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On the flow patterns and thermal control of radiative natural convective hybrid nanofluid flow inside a square enclosure having various shaped multiple heated obstacles

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Abstract

This investigation reveals the flow patterns of natural convective hybrid nanofluid inside a square enclosure. The enclosure is presumed to be filled with water-based ferrous-graphene nanoparticles and multiple heated obstacles with various shapes. Three types of heated obstacles namely circular, square, and diamond are considered to visualize the flow patterns. The bottom and left-sided walls are presumed to be uniformly heated, whereas the top surface is adiabatic and the right-sided wall is made isothermally cooled. Moreover, thermal radiation and magnetic effects are supposed to exist within the flow region. A complete investigation is conducted to extract that how these different shaped heated obstacles influence the hydrothermal pattern. Appropriate similarity variables translate the dimensional equation into non-dimensional. Later on, Galerkin finite element scheme is introduced to deal with those nondimensional flow equations. The grid independence, comparison test, and experimental validation are conducted to exhibit the competency of the current model. Several isotherms, streamlines, velocity distribution, and average Nusselt number plots are depicted to perceive the parametric impact on such cavity flow. These plots are made for dimensionless factors such as Rayleigh number a \(\left( {10^{3} \le {\text{Ra}} \le 10^{5} } \right)\), thermal radiation \(\left( {0.5 \le N \le 1.5} \right)\), Hartmann number \(\left( {5 \le {\text{Ha}} \le 15} \right)\), nanoparticle volume fraction \(\left( {0.00 \le \phi_{2} \le 0.04} \right)\). The consequences imply that the isotherms intensify for Rayleigh number and extreme distortion is noted for circular obstacle, while other parameters disclose opposite scenario in isotherms. The average Nusselt number diminishes for Hartmann number but amplifies for nanoparticle concentration. The maximum increment in heat transport is predicted for Rayleigh number variation and circular obstacles. It is approximately 27.39%. The lowest enhancement is provided by diamond-shaped obstacles.

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Data availability

All data that support the findings of this study are included within the article.

Abbreviations

\(\left( {u,v} \right)\) :

Velocity components (m s−1)

\(g\) :

Gravitation (m s−2)

\(L\) :

Square cavity length (m)

\(T_{{\text{h}}}\) :

Temperature of heated wall (K)

\(T_{{\text{c}}}\) :

Temperature of cold wall (K)

\(T\) :

Hybrid nanofluid temperature (K)

\(\rho\) :

Density (kg m−3)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\kappa\) :

Thermal conductivity (W m−1 K−1)

\(\rho C_{{\text{p}}}\) :

Heat capacitance (J m−3 K−1)

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\alpha\) :

Thermal diffusivity (m2s−1)

\(\sigma\) :

Electrical conductivity (Ω−1 m−1)

\(B_{0}\) :

Magnetic field (Ω1/2 m−1 s−1/2 kg1/2)

\(q_{{\text{r}}}\) :

Radiative heat flux (kg s−3)

\(\sigma^{*}\) :

Stefan Boltzmann constant (W m−2 K−4)

\(k^{*}\) :

Mean absorption coefficient (m−1)

\(\phi\) :

Nanoparticle volume fraction

\({\text{Ra}} = \frac{{g\beta_{{\text{f}}} \left( {T_{{\text{h}}} - T_{{\text{c}}} } \right)L^{3} }}{{\nu_{{\text{f}}} \alpha_{{\text{f}}} }}\) :

Rayleigh number

\(\Pr = \frac{{\mu_{{\text{f}}} \left( {\rho C_{{\text{p}}} } \right)_{{\text{f}}} }}{{\rho_{{\text{f}}} \kappa_{{\text{f}}} }}\) :

Prandtl number

\(N = \frac{{4\sigma^{*} T_{{\text{c}}}^{3} }}{{k^{*} \kappa_{{\text{f}}} }}\) :

Radiation parameter

\({\text{Ha}} = \frac{{\sigma_{{\text{f}}} B_{0}^{2} L^{2} }}{{\mu_{{\text{f}}} }}\) :

Hartmann number

\({\text{Nu}}\) :

Nusselt number

\({\text{Nu}}_{{{\text{avg}}}}\) :

Average Nusselt number

\({\text{f}}\) :

Base fluid

\({\text{nf}}\) :

Mono nanofluid

\({\text{hnf}}\) :

Hybrid nanofluid

\({\text{s}}\) :

Nanoparticle

1:

First particle

2:

Second particle

References

  1. S. Ostrach, Natural convection in enclosure. J. Heat Transf. 110, 1175–1190 (1988)

    Article  Google Scholar 

  2. M. Sankar, Y. Do, S. Ryu et al., Cooling of heat sources by natural convection heat transfer in a vertical annulus. Num. Heat Transf. Part A Appl. 68(8), 847–869 (2015)

    Article  ADS  Google Scholar 

  3. A. Rahimi, S.A. Dehghan, A. Kasaeipoor et al., A comprehensive review on natural convection flow and heat transfer: the most practical geometries for engineering applications. Int. J. Num. Methods. Heat Fluid Flow. 29(3), 834–877 (2019)

    Article  Google Scholar 

  4. D. Liu, W. Huang, N. Zhang, Numerical simulation of convection and heat transfer in Czochralski crystal growth by multiple-relaxation-time LBM. AIP Adv. 7, 075312 (2017). https://doi.org/10.1063/1.4995414

    Article  ADS  Google Scholar 

  5. K.S. Reddy, N.S. Kumar, An improved model for natural convection heat loss from modified cavity receiver of solar dish concentrator. Sol. Energy 83, 1884–1892 (2009)

    Article  ADS  Google Scholar 

  6. A.G.A. Ghani, M.M. Farid, X.D. Chen et al., Numerical simulation of natural convection heating of canned food by computational fluid dynamics. J. Food Eng. 41, 55–64 (1999)

    Article  Google Scholar 

  7. A.K. Datta, A.A. Teixeira, Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. J. Food Sci. 53, 191–195 (1988)

    Article  Google Scholar 

  8. L. Chen, X.R. Zhang, Natural convection supercritical fluid systems for geothermal, heat transfer, and energy conversion, in Energy Solutions to Combat Global Warming. Lecture Notes in Energy, vol. 33, ed. by X. Zhang, I. Dincer (Springer, Cham, 2017). https://doi.org/10.1007/978-3-319-26950-4_20

    Chapter  Google Scholar 

  9. F. Espinosa, R. Avila, J.G. Cervantes et al., Numerical simulation of simultaneous freezing–melting problems with natural convection. Nucl. Eng. Des. 232, 145–155 (2004)

    Article  Google Scholar 

  10. N. Mallya, S. Haussener, Buoyancy-driven melting and solidification heat transfer analysis in encapsulated phase change materials. Int. J. Heat Mass Transf. 164, 120525 (2021)

    Article  Google Scholar 

  11. S. Ostrach, Natural convection in enclosures. Adv. Heat Transf. 8, 161–227 (1972)

    Article  Google Scholar 

  12. G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution. Int. J. Num. Methods Fluids. 3, 249–264 (1983)

    Article  MATH  Google Scholar 

  13. G. de Vahl Davis, I.P. Jones, Natural convection in a square cavity: a comparison exercise. Int. J. Num. Methods Fluids. 3, 227–248 (1983)

    Article  MATH  Google Scholar 

  14. G.D. Mallinson, G. De Vahl Davis, Three-dimensional natural convection in a box: a numerical study. J. Fluid. Mech. 83, 1–31 (1977)

    Article  ADS  Google Scholar 

  15. J.L. Lage, A. Bejan, The Ra–Pr domain of laminar natural convection in an enclosure heated from the sider. Numer. Heat Transf. Part A 19, 21–41 (1991)

    Article  ADS  Google Scholar 

  16. C. Xia, J.Y. Murthy, Buoyancy-driven flow transitions in deep cavities heated from below. ASME Trans. J. Heat Transf. 124, 650–659 (2002)

    Article  Google Scholar 

  17. H.N. Dixit, V. Babu, Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method. Int. J. Heat Mass Transf. 49(3–4), 727–739 (2006)

    Article  MATH  Google Scholar 

  18. I. Sarris, G. Zikos, A. Grecos et al., On the limits of validity of the low magnetic Reynolds number approximation in MHD natural-convection heat transfer. Numer. Heat Transf. Part B 50, 158–180 (2006)

    Article  ADS  Google Scholar 

  19. M. Pirmohammadi, M. Ghassemi, Effect of magnetic field on convection heat transfer inside a tilted square enclosure. Int. Commun. Heat Mass Transf. 36, 776–780 (2009)

    Article  Google Scholar 

  20. M.A. Sheremet, I. Pop, Natural convection combined with thermal radiation in a square cavity filled with a viscoelastic fluid. Int. J. Num. Methods Heat Fluid Flow 28(3), 624–640 (2018)

    Article  Google Scholar 

  21. A.K. Alzahrani, S. Sivasankaran, M. Bhuvaneswari, Numerical simulation on convection and thermal radiation of Casson fluid in an enclosure with entropy generation. Entropy 22, 229 (2020). https://doi.org/10.3390/e22020229

    Article  ADS  MathSciNet  Google Scholar 

  22. A.G. Kamel, E.H. Haraz, S.N. Hanna, Numerical simulation of three-sided lid-driven square cavity. Eng. Rep. 2(4), e12151 (2020). https://doi.org/10.1002/eng2.12151

    Article  Google Scholar 

  23. S.S. Mendu, P.K. Das, Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method. Korea-Aust. Rheol. J. 32, 213–231 (2020)

    Article  Google Scholar 

  24. S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles. ASME. (1995), p. 66.

  25. M.U. Sajid, H.M. Ali, Recent advances in application of nanofluids in heat transfer devices: a critical review. Renew. Sustain. Energy Rev. 103, 556–592 (2019)

    Article  Google Scholar 

  26. S.O. Giwa, M. Sharifpur, M.H. Ahmadi et al., A review of magnetic field influence on natural convection heat transfer performance of nanofuids in square cavities. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09832-3

    Article  Google Scholar 

  27. C.J. Ho, W.K. Liu, Y.S. Chang et al., Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. Int. J. Therm. Sci. 49, 1345–1353 (2010)

    Article  Google Scholar 

  28. H. Nemati, M. Farhadi, K. Sedighi et al., Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the Lattice Boltzmann model. Sci. Iran. B 19(2), 303–310 (2012)

    Article  Google Scholar 

  29. B.C. Shekhar, N. Kishan, Finite element analysis of natural convective heat transfer in a porous square cavity filled with nanofluids in the presence of thermal radiation. J. Conf. Ser. 662, 012017 (2015)

    Article  Google Scholar 

  30. B.C. Shekhar, C. Haritha, N. Kishan, Magnetohydrodynamic convection in a porous square cavity filled by a nanofluid with viscous dissipation effects. Proc. Inst. Mech. Part E J. Process Mech. Eng. 233(3), 474–488 (2019)

    Article  Google Scholar 

  31. A. Bendaraa, M.M. Charafi, A. Hasnaoui, Numerical modeling of natural convection in horizontal and inclined square cavities filled with nanofluid in the presence of magnetic field. Eur. Phys. J. Plus. 134, 468 (2019)

    Article  Google Scholar 

  32. M. Hemmat Esfe, M. Afrand, S. Esfandeh, Investigation of the effects of various parameters on the natural convection of nanofluids in various cavities exposed to magnetic fields: a comprehensive review. J. Therm. Anal. Calorim. 140, 2055–2075 (2020)

    Article  Google Scholar 

  33. F. Nasri, Y.A. Rothan, R. Nciri et al., MHD natural convection of a Fe3O4–water nanofluid within an inside round diagonal corner square cavity with existence of magnetic source. Appl. Sci. 10, 3236 (2020). https://doi.org/10.3390/app10093236

    Article  Google Scholar 

  34. M.D. Massoudi, M.B. Ben Hamida, M.A. Almeshaal, Free convection and thermal radiation of nanofluid inside nonagon inclined cavity containing a porous medium influenced by magnetic field with variable direction in the presence of uniform heat generation/absorption. Int. J. Num. Methods Heat Fluid Flow 31(3), 933–958 (2021)

    Article  Google Scholar 

  35. P.S. Reddy, P. Sreedevi, Effect of thermal radiation and volume fraction on carbon nanotubes based nanofluid flow inside a square chamber. Alex. Eng. J. 60, 1807–1817 (2021)

    Article  Google Scholar 

  36. B. Takabi, A.M. Gheitaghy, M. Tazraei, Hybrid water-based suspension of Al2O3 and Cu nanoparticles on laminar convection effectiveness. J. Thermophys. Heat Transf. 30(3), 523–532 (2016)

    Article  Google Scholar 

  37. F. Jamil and H.M. Ali, Chapter 6-Applications of hybrid nanofluids in different fields, in Hybrid Nanofluids for Convection Heat Transfer (2020), pp. 215–254. https://doi.org/10.1016/B978-0-12-819280-1.00006-9.

  38. M.H. Esfe, M. Bahiraei, A. Mir, Application of conventional and hybrid nanofluids in different machining processes: a critical review. Adv. Colloid Interface Sci. 282, 102199 (2020)

    Article  Google Scholar 

  39. R.A. Kumar, M. Kavitha, P.M. Kumar et al., Numerical study of graphene-platinum hybrid nanofluid in microchannel for electronics cooling. Proc. Inst. Mech. E. Part C J. Mech. Eng. Sci. (2021). https://doi.org/10.1177/0954406220987261

    Article  Google Scholar 

  40. Y.M. Chu, K.S. Nisar, U. Khan et al., Mixed convection in MHD water-based molybdenum disulfide-graphene oxide hybrid nanofluid through an upright cylinder with shape factor. Water 12, 1723 (2020). https://doi.org/10.3390/w12061723

    Article  Google Scholar 

  41. T. Tayebi, A.J. Chamkha, Buoyancy-driven heat transfer enhancement in a sinusoidally heated enclosure utilizing hybrid nanofluid. Comput. Therm. Sci. 9(5), 405–421 (2017)

    Article  Google Scholar 

  42. H.A. Ashorynejad, A. Shahriari, MHD natural convection of hybrid nanofluid in an open wavy cavity. Res. Phys. 9, 440–455 (2018)

    Google Scholar 

  43. H. Bagheri, M. Behrang, E. Assareh et al., Free convection of hybrid nanofluids in a C-shaped chamber under variable heat flux and magnetic field: simulation, sensitivity analysis, and artificial neural networks. Energies 12, 2807 (2019). https://doi.org/10.3390/en12142807

    Article  Google Scholar 

  44. M. Ghalambaz, A. Doostani, E. Izadpanahi et al., Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity. J. Therm. Anal. Calorim. 139, 2321–2336 (2020)

    Article  Google Scholar 

  45. P. Sudarsana Reddy, P. Sreedevi, Entropy generation and heat transfer analysis of magnetic hybrid nanofluid inside a square cavity with thermal radiation. Eur. Phys. J. Plus. 136, 39 (2021). https://doi.org/10.1140/epjp/s13360-020-01025-z

    Article  Google Scholar 

  46. Z.H. Khan, W.A. Khan, M. Hamid et al., Finite element analysis of hybrid nanofluid flow and heat transfer in a split lid-driven square cavity with Y-shaped obstacle. Phys. Fluids 32, 093609 (2020)

    Article  ADS  Google Scholar 

  47. S. Munawar, N. Saleem, W.A. Khan et al., Mixed convection of hybrid nanofluid in an inclined enclosure with a circular center heater under inclined magnetic field. Coatings 11, 506 (2021). https://doi.org/10.3390/coatings11050506

    Article  Google Scholar 

  48. A. Bekele, M. Mishra, S. Dutta, Effects of delta-shaped obstacles on the thermal performance of solar air heater. Adv. Mech. Eng. (2011). https://doi.org/10.1155/2011/103502

    Article  Google Scholar 

  49. T.J. Young, K. Vafai, Convective flow and heat transfer in a channel containing multiple heated obstacles. Int. J. Heat Mass Transf. 41, 3279–3298 (1998)

    Article  MATH  Google Scholar 

  50. I.G. Anghel, H. Anglart, S. Hedberg, Experimental investigation of post-dryout heat transfer in annuli with flow obstacles. Nucl. Eng. Des. 246, 82–90 (2012)

    Article  Google Scholar 

  51. A. Tanase, D.C. Groeneveld, An experimental investigation on the effects of flow obstacles on single phase heat transfer. Nucl. Eng. Des. 288, 195–207 (2015)

    Article  Google Scholar 

  52. S. Hussain, S.E. Ahmed, T. Akbar, Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle. Int. J. Heat Mass Transf. 114, 1054–1006 (2017)

    Article  Google Scholar 

  53. S. Jakeer, P.B. Reddy, A.M. Rashad et al., Impact of heated obstacle position on magneto-hybrid nanofluid flow in a lid-driven porous cavity with Cattaneo–Christov heat flux pattern. Alex. Eng. J. 60(1), 821–835 (2021)

    Article  Google Scholar 

  54. A.I. Alsabery, T. Tayebi, H.T. Kadhim et al., Impact of two-phase hybrid nanofluid approach on mixed convection inside wavy lid-driven cavity having localized solid block. J. Adv. Res. 30, 63–74 (2021)

    Article  Google Scholar 

  55. S.E.J. Ahmed, Natural convection of dusty hybrid nanofluids in diverging-converging cavities including volumetric heat sources. Therm Sci. Eng. Appl. 13(1), 011018 (2021)

    Article  Google Scholar 

  56. A. Arshad, M. Jabbal, Y. Yan et al., A review on graphene based nanofluids: preparation, characterization and applications. J. Mol. Liq. 279, 444–484 (2019)

    Article  Google Scholar 

  57. I. Nkurikiyimfura, Y. Wang, Z. Pan, Heat transfer enhancement by magnetic nanofluids—a review. Renew. Sustain. Energy Rev. 21, 548–561 (2013)

    Article  Google Scholar 

  58. T. Basak, K.G. Ayappa, Influence of internal convection during microwave thawing of cylinders. AIChE J. 47, 835–850 (2001)

    Article  Google Scholar 

  59. J.N. Reddy, An Introduction to the Finite Element Method (McGraw-Hill, New York, 1993)

    Google Scholar 

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Acknowledgements

The author expresses his cordial thanks to the respected Editor in chief and honorable reviewer for their valuable suggestions and comments to improve the presentation of this article.

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  1. Department of Mathematics, M. A. C. M. High School, Malda, West Bengal, 732121, India

    Nilankush Acharya

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Acharya, N. On the flow patterns and thermal control of radiative natural convective hybrid nanofluid flow inside a square enclosure having various shaped multiple heated obstacles. Eur. Phys. J. Plus 136, 889 (2021). https://doi.org/10.1140/epjp/s13360-021-01892-0

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