# Thermogravitational Convection of Hybrid Nanofluid in a Porous Chamber with a Central Heat-Conducting Body

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}O

_{3}-SiO

_{2}/H

_{2}O) in a porous space with a central heat-conducting body has been presented and numerical analysis has been performed. Governing equations, transformed in terms of non-dimensional parameters, have been solved by a developed numerical algorithm based on the finite difference technique. The behavior of streamlines and isotherms was investigated, and the impact of various important characteristics is discussed. The variation in the average and local Nusselt numbers was studied; by selecting various appropriate nano-sized particle combinations in hybrid nanosuspension, the desired energy transport strength could be obtained. The results were compared and successfully validated with previous reported numerical and experimental data from the literature.

## 1. Introduction

_{2}O

_{3}–Cu/water, Fe

_{3}O

_{4}–graphene, graphene, Al

_{2}O

_{3}–SiO

_{2}, etc. In the last few years, such hybrid nanosuspensions have been employed in different engineering and industrial applications, including heat exchangers, solar collectors, chemical reactors, heat sinks, air conditioning systems, and others. Comprehensive reviews of hybrid nanofluids have been presented by Devi and Devi [21,22], Sarkar et al. [23], Akilu et al. [24], Sidik et al. [25], Sundar et al. [26], Babu et al. [17], Hayat and Nadeem [27], Yousef et al. [28], Sajid and Ali [29], Chamkha et al. [30], Izadi et al. [31,32], Suresh et al. [33,34], Soltani and Akbari [35], Leong et al. [36], Waini et al. [37,38,39], and Aly and Pop [40].

## 2. Control Equations and Conditions

_{h}) and the right border was cold (T = T

_{c}). The thermal-conducting body was placed in the center of the region. The hybrid nanofluid included two kinds of solid nano-sized additives; their characteristics are demonstrated in Table 1. Heat equilibrium between the liquid phase and nano-sized particles was assumed.

- hybrid nanosuspension density, ${\rho}_{hnf}={\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\rho}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\rho}_{\mathrm{Si}{\mathrm{O}}_{2}}+\left(1-{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}-{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}\right){\rho}_{f}$
- hybrid nanofluid buoyancy coefficient$${\left(\rho \beta \right)}_{hnf}={\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\left(\rho \beta \right)}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\left(\rho \beta \right)}_{\mathrm{Si}{\mathrm{O}}_{2}}+\left(1-{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}-{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}\right){\left(\rho \beta \right)}_{f}$$
- hybrid nanofluid heat capacitance$${\left(\rho c\right)}_{hnf}={\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\left(\rho c\right)}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\left(\rho c\right)}_{\mathrm{Si}{\mathrm{O}}_{2}}+\left(1-{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}-{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}\right){\left(\rho c\right)}_{f}$$
- hybrid nanofluid thermal conductivity$$\begin{array}{c}\frac{{\lambda}_{hnf}}{{\lambda}_{f}}=\left\{\frac{{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\lambda}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\lambda}_{\mathrm{Si}{\mathrm{O}}_{2}}}{{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}}+2{\lambda}_{f}+2\left({\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\lambda}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\lambda}_{\mathrm{Si}{\mathrm{O}}_{2}}\right)-2\left({\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}\right){\lambda}_{f}\right\}\times \hfill \\ \times {\left\{\frac{{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\lambda}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\lambda}_{\mathrm{Si}{\mathrm{O}}_{2}}}{{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}}+2{\lambda}_{f}-\left({\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}{\lambda}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}{\lambda}_{\mathrm{Si}{\mathrm{O}}_{2}}\right)+\left({\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}\right){\lambda}_{f}\right\}}^{-1}\hfill \end{array}$$
- hybrid nanofluid viscosity$${\mu}_{hnf}={\mu}_{f}{\left(1-{\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}-{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}\right)}^{-2.5}$$
- porous medium thermal conductivity saturated with hybrid nanofluid$${\lambda}_{mhnf}=\epsilon {\lambda}_{hnf}+\left(1-\epsilon \right){\lambda}_{s}$$
- and porous medium heat capacity ratio$$\eta =\epsilon +\left(1-\epsilon \right)\frac{{\left(\rho c\right)}_{s}}{{\left(\rho c\right)}_{hnf}}$$

_{mhnf}/λ

_{b}is the thermal conductivity ratio and H

_{1}(ϕ), H

_{2}(ϕ), H

_{3}(ϕ,ε), H

_{4}are given by

## 3. Computational Technique and Validation

^{6}, P = 6.82, Da = 10

^{−3}, ε = 0.8, ${\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}={\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}=0.01$. Steel was the material of the internal block, and the dimensionless size of the internal block δ = 0.5. Three different grids of 100 × 100 points, 200 × 200 points, and 400 × 400 points were investigated. Figure 4 demonstrates the influence of the mesh characteristics on the time profiles of the mean Nusselt number of the heated border.

## 4. Results and Discussion

^{6}), Prandtl number (Pr = 6.82), Darcy number (Da = 10

^{−4}–10

^{−1}), porosity (ε = 0.8), nanoparticles’ volume fraction, and internal block material (${\varphi}_{\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}}+{\varphi}_{\mathrm{Si}{\mathrm{O}}_{2}}={\varphi}_{1}+{\varphi}_{2}=0.0-0.04$) (glass, steel, copper). The influence of these mentioned parameters on the hybrid nanofluid circulation and energy transference within the enclosure was tested. The isolines of ψ and θ and profiles of Nu and $\overline{Nu}$ were investigated in Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9.

^{−4}), a weak clockwise circulation appeared inside the region, while the temperature field illustrated the dominant heat conduction. A rise in Da resulted in a strengthening of liquid motion, causing a small distortion of isotherms. The latter reflected an interaction between the hot liquid in the upper part with a cold right wall and the cold liquid in the bottom part with a hot left border. A further increase in the porous medium’s permeability caused a strengthening of the convective circulation and more essential distortion of the temperature pattern, with a generation of boundary layers by the isothermal borders. It is worth highlighting that for Da ≥ 10

^{−2}, the streamlines illustrated a formation of irregular circulation where one could find the boundary layer separation near the surface of the internal block from the leeward side. The addition of nano-sized particles reflected the appearance of some differences in the temperature field, while the isolines of stream function had weak changes. The isotherms described a less strong cooling of the lower zone and less intensive heating of the upper zone with nano-sized particles. It is important to emphasize the temperature changes within the solid block when the nanoparticles’ volume fraction was increased. In the considered case, nanoadditives were introduced for 2% of Al

_{2}O

_{3}and 2% of SiO

_{2}.

^{−4}) characterized a constant magnitude of Nu where the heat convection was very low. For Da = 10

^{−3}, Nu diminished with the y-coordinate owing to a reduction in the temperature gradient from the bottom border, where an interaction between the cold liquid and hot wall occurred, to the upper one, where it was possible to reveal an enlargement of the thermal boundary layer. For Da ≥ 10

^{−2}, Nu rose with y for a short zone (y < 0.2) and after that Nu decreased. The small increase in Nu that occurred for y < 0.2 can be explained by a vertical displacement of the interaction zone between the cold liquid and hot surface of the bottom part. Moreover, a rise in the Darcy number (Da ≥ 10

^{−2}) did not cause any essential changes in the upper part of the hot wall, while Nu increased in the bottom part with Da. The addition of nanoadditives characterized a diminution of Nu in the lower zone and an increase in Nu in the top part for Da < 10

^{−2}. For Da ≥ 10

^{−2}, Nu decreased with φ. Moreover, Nu increased with the growth in Da in the lower part of the cavity and it decreased with Da in the upper part. This confirms that heat transport is enhanced there due to the heated left border.

^{−2}), a rise in the internal solid block material’s heat conductivity resulted in a reduction in the mean Nu. Such behavior is explained by a stronger interaction between the cold nanosuspension and hot wall in the bottom part. It should be noted also that with an increase in the solid block’s heat conductivity, the transition for two zones of Da, namely, (10

^{−3}, 10

^{−2}) and (10

^{−2}, 10

^{−1}), became inconspicuous. A rise in the concentration of nano-sized particles characterized a diminution of average Nu and this reduction became great for high Da. Additionally, a rise in the nanoadditives’ concentration for low Darcy numbers (10

^{−4},10

^{−3}) of the considered internal solid block materials did not have a strong influence on average Nu.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Izadi, S.; Armaghani, T.; Ghasemiasl, R.; Chamkha, A.J.; Molana, M. A comprehensive review on mixed convection of nanofluids in various shapes of enclosures. Powder Technol.
**2019**, 343, 880–907. [Google Scholar] [CrossRef] - Choi, S.U.S. Enhancing thermal conductivity of fluids with nanoparticles. In Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, FED 231/MD, San Francisco, CA, USA, 12–17 November 1955; Volume 6, pp. 99–105. [Google Scholar]
- Das, S.K.; Choi, S.U.S.; Yu, W.; Pradeep, Y. Nanofluids: Science and Technology; Wiley: Hoboken, NJ, USA, 2008. [Google Scholar]
- Minkowycz, W.J.; Sparrow, E.M.; Abraham, J.P. Nanoparticle Heat Transfer and Fluid Flow; CRC Press: Boca Raton, FL, USA, 2013. [Google Scholar]
- Shenoy, A.; Sheremet, M.; Pop, I. Convective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media and Nanofluids; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
- Nield, D.A.; Bejan, A. Convection in Porous Media, 5th ed.; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Ambreen, T.; Kim, M.-H. Influence of particle size on the effective thermal conductivity of nanofluids: A critical review. Appl. Energy
**2020**, 264, 114684. [Google Scholar] [CrossRef] - Hemmat Esfe, M.; Hassan Kamyab, M.; Valadkhani, M. Application of nanofluids and fluids in photovoltaic thermal system: An updated review. Sol. Energy
**2020**, 199, 796–818. [Google Scholar] [CrossRef] - Pandya, N.S.; Shah, H.; Molana, M.; Tiwari, A.K. Heat transfer enhancement with nanofluids in plate heat exchangers: A comprehensive review. Eur. J. Mech./B Fluids
**2020**, 81, 173–190. [Google Scholar] [CrossRef] - Ahmadi, M.H.; Ghazvini, M.; Sadeghzadeh, M.; Nazari, M.A.; Ghalandari, M. Utilization of hybrid nanofluids in solar energy applications: A review. Nano-Struct. Nano-Objects
**2019**, 20, 100386. [Google Scholar] [CrossRef] - Pordanjani, A.H.; Aghakhani, S.; Afrand, M.; Mahmoudi, B.; Mahian, O.; Wongwises, S. An updated review on application of nanofluids in heat exchangers for saving energy. Energy Convers. Manag.
**2019**, 198, 111886. [Google Scholar] [CrossRef] - Mahian, O.; Kolsi, L.; Amani, M.; Estelle, P.; Ahmadi, G.; Kleinstreuer, C.; Marshall, J.S.; Siavashi, M.; Taylor, R.A.; Niazmand, H.; et al. Recent advances in modeling and simulation of nanofluid flows—Part I: Fundamentals and theory. Phys. Rep.
**2019**, 790, 1–48. [Google Scholar] [CrossRef] - Mahian, O.; Kolsi, L.; Amani, M.; Estelle, P.; Ahmadi, G.; Kleinstreuer, C.; Marshall, J.S.; Taylor, R.A.; Abu-Nada, E.; Rashidi, S.; et al. Recent advances in modeling and simulation of nanofluid flows—Part II: Applications. Phys. Rep.
**2019**, 791, 1–59. [Google Scholar] [CrossRef] - Keshteli, A.N.; Sheikholeslami, M. Nanoparticle enhanced PCM applications for intensification of thermal performance in building: A review. J. Mol. Liq.
**2019**, 274, 516–533. [Google Scholar] [CrossRef] - Groşan, T.; Sheremet, M.A.; Pop, I. Heat transfer enhancement in cavities filled with nanofluids. In Advances Heat Transfer Fluids: From Numerical to Experimental Techniques; Minea, A.A., Ed.; CRC Press: Boca Raton, FL, USA, 2017; pp. 267–284. [Google Scholar]
- Sajid, M.U.; Ali, H.M. Recent advances in application of nanofluids in heat transfer devices: A critical review. Renew. Sustain. Energy Rev.
**2019**, 103, 556–592. [Google Scholar] [CrossRef] - Ranga Babu, J.A.; Kiran Kumar, K.; Srinivasa Rao, S. State-of-art review on hybrid nanofluids. Renew. Sustain. Energy Rev.
**2017**, 77, 551–565. [Google Scholar] [CrossRef] - Huminic, G.; Huminic, A. Hybrid nanofluids for heat transfer applications—A state of the art review. Int. J. Heat Mass Transf.
**2018**, 125, 82–103. [Google Scholar] [CrossRef] - Huminic, G.; Huminic, A. Entropy generation of nanofluid and hybrid nanofluid flow in thermal systems: A review. J. Mol. Liq.
**2020**, 302, 112533. [Google Scholar] [CrossRef] - Salman, S.; Abu Talib, A.R.; Saadon, S.; Hameed Sultan, M.T. Hybrid nanofluid flow and heat transfer over backward and forward steps: A review. Powder Technol.
**2020**, 363, 448–472. [Google Scholar] [CrossRef] - Devi, S.U.; Devi, S.A. Numerical investigation of three-dimensional hybrid Cu–Al2O3/water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating. Can. J. Phys.
**2016**, 94, 490–496. [Google Scholar] [CrossRef] - Devi, S.U.; Devi, S.A. Heat transfer enhancement of Cu–Al2O3/water hybrid nanofluid flow over a stretching sheet. J. Niger. Math. Soc.
**2017**, 36, 419–433. [Google Scholar] - Sarkar, J.; Ghosh, P.; Adil, A. A review on hybrid nanofluids: Recent research, development and applications. Renew. Sustain. Energ. Rev.
**2015**, 43, 164–177. [Google Scholar] [CrossRef] - Akilu, S.; Sharma, K.V.; Baheta, A.T.; Mamat, R. A review of thermophysical properties of water based composite nanofluids. Renew. Sustain. Energ. Rev.
**2016**, 66, 654–678. [Google Scholar] [CrossRef] [Green Version] - Sidik, N.A.; Adamu, I.M.; Jamil, M.M.; Kefayati, G.H.; Mamat, R.; Najafi, G. Recent progress on hybrid nanofluids in heat transfer applications: A comprehensive review. Int. Commun. Heat Mass Transf.
**2016**, 78, 68–79. [Google Scholar] [CrossRef] - Sundar, L.S.; Sharma, K.V.; Singh, M.K.; Sousa, A.C. Hybrid nanofluids preparation, thermal properties, heat transfer and friction factor—A review. Renew. Sustain. Energ. Rev.
**2017**, 68, 185–198. [Google Scholar] [CrossRef] - Hayat, T.; Nadeem, S. Heat transfer enhancement with Ag–CuO/water hybrid nanofluid. Results Phys.
**2017**, 7, 2317–2324. [Google Scholar] [CrossRef] - Yousefi, M.; Dinarvand, S.; Yazdi, M.E.; Pop, I. Stagnation-point flow of an aqueous titania-copper hybrid nanofluid toward a wavy cylinder. Int. J. Numer. Methods Heat Fluid Flow
**2018**, 28, 1716–1735. [Google Scholar] [CrossRef] - Sajid, M.U.; Ali, H.M. Thermal conductivity of hybrid nanofluids: A critical review. Int. J. Heat Mass Transf.
**2018**, 126, 211–234. [Google Scholar] [CrossRef] - Chamkha, A.J.; Miroshnichenko, I.V.; Sheremet, M.A. Numerical analysis of unsteady conjugate natural convection of hybrid water-based nanofluid in a semicircular cavity. J. Therm. Sci. Eng. Appl.
**2017**, 9, 041004. [Google Scholar] [CrossRef] - Izadi, M.; Mohebbi, R.; Karimi, D.; Sheremet, M.A. Numerical simulation of natural convection heat transfer inside a ┴ shaped cavity filled by a MWCNT-Fe3O4/water hybrid nanofluids using LBM. Chem. Eng. Process. Process Intensif.
**2018**, 125, 56–66. [Google Scholar] [CrossRef] - Izadi, M.; Oztop, H.F.; Sheremet, M.A.; Mehryan, S.A.M.; Abu-Hamdeh, N. Coupled FHD-MHD free convection of a hybrid nanoliquid in an inversed T-shaped enclosure occupied by partitioned porous media. Numer. Heat Transf. A
**2019**, 76, 479–498. [Google Scholar] [CrossRef] - Suresh, S.; Venkitaraj, K.P.; Selvakumar, P.; Chandrasekar, M. Synthesis of Al2O3–Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloid. Surf. A-Phys. Eng. Asp.
**2011**, 388, 41–48. [Google Scholar] [CrossRef] - Suresh, S.; Venkitaraj, K.P.; Selvakumar, P.; Chandrasekar, M. Effect of Al2O3–Cu /water hybrid nanofluid in heat transfer. Exp. Therm. Fluid Sci.
**2012**, 38, 54–60. [Google Scholar] [CrossRef] - Soltani, O.; Akbari, M. Effects of temperature and particles concentration on the dynamic viscosity of MgO-MWCNT/ethylene glycol hybrid nanofluid: Experimental study. Phys. E Low Dimens. Syst. Nanostruct.
**2016**, 84, 564–570. [Google Scholar] [CrossRef] - Leong, K.Y.; Ahmad, K.K.; Ong, H.C.; Ghazali, M.J.; Baharum, A. Synthesis and thermal conductivity characteristic of hybrid nanofluids–a review. Renew. Sustain. Energ. Rev.
**2017**, 75, 868–878. [Google Scholar] [CrossRef] - Waini, I.; Ishak, A.; Pop, I. Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid. Int. J. Heat Mass Transf.
**2019**, 136, 288–290. [Google Scholar] [CrossRef] - Waini, I.; Ishak, A.; Pop, I. Flow and heat transfer along a permeable stretching/shrinking curved surface in a hybrid nanofluid. Phys. Scr.
**2019**, 94, 105219. [Google Scholar] [CrossRef] - Waini, I.; Ishak, A.; Pop, I. Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface. Int. J. Numer. Methods Heat Fluid Flow
**2019**, 29, 3110–3127. [Google Scholar] [CrossRef] - Aly, E.; Pop, I. MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition. Int. J. Numer. Methods Heat Fluid Flow
**2019**, 29, 3012–3038. [Google Scholar] [CrossRef] - Ghalambaz, M.; Sheremet, M.A.; Mehryan, S.A.M.; Kashkooli, F.M.; Pop, I. Local thermal non-equilibrium analysis of conjugate free convection within a porous enclosure occupied with Ag-MgO hybrid nanofluid. J. Therm. Anal. Calorim.
**2019**, 135, 1381–1398. [Google Scholar] [CrossRef] - Pop, I.; Sheremet, M.A.; Grosan, T. Thermal convection of nanoliquid in a double-connected chamber. Nanomaterials
**2020**, 10, 588. [Google Scholar] [CrossRef] [Green Version] - Sivaraj, C.; Sheremet, M.A. MHD natural convection in an inclined square porous cavity with a heat conducting solid block. J. Magn. Magn. Mater.
**2017**, 426, 351–360. [Google Scholar] [CrossRef] - Sheremet, M.A.; Pop, I.; Oztop, H.F.; Abu-Hamdeh, N. Natural convection of nanofluid inside a wavy cavity with a non-uniform heating: Entropy generation analysis. Int. J. Numer. Methods Heat Fluid Flow
**2017**, 27, 958–980. [Google Scholar] [CrossRef] - Astanina, M.S.; Sheremet, M.A.; Oztop, H.F.; Abu-Hamdeh, N. MHD natural convection and entropy generation of ferrofluid in an open trapezoidal cavity partially filled with a porous medium. Int. J. Mech. Sci.
**2018**, 136, 493–502. [Google Scholar] [CrossRef] - Shulepova, E.V.; Sheremet, M.A.; Oztop, H.F.; Abu-Hamdeh, N. Mixed convection of Al2O3–H2O nanoliquid in a square chamber with complicated fin. Int. J. Mech. Sci.
**2020**, 165, 105192. [Google Scholar] [CrossRef] - Das, M.K.; Reddy, S.K. Conjugate natural convection heat transfer in an inclined square cavity containing a conducting block. Int. J. Heat Mass Transf.
**2006**, 49, 4987–5000. [Google Scholar] - Garoosi, F.; Rashidi, M.M. Two phase flow simulation of conjugate natural convection of the nanofluid in a partitioned heat exchanger containing several conducting obstacles. Int. J. Mech. Sci.
**2017**, 130, 282–306. [Google Scholar] [CrossRef] [Green Version]

**Figure 5.**Isolines of ψ and θ for the steel internal block:

**a**shows a Darcy number (Da) = 10

^{−4},

**b**shows Da = 10

^{−3},

**c**shows Da = 10

^{−2},

**d**shows Da = 10

^{−1}.

**Figure 6.**Profiles of the local Nusselt number (Nu) for the steel internal block, various Darcy numbers and nanoparticles’ concentration.

**Figure 7.**Isolines of ψ and θ for Da = 10

^{−2}:

**a**shows the glass internal block,

**b**shows the steel internal block,

**c**shows the copper internal block.

**Figure 8.**Profiles of the mean Nusselt number for various Darcy numbers and nanoadditives’ concentrations:

**a**shows for the glass internal block,

**b**shows for the steel internal block,

**c**shows for the copper internal block.

**Figure 9.**Profiles of average Nu for various Darcy numbers, nanoadditives’ concentrations and internal solid block materials.

Physical Properties | Host Fluid (Water) | Al_{2}O_{3} | SiO_{2} | Aluminum (Solid Matrix) | Central Block Material | ||
---|---|---|---|---|---|---|---|

Glass | Steel | Copper | |||||

c_{p} (J·kg^{−1}·K^{−1}) | 4179 | 765 | 703 | 880 | 750 | 460 | 380 |

ρ (kg·m^{−3}) | 997.1 | 3970 | 2200 | 2700 | 2600 | 7800 | 8960 |

λ (W·m^{−1}·K^{−1}) | 0.613 | 40 | 1.2 | 211 | 0.65 | 46 | 385 |

β × 10^{−5} (K^{−1}) | 21.0 | 0.85 | 6.0 | – | – | – | – |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

A. Sheremet, M.; Cimpean, D.S.; Pop, I.
Thermogravitational Convection of Hybrid Nanofluid in a Porous Chamber with a Central Heat-Conducting Body. *Symmetry* **2020**, *12*, 593.
https://doi.org/10.3390/sym12040593

**AMA Style**

A. Sheremet M, Cimpean DS, Pop I.
Thermogravitational Convection of Hybrid Nanofluid in a Porous Chamber with a Central Heat-Conducting Body. *Symmetry*. 2020; 12(4):593.
https://doi.org/10.3390/sym12040593

**Chicago/Turabian Style**

A. Sheremet, Mikhail, Dalia Sabina Cimpean, and Ioan Pop.
2020. "Thermogravitational Convection of Hybrid Nanofluid in a Porous Chamber with a Central Heat-Conducting Body" *Symmetry* 12, no. 4: 593.
https://doi.org/10.3390/sym12040593