with various locations of the cylinder in the parametric CFD configuration when compared to optimum cases using NF1 and NF2. The enhancements are significant especially when using the second nanofluid NF2 when the locations are varied at Rew = 0.

When NF1 is used, the impacts of the location at Yp = 0.65 seem to be significant at Re = 0 and Rew = 3000. These results show that significant variations in the generated power are obtained when the parametric CFD are compared with the optimum case, while using a rotating object in the ventilated cavity becomes advantageous when optimization algorithms are used along with the CFD simulations. Considering the computational cost of the fully coupled system of a 3D vented cavity with TEG, the importance of using optimization becomes apparent.

4. Conclusions

CFD simulation and optimization for the performance improvement of a TEG-installed cavity with multiple ports were conduced using an inner rotating cylinder and shear thinning nanofluid. The following conclusions were obtained:

• For higher values of Rew, more power was generated when NF1 was used, while 49% enhancement in the power was obtained when cases with the lowest and highest Rew were compared.
• The power generation features with varying Rew were different when using NF2. In this case, the power increased by about 76.3% and 103.2% at Rew = −3000 and Rew = 3000 in comparison to the motionless cylinder case at Rew = 0.
• The generated power difference of nanofluids NF1 and NF2 was the maximum at Rew = 0, which was calculated as 68.5%.
• The power characteristics behaved differently when NF1 and NF2 were compared. When the location of the cylinder was changed, up to 61% variation in the power generation was obtained.
• The optimum configurations were achieved as (Rew, R, Yp, Zp) = (3000, 0.3 Hm, 0.479, 0.65) for NF1 and (Rew, R, Yp, Zp) = (3000, 0.3 Hm, 0.49, 0.65) for NF2.
• When the optimum case was considered, the generated power was 11.5% higher for NF1 and 161% higher for NF2 in the no-object case.
• Profound variations in the output power were observed when the optimum configuration was compared with parametric CFD. By using the optimization, installing a rotating object in the vented cavity became advantageous for the power increase of the TEG-installed system when both shear thinning nanofluids were used.
• The computational cost of the high-fidelity coupled system was significantly reduced when optimization was used instead of parametric CFD.