# The Impact of Cavities in Different Thermal Applications of Nanofluids: A Review

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_{2}Research Center, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Malaysia

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## Abstract

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## 1. Introduction

#### 1.1. Buongiorno Nanofluid Model

- The flow is incompressible;
- There is no chemical reaction between them;
- The effect of external force is neglected;
- The dilute mixture is less than one;
- There is no effect of viscous dissipation;
- No consideration is given to radiative heat transfer;
- Local thermal equilibrium between nanoparticles and clear fluid.

#### 1.2. Tiwari and Das Nanofluid Model

- The fluid is laminar, Newtonian, incompressible, and unsteady.
- The nanoparticles are considered to have a homogeneous shape and size.
- The fluid phase and nanoparticles are thermally balanced and flow at the same rate.
- In comparison to other types of heat transmission, radiation heat transfer between sides is insignificant.
- Excluding for the density changes in the buoyancy force, which is dependent on the Boussinesq approximation, the thermophysical parameters of the nanofluid are considered to remain constant.

## 2. The Role of Cavities in Nanofluid Transport

_{2}O

_{3}nanofluid in a rectangular enclosure heated from below. Solomon et al. [39,40] investigated the effect of the cavity aspect ratio on natural convection. Iachachene et al. [41] conducted a numerical study on melting paraffin wax embedded in a trapezoidal cavity using the enthalpy–porosity technique. Bairi [42] investigated the nanofluid transport in a porous hemisphere filled with a ZnO–H

_{2}O nanofluid. Heris et al. [43] thoroughly investigated the impact of using three different turbine oil-based nanofluids in a cubic cavity with Al

_{2}O

_{3}, TiO

_{2}, and CuO nanoparticles on flow structures and energy transfer.

#### 2.1. Effect of the Nanoparticle Concentration in Cavities

#### 2.2. Effect of the Nanoparticles in Cavities

#### 2.3. Effect of the Cavities’ Inclination Angle

#### 2.4. Effect of the Heater and Cooler Inside Cavities

#### 2.5. Effect of the Magnetic Field in Cavities

_{3}O

_{4}are introduced into the mixture, there is an increase in the temperature gradient. This increase can be seen to be more noticeable when there is also a magnetic field within the vicinity. When the system is operating in a conduction mode, the addition of Fe

_{3}O

_{4}has a significant impact on the thermal conductivity of the system. Therefore, an increase in the Lorentz force results in an increase in the rate of heat transfer. However, the opposite is true when it comes to the buoyancy force; an increase in the buoyancy force results in a decrease in the rate of heat transfer. It indicates that the impact of adding nanoparticles to a base fluid will decrease as the strength of the convective heat transfer increases. This is because the convective heat transfer will become stronger as time goes on.

_{2}O

_{3}–water nanofluid on laminar natural convection heat transfer was investigated while a magnetic field was present in an open cavity. The heat-transfer mechanism under study was natural convection. It causes the heat transfer to become more efficient by increasing the volume fraction in several different Hartmann numbers, which in turn causes the heat transfer to become more effective. In addition, it makes perfect sense that nanoparticles would have a further significant influence on the isotherm at the value of 104 in the direction of pure fluid at the value of 0. The isotherms of the nanofluid and the fluid perfectly overlap each other at the open boundary, but as they move closer to the hot wall, they start to move further and further apart from each other. Because of this, the effect of the nanoparticle is negligible at the open boundary partition; however, the effect gradually increases as the fluid moves inside the enclosure. In addition, an increase in the Hartmann number causes a decrease in the maximum value of the stream function, while the rate at which this occurs varies depending on the Rayleigh number. This is because the maximum value of the stream function is proportional to the Hartmann number. As an illustration, when going from Ha = 0 to 30, the values of the maximum stream function decrease by 63%, 41%, and 29%, respectively. The Rayleigh numbers Ra = 10

^{4}, 10

^{5}, and 10

^{6}correspond, respectively, to these percentages. Because of this, the influence of the magnetic field on the circulation of the fluid loses some of its significance as the Rayleigh number increases. The effect of nanoparticles on streamlines becomes abundantly clear when the values of the maximum stream function and the motivation of streamlines both increase for varying Hartmann and Rayleigh numbers. As a direct consequence of this, the presence of nanoparticles in an open enclosure has the effect of enhancing the buoyancy-driven circulations within the space. In addition, nanoparticles of varying Hartmann and Rayleigh numbers exhibit a wide range of behaviors on the streamlines due to the erratic manner in which they raise the maximum stream function.

_{3}O

_{4}nanoparticles, researchers [72] investigate how the influence of Lorentz forces will affect ferrofluid-free convection when there is thermal radiation present in a tilted cavity. This is tested in order to determine how the influence of Lorentz forces will affect ferrofluid-free convection. The rate of heat transfer is positively influenced by the effect that the radiation parameter has on the nanofluid. This effect’s significance is heightened when a magnetic field is present in the system. Ghalambaz et al. [73] studied the effect of a changing magnetic field on the heat transfer of a nanofluid made of Fe

_{3}O

_{4}and water. They carried out their work in a half annulus cavity.

^{3}, 10

^{4}, and 10

^{5}), a wide range of Rayleigh Hartmann numbers (Ha = 0, 20, 40, and 60), and dimensionless heat generation or absorption (q = 10, 5, 0, 5, and 10) were computed. When the Hartmann number increases (Ha = 20, 40, and 60), the Lorentz force, which is generated as a result of the magnetic field effect, becomes higher than the buoyancy force. This is because the magnetic field effect generates the Lorentz force. This results in a reduction in the intensity of the flow circulation, which, in turn, causes the convection effect to start becoming less effective. As the Hartmann number increases, the cell center will move deeper and deeper into the cavity until it reaches its lowest point. This will continue until the cavity has reached its maximum depth.

^{3}, the effect of the Hartmann number on the isotherms is more pronounced than it is at an Ra value of 10

^{4}, which is the point at which the disparity between the two compared isotherms begins to grow noticeably. At a Reynolds number of 105, when the power of the convective flow begins to increase, the effect of the convective heat transfer begins to become more significant, and distinct boundary layers begin to form along the active wall of the cavity. These changes take place in the cavity. Because heat moves in this way, convective heat transfer is the most common way for heat to move from one place to another. In addition, the convection effects become more pronounced as the Rayleigh number increases, which causes the isotherms to become more warped. This occurs because the Rayleigh number is increasing. An increase in the Hartmann number on a global scale causes an increase in the Lorenz force, which ultimately results in a significant reduction in the convection that is occurring. When a magnetic field is applied, the temperature intensities of the fluid that is contained within the cavity decrease. This phenomenon is most pronounced at higher Rayleigh numbers.

_{2}O

_{3}, Fe

_{2}O

_{3}, Ag, TiO

_{2}, and Cu–Al

_{2}O

_{3}–water nanoparticles have previously been used in MHD convection studies (within a cavity). The presence of a magnetic field was found to increase the thermal and convective properties of magnetic nanofluids. However, more extensive experimental research in this area is required. There are many engineering and industrial uses for the effects of non-uniform temperature changes on square cavities. These uses include cooling nuclear reactors, the polymer and metallurgy industries, solar collectors, and other similar uses.

## 3. Effect of Cavities in Microchannel Heat Exchangers

_{2}O

_{3}and water. Malekshah et al. [118] conducted research on the convective flow that occurs in overheat-dispersing fins. The active fins, which serve as heat sinks, are the primary application of the current problem. This application can be found in the process of cooling an electronic package. In terms of thermal performance, the taller fins are superior to the wider fins in terms of efficiency and effectiveness. Because of the favorable impact that nanofluid has on cooling performance, the use of this substance in electronic packaging for cooling purposes is strongly encouraged.

## 4. Effect of Cavities in Solar Collectors

_{2}-based nanofluids as the concentrating solar power system’s working fluid. Thermal parameters of the nanofluid, such as isobaric specific heat and thermal conductivity, were considered. They discovered that using the TiO2-based nanofluid instead of the base fluid enhanced the thermal efficiency of the concentrating systems by up to 35%. Ref. [139] investigated the effect of several nanofluids as the heat transfer fluid in concentrating solar power systems. They discovered a variety of nanoparticles, including Cu, Ag, and Ni. The results showed that the thermal properties of nanofluids based on Cu and Ag increased, whereas the thermal characteristics of nanofluids based on Ni decreased.

## 5. Future Recommendations

- The internal nanofluids’ ability to generate heat convection and entropy depends on the cavity’s aspect ratio, so it is suggested that more research be focused on using inclined shape cavities in artificial neural networks.
- According to the literature, it is observed that the size of nanoparticles is very important in improving the heat-transfer rate; for smaller sizes, greater heat transfer is attained. After reviewing the many research articles it is recommended that a size of nanoparticles between 10 and 50 nm is more stable in base fluids in cavities at the specified temperature gradient. As a result, the most significant heat transmission may be obtained by making the diameter of the nanoparticles smaller in the cavity. It is suggested that research should focus on different shapes of nanoparticles smaller than 10 nm, with the same design of cavities in microchannel heat exchangers and solar collectors to improve performance.
- In the literature, it is reported that microchannel heat exchangers with circular cavities provide the highest performance. Even though circular cavities provide the best performance in micro heat exchangers, microchannel heat exchangers with square cavities have more applications in related industries, so different shapes of cavities, such as cubical, hexagonal, and conical, should be used in micro heat exchangers in the future.
- In solar collectors, different cavities such as square, rectangular, and triangular cavities are used, and the best results are observed with the use of these cavities, but there is less research focused on conical, hexa-conical, and other novel optimal cavity geometries, so it is recommended that in future research, more focus be given to these types of geometries.

## 6. Conclusions

- (a)
- In heat exchangers and solar collectors, the use of a specific shape and design of the cavity provides better results. The shape of the cavities depends on how they will be used, so it is important for thermal systems to have the right cavities.
- (b)
- In the literature, it is reported that L-shaped cavities are used in the cooling systems of nuclear, chemical, and electronic components and give suitable results.
- (c)
- It has been seen that the size of the channels in heat exchangers changes depending on what they are used for. In land-based systems, the smaller the channel, the better the results. This is because the smaller the channel, the smaller the hydraulic diameter, which is what makes the heat transfer work so well. This causes a big drop in pressure. When figuring out how to use microchannel heat exchangers in space, we can make the channels bigger to make them more effective. This is because the pressure drop across the system needs to be kept as low as possible to obtain the best heat-transfer rate.
- (d)
- Different shapes of cavities including square, circular, trapezoidal, rectangular, and others are used in microchannel heat exchangers. From the literature, it is observed that the circular cavities provide the best performance because they provide a high heat-transfer rate with low pumping power and are most efficient at low Reynolds numbers.
- (e)
- The use of nanofluids has been found to improve thermal performance in all the cavities studied. According to the experimental data, nanofluid use has been proven to be a dependable solution for enhancing thermal efficiency. The average thermal efficiency improvement using nanofluids is 12.90% for the hemispherical cavity, 5.84% for the cubical cavity, and 1.44% for the cylindrical cavity.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\mathrm{Ra}$ | Rayleigh number |

$\mathrm{Be}$ | Bejan number |

${\mathrm{K}}_{\mathrm{r}}$ | Thermal conductivity ratio of solid wall to pure fluid |

$\mathrm{v}$ | Velocity |

$\mathsf{\phi}$ | Nanoparticle volume fraction |

$\mathsf{\rho}$ | Density of the fluid |

$\mathrm{T}$ | Temperature of the fluid |

$\mathsf{\tau}$ | Stress tensor |

${\mathrm{D}}_{\mathrm{B}}$ | Brownian diffusion coefficient |

${\mathrm{D}}_{\mathrm{T}}$ | Thermal diffusion coefficient |

$\mathrm{p}$ | Pressure |

$\mathrm{c}$ | Specific heat |

$\mathrm{k}$ | Thermal conductivity |

${\mathsf{\rho}}_{\mathrm{p}}$ | Density of the nanoparticles |

${\mathrm{c}}_{\mathrm{p}}$ | Nanoparticle specific heat |

$\mathrm{t}$ | Time |

$\mathsf{\mu}$ | Dynamic viscosity |

${\mathrm{d}}_{\mathrm{p}}$ | Nanoparticle diameter |

$\mathsf{\beta}$ | Volumetric thermal expansion coefficient |

${\mathrm{k}}_{\mathrm{B}}$ | Boltzmann’s constant |

${\nabla}^{2}$ | Laplacian operator |

$\mathrm{y}$ | Rectangular coordinate |

${\mathsf{\epsilon}}_{\mathrm{p}}$ | Momentum eddy diffusivity |

${\mathsf{\epsilon}}_{\mathrm{M}}$ | Energy eddy diffusivity |

${\mathsf{\epsilon}}_{\mathrm{H}}$ | Particle eddy diffusivity |

$\mathrm{f}$ | Friction factor |

$\mathrm{Re}$ | Reynolds number |

$\mathrm{Pr}$ | Prandtl number |

${\mathsf{\delta}}_{\mathrm{v}}$ | Laminar sublayer |

$\mathrm{Nu}$ | Nusselt number |

${\mathrm{Nu}}_{\mathrm{tot}}^{-}$ | Average total Nusselt number |

$\mathrm{D}$ | Solid block |

$\mathrm{Ri}$ | Richardson number |

$\mathrm{Ha}$ | Hartmann number |

$\mathrm{R}$ | Radius of the cylinder |

$\mathrm{Np}$ | Nanoparticle |

$\mathrm{Le}$ | Lewis number |

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**Figure 3.**Impact of different aspect ratios on cavities [39].

Ref. | Cavity Geometry | Nanoparticles and Their Size (nm) | Concentration of Nanoparticles | Cavity Inclination Angle | Results |
---|---|---|---|---|---|

[25] | Square | Fe_{3}O_{4}, Ha = 0–10 | $\mathsf{\Phi}$= 0.01–0.04% | - | Heat transfer increases with the increase in Lorentz force effect. |

[26] | L-shaped | Ag | $\mathsf{\Phi}$ = 0.06% | 0, 30, 60, 90 | The inclination angle has a direct correlation to the amount of heat transferred. |

[27] | Isosceles Triangular | Al_{2}O_{3}, d_{p} = 10 nm,Ha = 0, 25, 50 | $\mathsf{\Phi}$ = 0.06% | $\frac{\pi}{12}$ | As Ha and the angle of inclination of the magnetic field went up, the rate of heat transfer went down. |

[28] | Closed elbow-shaped | Cu | $\mathsf{\Phi}$ = 0–0.06% | - | Heat transfer increases due to high nanoparticle volume fraction. |

[29] | Trapezoidal | CuO Ha = 0, 10, 50, 100 d _{p} = 29 nmthe angle inclination of magnetic field = 0–$\pi $ | $\mathsf{\Phi}$ = 0–0.04% | - | The heat transmission rate drops as $\mathrm{Ha}$ rises and increases with a high nanoparticle volume fraction. |

[30] | Shallow | Al_{2}O_{3}, d_{p} = 10 nm | $\mathsf{\Phi}$ = 0–0.04% | - | Radiative heat transfer mixed with natural convection may impact the flow field and cause the rise in Nusselt number (Nu). Thermal radiation research is highly beneficial in the enrichment of heat-transfer rate. |

[31] | Wavy-walled | Al_{2}O_{3} | $\mathsf{\Phi}$ = 0–0.04% | $0\u2013\pi $/2 | Inclination angle and undulation number are non-monotonic functions of heat transmission and fluid flow. |

[32] | Open wavy | - | - | - | The average Nusselt and Sherwood values can continuously be improved using wavy surface design parameters. |

[33] | Porous wavy | - | - | - | Localized heat source affects nanofluid flow and heat transmission rate. |

[34] | Vented | CuO, Ha = 0 and 40 d _{p} = 29 nm, the magnetic field inclination angle = 0–$\pi $/2 | $\mathsf{\Phi}$ = 0–0.03% | - | In the absence of MHD effect, the nanoparticles increase heat transfer up to 9–9.5%. |

[35] | Inclined wavy | CuO, Ha= 0–100, the angle inclination of magnetic field = 0–$\pi $ | $\mathsf{\Phi}$ = 0–0.05% | $0\u2013\pi $ | Changing cavity inclination angle affects convective heat transfer. Heat transmission rate increases with nanoparticle volume fraction. |

[36] | Circular | MWCNT-Fe_{3}O_{4}/H_{2}O, Ha = 0–50 | $\mathsf{\Phi}$ = 0–0.03% | - | Convective heat transfer is enhanced by ejecting ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}-\mathrm{MWCNT}$ hybrid nanoparticles into the host fluid. |

[37] | Square | Copper | $\mathsf{\Phi}$ = 0–0.03% | - | Heat-transfer rate decreases with increasing solid volume fraction for a given Ra, but increases with increasing nanoparticle volume fraction. |

[38] | Rectangular | Al_{2}O_{3} | $\mathsf{\Phi}$ = 0.0–0.05% | - | Al_{2}O_{3}/H_{2}O nanofluids are morestable than ordinary fluids in a heated rectangular chamber. |

[39] | Rectangular | Al_{2}O_{3} | - | - | Aspect ratio affects heat transfer coefficient and Nusselt number. |

[40] | Porous square | Al_{2}O_{3}, d_{p} = 30 nm | $\mathsf{\Phi}$ = 0.05–0.4% | - | The porous cavity increases the 10% heat-transfer rate with a 0.05% concentration of nanofluid volume fraction. |

[41] | Trapezoidal | Paraffin wax, Graphine | Φ = 0.05 | - | Rearranging the direction of the trapezoidal cavity resulted in higher melting. |

[42] | Hemispherical | Water-ZnO | - | - | The nanofluid saturated in the porous media improves natural convective heat transfer for the given problem. |

[43] | Inclined cube | Al_{2}O_{3}, TiO_{2}, CuO | - | 0, 45, 90 | Compared to the nanofluids, turbine oil has the maximum Nu anywhere at the inclination angle of the cavity. |

Ref. | Numerical Method | Material of Nanoparticles | Range of Ra | Range of Le | Size of Nanoparticles | Nanoparticle Volume Fraction | Inclination Angle of Cavity/Magnetic Field | Range of Pr |
---|---|---|---|---|---|---|---|---|

[44] | FVM | Al_{2}O_{3} | ${10}^{2}\le \mathrm{Ra}\le {10}^{6}$ | $2.62\times {10}^{5}\le \mathrm{Le}\le 1.05\times {10}^{6}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | $0\xb0\le \theta \le 60\xb0$ | 4.623 |

[45] | FEM | Al_{2}O_{3} | - | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[46] | FDM | Al_{2}O_{3} | ${10}^{2}\le \mathrm{Ra}\le {10}^{6}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[47] | FEM | Al_{2}O_{3} | ${10}^{3}\le \mathrm{Ra}\le {10}^{6}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[48] | FDM | - | ${10}^{3}\le \mathrm{Ra}\le {10}^{6}$ | 1000 | - | - | - | 7.0 |

[49] | FVM | Cu, Al_{2}O_{3}, TiO_{2} | ${10}^{4}\le \mathrm{Ra}\le {10}^{7}$ | - | $25\mathrm{nm}\le {\mathrm{d}}_{\mathrm{p}}\le 145\mathrm{nm}$ | $0.01\le \mathsf{\phi}\le 0.05$ | - | 4.623 |

[50] | FEM | Al_{2}O_{3} | ${10}^{4}\le \mathrm{Ra}\le {10}^{7}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[51] | FEM | Al_{2}O_{3} | ${10}^{2}\le \mathrm{Ra}\le {10}^{6}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[52] | FEM | Al_{2}O_{3} | ${10}^{3}\le \mathrm{Ra}\le {10}^{6}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[53] | FDM | Al_{2}O_{3} | $\mathrm{Ra}={10}^{5}$ | 15,267.8 | 47 nm | $0.01\le \mathsf{\phi}\le 0.05$ | $0\xb0\le \theta \le 150\xb0$ | 6.51 |

[54] | FEM | Al_{2}O_{3} | - | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.05$ | - | 4.623 |

[55] | FDM | CuO | ${10}^{4}\le \mathrm{Ra}\le {10}^{6}$ | 9460.61 | 29 nm | $0\le \mathsf{\phi}\le 0.09$ | - | 6.53 |

[56] | FDM | Al_{2}O_{3} | ${10}^{2}\le \mathrm{Ra}\le {10}^{6}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | 45° | 4.623 |

[57] | FDM | Al_{2}O_{3} | ${10}^{2}\le \mathrm{Ra}\le {10}^{6}$ | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | - | 4.623 |

[58] | FDM | - | ${10}^{4}\le \mathrm{Ra}\le {10}^{6}$ | 1000 | - | - | - | 6.82 |

[59] | LBM | CuO | ${10}^{3}\le \mathrm{Ra}\le {10}^{6}$ | - | - | $0.01\le \mathsf{\phi}\le 0.05$ | - | 6.2 |

[60] | FVM | Cu, Al_{2}O_{3}, TiO_{2} | ${10}^{4}\le \mathrm{Ra}\le {10}^{7}$ | - | $25\mathrm{nm}\le {\mathrm{d}}_{\mathrm{p}}\le 145\mathrm{nm}$ | $0.01\le \mathsf{\phi}\le 0.05$ | - | - |

[61] | FVM | Cu, Al_{2}O_{3}, TiO_{2} | ${10}^{3}\le \mathrm{Ra}\le {10}^{7}$ | - | $25\mathrm{nm}\le {\mathrm{d}}_{\mathrm{p}}\le 145\mathrm{nm}$ | $0.01\le \mathsf{\phi}\le 0.05$ | - | - |

[62] | FVM | - | - | $1\le \mathrm{Le}\le 10$ | - | - | $0\xb0\le \theta \le 270\xb0$ | $0.054\le \mathrm{Pr}\le 10$ |

[63] | SIMULATION | Al_{2}O_{3} | ${10}^{7}\le \mathrm{Ra}\le {10}^{9}$ | - | $50\mathrm{nm}\le {\mathrm{d}}_{\mathrm{p}}\le 150\mathrm{nm}$ | $0.01\le \mathsf{\phi}\le 0.03$ | - | $7.0022\le \mathrm{Pr}\le 7.3593$ |

[64] | Hybrid LBM & TVD | Al_{2}O_{3} | ${10}^{3}\le \mathrm{Ra}\le {10}^{5}$ | - | $25\mathrm{nm}\le {\mathrm{d}}_{\mathrm{p}}\le 150\mathrm{nm}$ | $0.01\le \mathsf{\phi}\le 0.04$ | - | - |

[65] | FDM | Carbon Nanotubes | $10\le \mathrm{Ra}\le 10$ | $1\le \mathrm{Le}\le 10$ | $0.01\le \mathsf{\phi}\le 0.05$ | - | - | |

[66] | FVM | CuO, Al_{2}O_{3}, TiO_{2} | - | - | $25\mathrm{nm}\le {\mathrm{d}}_{\mathrm{p}}\le 100\mathrm{nm}$ | $0.01\le \mathsf{\phi}\le 0.04$ | - | - |

[67] | FEM | - | ${10}^{4}\le \mathrm{Ra}\le {10}^{6}$ | - | - | - | - | 6.2 |

[68] | FEM | - | ${10}^{3}\le \mathrm{Ra}\le {10}^{6}$ | $10\le \mathrm{Le}\le 100$ | - | - | - | 6.2 |

[69] | FVM | - | $30\le \mathrm{Ra}\le 300$ | $1\le \mathrm{Le}\le 100$ | - | - | - | - |

[70] | FEM | Al_{2}O_{3} | - | $3.5\times {10}^{5}$ | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | 4.623 | |

[71] | FEM | - | $100\le \mathrm{Ra}\le 300$ | $1\le \mathrm{Le}\le 10$ | - | - | - | - |

[72] | FVM | Al_{2}O_{3}, CuO | ${10}^{2}\le \mathrm{Ra}\le {10}^{4}$ | - | 33 nm | $0.01\le \mathsf{\phi}\le 0.04$ | $0\xb0\le \theta \le 60\xb0$ | 10 |

[73] | FEM | - | 100 | 1000 | - | - | - | - |

[74] | FEM | - | 100 | 1000 | - | - | - | - |

Ref. | Cavities Geometry | Nanoparticles and Their Size (nm) | Hartmann Number | Cavity Inclination Angle | Results |
---|---|---|---|---|---|

[25] | Square | Fe_{3}O_{4} | Ha = 0–10 | Heat transfer increases with the increase in Lorentz force. | |

[77] | Finned | Cu | Ha = 0–50 | 0–90 | At 90 degrees highest heat transfer achieved and at 30 degrees lowest heat transfer achieved. |

[78] | Porous open | Cu, d_{p} = 29 nm | Ha = 0–60 | - | Heat transfer increases with increase in Darcy number. |

[79] | Open | Al_{2}O_{3} | Ha = 0–90 | - | $\mathrm{Ra}={10}^{4}$ has the largest particle effect at Ha = 30, and for Ra = ${10}^{5}$ at Ha = 60. |

[29] | Trapezoidal | CuO, d_{p} = 29 nm | Ha = 0, 10, 50, 100 | $0\u2013\pi $ | The heat transmission rate drops as $\mathrm{Ha}$ rises and increases with high nanoparticle volume fraction. |

[80] | U-shaped | Fe_{2}O_{3} | Ha = 0–30 | - | Influence of n and Ha on heat transport was studied. |

[81] | Irregular cavity | Fe_{2}O_{3}, d_{p} = 47 nm | Ha = 0–40 | $0\u2013\pi $/2 | Nusselt number rises with inclination angle, falls with Ha. |

[82] | Half-annulus | Fe_{3}O_{4} | Ha = 0, 20, 40, 80 | - | Due to Lorentz force from a greater magnetic field, low Eckert and Hartmann numbers decrease the Nusselt number. |

[83] | Rectangular | Cu | Ha = 0–60 | - | For Ha values between 9 and 12, the heat transmission is not affected by the concentration of nanoparticles. |

[34] | Vented | CuO, d_{p} = 29 nm | Ha = 0 and 40 | $0\u2013\pi $/2 | In the absence and presence of a magnetic field, nanoparticles increase heat transmission by 9–9.5%. |

[35] | Inclined wavy | CuO | Ha = 0–100 | $0\u2013\pi $ | Changing cavity tilt affects convective heat transmission. Heat transmission rate increases with nanoparticle volume fraction. |

[84] | Lid-driven | Cu | Ha = 0–50 | 0–90 | Average heat transmission increases 239.35% at Richardson number 100 vs. 1. |

[85] | Curved | Fe_{3}O_{4}, d_{p} = 47 nm | Ha = 0–60 | - | Temperature gradient reduces with enhancement of radiation influence. |

[86] | Rectangular | Cu | Ha = 0–100 | 0–90 | The average Nusselt number rises with magnetic field inclination. |

[87] | Hexagonal | Al_{2}O_{3} | Ha = 0–100 | - | The analysis shows improved convection, velocity, and thermal results for Rayleigh number, but the opposite for Hartmann number and nanoparticle concentration. |

[88] | Square | Ag | - | - | Silver nanoparticles dispersed in water increase heat transfer from 6.3% to 12.4%. |

[89] | Porous cavity | Cu, d_{p} = 47 nm | Ha = 0–40 | - | Radiation parameter increases heat transport, while Hartmann number decreases it. |

[90] | Porous lid-driven | Cu, d_{p} = 45 nm | Ha = 0–40 | - | Temperature gradient decreases with Ha and increases with Re. |

[91] | Ventilated cube | ZnO | Ha = 100 | 0, 45, 90, 235 | In a magnetic field, $\omega $ = 45° offers the best heat-transfer rate, whatever the Reynolds number. |

[92] | Square | TiO_{2} | - | - | Radiation parameter (R) increases heat transfer from hot wall to cold wall. |

[93] | Inclined square | Al_{2}O_{3}, d_{p} = 47 nm | Ha = 0–40 | - | Increasing Rayleigh and decreasing Hartmann increase the heat-transfer rate. For Hartmann number growing from 0 to 40, the Nusselt number drops up to 27%. |

[94] | Tilted triangular | Al_{2}O_{3}, d_{p} = 47 nm | Ha = 0, 20, 40 | 45 | The magnetic field angle does not affect heat transport, entropy generation, or Be. The 90-degree angle had the maximum transfer rate and entropy creation. |

[95] | Rectangular | Al_{2}O_{3}, d_{p} = 47 nm | Ha = 0, 30, 60 | 0–90 | Increasing the magnetic field angle decreases heat transfer and entropy formation and raises Bejan number. |

[96] | Trapezoidal | Carbon Nanotube (CNT) | Ha = 0–50 | - | Magnetic field effects limited effective convection, although CNT particles increased the average Nu value by 84.3%. |

[97] | Inclined | CuO, d_{p} = 29 nm | 0–50 | 0–90 | Increasing Hartmann number from 0 to 50 reduces Nusselt number by 32% and 34% for water and nanofluid, respectively. |

[98] | Inclined square | Al_{2}O_{3}, d_{p} = 47 nm | Ha = 0–40 | 0–90 | An increase in Ha lowered heat transport and entropy by 45% and 35%, respectively. |

[54] | Double lid-driven square | Al_{2}O_{3}, d_{p} = 33 nm | Ha = 0–50 | 45 | A rise in Reynolds number or reduction of Hartmann number can increase the heat-transfer rate. |

[99] | Wavy | Cu | Ha = 0–50 | 0–360 | Bejan number decreases when Hartmann number, irreversibility distribution ratio, and Richardson number rise. |

[100] | Cubic | Cu, Al_{2}O_{3}, TiO_{2} | - | - | The Bejan number decreases with a higher Hartmann number, larger irreversibility ratio, and lower Richardson number. |

[101] | Lid-driven | Au, SWCNT, d _{p} of Au= 50 nmd _{p} of SWCNT = 70 nm | Ha = 0–40 | - | Nanoparticles and nanofluid velocity affect heat-transfer efficiency. |

Ref. | Cavity Geometry | Results |
---|---|---|

[125] | Rectangular | $\mathrm{At}50\xb0$ the best performance was achieved. |

[126] | Triangular | $\mathrm{At}60\xb0$ the best performance was achieved. |

[127] | Triangular pyramid | Inclination improves triangular pyramid solar still by 79.05 percent. |

[128] | V-down ribs | Maximum heat-transfer rate is attained at roughness pitch at 45°. |

[129] | V-rib triangular | Ribbed triangular duct solar air heater ($45\xb0$) is superior over various configurations of the ribbed rectangular duct solar air heater at higher mass flow rate. |

[130] | Trapezoidal | Thermal stratification in the storage cavity affects energy savings. |

[131] | Trapezoidal | Stability deteriorates with the temperature gradient. |

[132] | Trapezoidal | The cavity was stable and convective. |

[133] | Trapezoidal | Round pipe (multi-tube) receivers absorb more solar radiation than rectangular pipe receivers. |

[134] | Circular | Circular geometry and vented absorber plates promote turbulence-induced heat transfer. |

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## Share and Cite

**MDPI and ACS Style**

Zafar, M.; Sakidin, H.; Sheremet, M.; Dzulkarnain, I.; Nazar, R.M.; Hussain, A.; Said, Z.; Afzal, F.; Al-Yaari, A.; Khan, M.S.;
et al. The Impact of Cavities in Different Thermal Applications of Nanofluids: A Review. *Nanomaterials* **2023**, *13*, 1131.
https://doi.org/10.3390/nano13061131

**AMA Style**

Zafar M, Sakidin H, Sheremet M, Dzulkarnain I, Nazar RM, Hussain A, Said Z, Afzal F, Al-Yaari A, Khan MS,
et al. The Impact of Cavities in Different Thermal Applications of Nanofluids: A Review. *Nanomaterials*. 2023; 13(6):1131.
https://doi.org/10.3390/nano13061131

**Chicago/Turabian Style**

Zafar, Mudasar, Hamzah Sakidin, Mikhail Sheremet, Iskandar Dzulkarnain, Roslinda Mohd Nazar, Abida Hussain, Zafar Said, Farkhanda Afzal, Abdullah Al-Yaari, Muhammad Saad Khan,
and et al. 2023. "The Impact of Cavities in Different Thermal Applications of Nanofluids: A Review" *Nanomaterials* 13, no. 6: 1131.
https://doi.org/10.3390/nano13061131