Skip to main content
SpringerLink
Log in

Analysis of Natural Convection–Radiation Interaction Flow in a Porous Cavity with Al2O3–Cu Water Hybrid Nanofluid: Entropy Generation

  • Research Article-Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

A numerical treatment of the interaction between two models of heat transfer, namely, surface thermal radiation and natural convection, of micropolar loaded with Al2O3 and Cu nanoparticles within a porous cavity in the presence of MHD of inclination \(\Phi \) with entropy analysis is presented. Both 1st and 2nd laws of thermodynamic are applied to analyze the problem. The 2-D steady-state flow governing equations have been resolved via Alternating Direction Implicit (ADI) based on the concept of the finite volume method. The exhibited physical factors are the heat source length \(0.2 \leqslant B \leqslant 0.8\), the heat generation/absorption \(-2 \leqslant Q \leqslant 2\), the radiation factor \(0 \leqslant {R}_{d} \leqslant 1.0\), the vortex viscosity parameter \(0 \leqslant k \leqslant 2\), Hartmann number \(0 \leqslant Ha \leqslant 100\), the inclination angle \(0 \leqslant \Phi \leqslant \pi \) and and the alumina-copper volume fraction \(1\mathrm{\%} \leqslant {\varphi }_{\mathrm{Al}},{\varphi }_{\mathrm{Cu}} \leqslant 5\mathrm{\%}\). The presented computations are portrayed graphically. The outcomes illustrate that the average Nusselt number weakens with larger values of vortex parameter \(k\) whereas strengthens due to total solid volume fraction \(\varphi ({\varphi }_{\mathrm{Al}}+{\varphi }_{\mathrm{Cu}})\). In addition, \({R}_{d}\) leads to strengthen the global entropy generation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Chang, L.C.; Yang, K.T.; Lloyd, J.R.: Radiation-natural convection interactions in two-dimensional complex enclosures. J. Heat Transfer 105, 89–95 (1983)

    Article  Google Scholar 

  2. Akiyama, M.; Chong, Q.P.: Numerical analysis of natural convection with surface radiation in a square enclosure. Numer. Heat Transter Part A 31, 419–433 (1997)

    Article  Google Scholar 

  3. Ramesh, N.; Venkateshan, S.P.: Effect of surface radiation on natural convection in a square enclosure. J. Thermophys. Heat Transfer 13, 299–301 (1999)

    Article  Google Scholar 

  4. Saravanan, S.; Sivaraj, C.: Coupled thermal radiation and natural convection heat transfer in a cavity with a heated plate inside. Int. J. Heat Fluid Flow 40, 54–64 (2013)

    Article  Google Scholar 

  5. Alvarado, R.; Xaman, J.; Hinojosa, J.; Alvareza, G.: Interaction between natural convection and surface thermal radiation in tilted slender cavities. Int. J. Therm. Sci. 47, 355–368 (2008)

    Article  Google Scholar 

  6. Chamkha, A.J.; Rashad, A.M.; Mansour, M.A.; Armaghani, T.; Ghalambaz, M.: Effects of heat sink and source and entropy generation on MHD mixed convection of a Cu-water nanofluid in a lid-driven square porous enclosure with partial slip. Phys. Fluids 29, 052001 (2017)

  7. Balaji, C.; Venkateshan, S.P.: Correlations for free convection and surface radiation in a square cavity. Int. J. Heat Fluid Flow 15, 249–252 (1994)

    Article  Google Scholar 

  8. Ahmed, S.E.; Oztop, H.F.; Al-Salem, K.: Natural convection coupled with radiation heat transfer in an inclined porous cavity with corner heater. Comput. Fluids 102, 74–84 (2014)

    Article  Google Scholar 

  9. Rebhi, R.; Hadidi, N.; Mamou, M.; Khechiba, K.; Bennacer, R.: The onset of unsteady double-diffusive convection in a vertical porous cavity under a magnetic field and submitted to uniform fluxes of heat and mass. Special Top. Rev. Porous Media Int. J. 11(3):259–285 (2020)

  10. Redha, R.; Noureddine, H.; Rachid, B.: Non-Darcian effect on double-diffusive natural convection inside an inclined square Dupuit-Darcy porous cavity under a magnetic field. Therm Sci 25(1) Part A, 121–132 (2021)

  11. Sivaraj, C.; Sheremet, M.A.: Natural convection coupled with thermal radiation in a square porous cavity having a heated plate inside. Transp. Porous Med. 114, 843–857 (2016)

    Article  MathSciNet  Google Scholar 

  12. Badruddin, I.A.; Zainal, Z.A.; Narayana, P.A.A.; Seetharamu, K.N.: Heat transfer in porous cavity under the influence of radiation and viscous dissipation. Int. J. Heat Mass Transf. 33, 491–499 (2006)

    Article  Google Scholar 

  13. Mahapatra, T.R.; Pal, D.; Mondal, S.: Influence of thermal radiation on non-Darcian natural convection in a square cavity filled with fluid saturated porous medium of uniform porosity. Nonlinear Anal. Model. Control 17, 223–237 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. House, J.M.; Beckermann, C.; Smith, T.F.: Effect of a centered conducting body on natural convection heat transfer in an enclosure. Numerical Heat Transfer 18, 213–225 (1990)

    Article  Google Scholar 

  15. Bouali, H.; Mezrhab, A.; Amaoui, H.; Bouzidi, M.: Radiation-natural convectionheat transfer in an inclined rectangular enclosure. Int. J. Therm. Sci. 45, 553–566 (2006)

    Article  Google Scholar 

  16. Hossain, M.A.; Saleem, M.; Saha, S.C.; Nakayama, A.: Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls. Appl. Math. Mech. 34, 687–702 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kassemi, M.; Naraghi, M.H.N.: Analysis of radiation-natural convection interactions in 1-g and low-g environments using the discrete exchange factor method. Int. J. Heat Mass Transfer 36(17), 4141–4149 (1993)

    Article  MATH  Google Scholar 

  18. Mezrhab, A.; Jami, M.; Bouzidi, M.; Lallemand, P.: Analysis of radiation-natural convection in a divided enclosure using the lattice Boltzmann method. Comput. Fluids 36, 423–434 (2007)

    Article  MATH  Google Scholar 

  19. Alilat, D.; Alliche, M.; Rebhi, R.; Borjini, M.N.: Internal and porosity effects on Dupuit-Darcy natural convection of Cu-water nanofluid saturated high thermal conductive porous medium. Special Top. Rev. Porous Media Int. J. 11(5), 453–475 (2020)

  20. Alilat, D.; Alliche, M.; Rebhi, R.; Chamkha, A.J.: Inertial effects on the hydromagnetic natural convection of SWCNT-water nanofluid-saturated inclined rectangular porous medium. Int. J. Fluid Mech. Res. 47(5): 461–483 (2020)

  21. Mezrhab, A.; Bouali, H.; Amaoui, H.; Bouzidi, M.: Computation of combined natural-convection and radiation heat transfer in a cavity having a square body at its center. Appl. Energy 83, 1004–1023 (2006)

    Article  Google Scholar 

  22. Tiwari, A.; Singh, A.; Chandran, P.; Sacheti, N.: Natural convection in a cavity with a sloping upper surface filled with an anisotropic porous material. Acta Mech. 223, 95–108 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Jawad, R.; Azizah, M.R.; Zurni, O.: Numerical investigation of copper-water (Cu-water) nanofluid with di erent shapes of nanoparticles in a channel with stretching wall: Slip effects. Math. Comput. Appl. 21, 43–58 (2016)

    Google Scholar 

  24. Khanafer, K.; Vafai, K.; Lightstone, M.: Buoyancy-driven heat transfer enhancement in a two dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transfer 46, 3639–3653 (2003)

    Article  MATH  Google Scholar 

  25. Oztop, H.F.; Abu-Nada, E.: Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow 29, 1326–1336 (2008)

    Article  Google Scholar 

  26. Mahdy, A.; Chamkha, A.J.: Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanofluid of moving stretched porous wedge. Int. J. Numer. Meth. Heat Fluid Flow 28(11), 2567–2580 (2018)

    Article  Google Scholar 

  27. Mahdy, A.: Non-Newtonian nanofluid free convectionflow subject to mixed thermal boundary conditions about a vertical cone 2014. J. Braz. Soci. Mech. Sci. Engin. 36(4), 951–960 (2014)

    Article  Google Scholar 

  28. Esfe, M.H.; Wongwises, S.; Rejvani, M.: Prediction of thermal conductivity of carbon nanotube-EG nanofluid using experimental data by ANN. Curr Nanosci. 13, 1–6 (2017)

    Article  Google Scholar 

  29. Momin, G.G.: Experimental investigation Of mixed convection with water-Al2O3 and hybrid nanofluid in inclined tube for laminar flow. Int. J. Sci. Technol. Res. 2, 195 (2013)

    Google Scholar 

  30. Takabi, B.; Shokouhmand, H.: Effects of Al2O3-Cu/water hybrid nanofluid on heat transfer and flow characteristics in turbulent regime. Int. J. Mod. Phys. C. 26, 1550047 (2015)

    Article  Google Scholar 

  31. Takabi, T.; Salehi, S.: Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Adv. Mech. Eng. 6: 147059 (2014)

  32. Suriya Uma Devi, S.; Anjali Devi, S.P.: Numerical investigation of three-dimensional hybrid Cu-Al O /water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating. Can. J. Phys. 94: 490–496 (2016)

  33. Huang, D.; Wu, Z.; Sunden, B.: Effects of hybrid nanofluid mixture in plate heat exchangers. Exp Thermal Fluid Sci. 72, 190–196 (2016)

    Article  Google Scholar 

  34. Sundar, L.S.; Singh, M.K.; Sousa, A.C.: Enhanced heat transfer and friction factor of MWCNT-Fe3O4/water hybrid nanofluids. Int. Commun. Heat Mass Transfer 52, 73–83 (2014)

    Article  Google Scholar 

  35. Suresh, S.; Venkitaraj, K.; Selvakumar, P.; Chandrasekar, M.: Synthesis of Al2O3-Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids Surf. A 388, 41–48 (2011)

    Article  Google Scholar 

  36. Gorla, S.R.; Siddiqa, S.; Mansour, M.; Rashad, A.; Salah, T.: Heat source/sink effects on a hybrid nanofluid filled porous cavity. J. Thermophys. Heat Transfer 31(4), 847–857 (2017)

    Article  Google Scholar 

  37. Madhesh, D.; Parameshwaran, R.; Kalaiselvam, S.: Experimental investigation on convective heat transfer and rheological characteristics of Cu-TiO 2 hybrid nanofluids. Exp Thermal Fluid Sci. 52, 104–115 (2014)

    Article  Google Scholar 

  38. Tayebi, T.; Chamkha, A.J.: Free convection enhancement in an annulus between horizontal confocal elliptical cylinders using hybrid nanofluids. Numer. Heat Transfer Part A 70(10), 1141–1156 (2016)

    Article  Google Scholar 

  39. Sarkar, J.; Ghosh, P.; Adil, A.: A review on hybrid nanofluids: recent research, development and applications. Renew Sustain Energy Rev. 43, 164–177 (2015)

    Article  Google Scholar 

  40. Bejan, A.: Second-law analysis in heat and thermal design. Adv. Heat Transfer 15, 1–58 (1982)

    Article  Google Scholar 

  41. Bejan, A.: Entropy generation minimization, 2nd edn. CRC, Boca Raton (1996)

    MATH  Google Scholar 

  42. Bejan, A.: A study of entropy generation in fundamental convective heattransfer. J. Heat Transf. 101(4), 718–725 (1979)

    Article  Google Scholar 

  43. Rashad, A.M.; Armaghani, T.; Chamkha, A.J.; Mansour, M.A.: Entropy generation and MHD natural convection of a nano uid in an inclined square porous cavity: Effects of a heat sink and source size and location. Chinese J. Physic 56, 193–211 (2018)

    Article  Google Scholar 

  44. Bouabid, M., Magherbi, M., Hidouri, N., Ben Brahim, A.: Entropy generation at natural convection in an inclined rectangular cavity. Entropy 13, 1020–1033 (2011)

  45. Kaluri, R.S.; Basak, T.: Analysis of entropy generation for distributed heating in processing of materials by thermal convection. Int. J. Heat Mass Transfer 54, 2578–2594 (2011)

    Article  MATH  Google Scholar 

  46. Famouri, M.; Hooman, K.: Entropy generation for natural convection by heated partitions in a cavity. Int. Commun. Heat Mass Transfer 35, 492–502 (2008)

    Article  Google Scholar 

  47. Morsli, S.; Sabeur-Bendehina, A.: Numerical study on natural convection and entropy generation in squares and corrugated cavities. J. Phys. Conf. Ser. 574: 012113 (2015)

  48. Mansour, M.A.; Mahdy, A.; Ahmed, S.E.; Mohamed, S.S.: Entropy analysis for unsteady MHD boundary layer flow and heat transfer of Casson fluid over a stretching sheet. Walailak J. Sci. Tech. WJST 14(2), 169–187 (2017)

    Google Scholar 

  49. Ismael, M.A.; Armaghani, T.; Chamkha, A.J.: Conjugate heat transfer and entropy generation in a cavity filled with a nanofluid saturated porous media and heated by a triangular solid. J. Taiwan Inst. Chem. Eng. 59, 138–151 (2016)

    Article  Google Scholar 

  50. Mahdy, A.: Entropy generation of tangent hyperbolic nanofluid flow past a stretched permeable cylinder: variable wall temperature. Proc. IMechE Part E J. Process Mech. Eng. 233(3): 570–580 (2019)

  51. Martyushev, S.G.; Sheremet, M.A.: Characteristics of Rosseland and P-1 approximations in modeling nonstationary conditions of convection-radiation heat transfer in an enclosure with a local energy source. J. Eng. Thermophys. 21, 111–118 (2012)

    Article  Google Scholar 

  52. Astanina, M.S.; Sheremet, M.A.; Umavathi, J.C.: Unsteady natural convection with temperature dependent viscosity in a square cavity filled with a porous medium. Transp. Porous Media 110, 113–126 (2015)

    Article  MathSciNet  Google Scholar 

  53. Maxwell, J.: A treatise on electricity and magnetism, 2nd edn. Oxford University Press, Cambridge (1904)

    MATH  Google Scholar 

  54. Brinkman, H.C.: The viscosity of concentrated suspensions and solutions. J. Chem. Phys. 20, 571 (1952)

    Article  Google Scholar 

  55. Mahmud, S.; Fraser, R.A.: Magnetohydrodynamic free convection and entropy generation in a square porous cavity. Int. J. Heat Mass Transfer 47, 3245–3256 (2004)

    Article  MATH  Google Scholar 

  56. Magherbi, M.A.; Abbassi, A.; Brahim, A.B.: Entropy generation at the onset of natural convection. Int. J. Heat Mass Transfer 46, 3441–3450 (2003)

    Article  MATH  Google Scholar 

  57. Kim, B.S.; Lee, D.S.; Ha, M.Y.; Yoon, H.S.: A numerical study of natural convection in a square enclosure with a circular cylinder at di erent vertical locations. Int. J. Heat Mass Transfer 51(7–8), 1888–1906 (2008)

    Article  MATH  Google Scholar 

  58. Ilis, G.G.; Mobedi, M.; Sunden, B.: Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls. Int. Commun. Heat Mass Transfer 35, 696–703 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Khalid University, Abha, 62529, Saudi Arabia

    S. E. Ahmed

  2. Mathematics Department, Faculty of Science, South Valley University, Qena, 83523, Egypt

    S. E. Ahmed & A. Mahdy

  3. Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt

    M. A. Mansour

Authors
  1. S. E. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Mansour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Mahdy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Mahdy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmed, S.E., Mansour, M.A. & Mahdy, A. Analysis of Natural Convection–Radiation Interaction Flow in a Porous Cavity with Al2O3–Cu Water Hybrid Nanofluid: Entropy Generation. Arab J Sci Eng 47, 15245–15259 (2022). https://doi.org/10.1007/s13369-021-06495-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-06495-6

Keywords

Search

Navigation