Skip to main content

Comparative studies on air, water and nanofluids based Rayleigh–Benard natural convection using lattice Boltzmann method: CFD and exergy analysis


The present study incorporates laminar natural convection and entropy generation in Rayleigh–Benard (R–B) convection with air, water and alumina–water nanofluid as working fluids. The fluid flow and energy equations are solved using D2Q9 and D2Q5 LBM models, respectively. The effects of Rayleigh numbers (Ra = 5 × 103, 104, 105) and volume fractions (\(\emptyset\) = 0 to 0.08) of nanoparticles on heat transfer and irreversibility are investigated. Results show that the heat transfer evaluated based on Nusselt number is enhanced due to addition of nanoparticles in the base fluid. The maximum enhancement in Nusselt number is found to be 13.93% at Ra = 105 with 8% of nanoparticle in base fluid. The various irreversibilities considered in this study are thermal, fluid flow and total irreversibility, where fluid flow and total irreversibilities in the study depend on irreversibility ratio. The irreversibility ratios taken into account are 10–2, 10–3, 10–4 and 10–5. One facet of study shows the deviation in onset of critical Rayleigh number for air is 1.58%. The other facet indicates dimensionless heat transfer, fluid flow and total irreversibility decrease with the increase in volume fraction of nanoparticles in the base fluid. The analyzed results of irreversibilities are presented in normalized form. In addition, dimensionless entropy generation maps and Bejan number contours are also plotted.

This is a preview of subscription content, access via your institution.

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20



Bejan number

C p :

Specific heat capacity (J kg1 K1)

g :

Gravity (m s2)

H :

Height (m)

k :

Thermal conductivity (W m1 K1)

h :

Convective heat transfer coefficient (W m2 K1)


Prandtl number


Rayleigh number

S T,l :

Local entropy (J K1)

T :

Temperature (K)

u,v :

Dimensional velocity components in x and y coordinates (m s1)

U,V :

Non-dimensional velocity components in X and Y directions

W :

Width (m)

x,y :

Cartesian coordinates (m)

X,Y :

Non-dimensional coordinates

\(\alpha\) :

Thermal diffusivity (m2 s1)

\(\beta\) :

Thermal expansion coefficient (K1)

\(\rho\) :

Density (Kg m3)


Dynamic viscosity (kg m1 s1)

\(\varphi\) :

Irreversibility parameter

\(\upsilon\) :

Kinematic viscosity (m2 s1)

\(\theta\) :

Non-dimensional temperature

\(\emptyset\) :

Volume fractions of nanoparticles

\(\eta\) :

Normalized average Bejan Number






Pure fluid








  1. 1.

    Xu A, Shi L, Zhao TS. Accelerated lattice Boltzmann simulation using GPU and Open ACC with data management. Int J Heat Mass Transf. 2017;109:577–88.

    Article  Google Scholar 

  2. 2.

    Chen S, Doolen GD. Lattice Boltzmann Method For Fluid Flows. Annu Rev Fluid Mech. 1998;30:329–64.

    Article  Google Scholar 

  3. 3.

    Perumal DA, Dass AK. A Review on the development of lattice Boltzmann Computation of macro fluid flows and heat transfer. Alexandria Eng J. 2015;54:955–71.

    Article  Google Scholar 

  4. 4.

    Xu A, Shyy W, Zhao TS. Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries. Acta Mech Sin. 2017;33:555–74.

    CAS  Article  Google Scholar 

  5. 5.

    Xia C, Murthy JY. Buoyancy-driven flow transitions in deep cavities heated from below. J Heat Transf. 2002;124(4):650–9.

    Article  Google Scholar 

  6. 6.

    Hartlep T, Tilgner A, Busse FH. Large scale structures in Rayleigh–Benard convection at high Rayleigh numbers. Phys Rev Lett. 2003;91(6):8–11.

    Article  CAS  Google Scholar 

  7. 7.

    Shan X. Simulation of Rayleigh–Benard convection using a lattice Boltzmann method. Phys Rev E. 1997;55(3):2780–8.

    CAS  Article  Google Scholar 

  8. 8.

    Cross MC, Hohenberg PC. Pattern formation outside of equilibrium. Rev Mod Phys. 1993;65(3):851–1112.

    CAS  Article  Google Scholar 

  9. 9.

    Xu K, Lui SH. Rayleigh–Benard simulation using the gas-kinetic Bhatnagar–Gross–Krook scheme in the incompressible limit. Phys Rev E. 1999;60(1):464–70.

    CAS  Article  Google Scholar 

  10. 10.

    Xu A, Shi L, Xi HD. Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number. Int J Heat Mass Transf. 2019;140:359–70.

    Article  Google Scholar 

  11. 11.

    Choi SUS, Eastman J. Enhancing thermal conductivity of fluids with nanoparticles. Tech Rept: Argonne National Lab, USA; 1995.

    Google Scholar 

  12. 12.

    Putra N, Roetzel W, Das SK. Natural convection of nanofluids. Heat Mass Transf. 2003;39:775–84.

    Article  Google Scholar 

  13. 13.

    Wen D, Ding Y. Formulation of nanofluids for natural convective heat transfer Applications. Int J Heat Fluid Flow. 2005;26(6):855–64.

    CAS  Article  Google Scholar 

  14. 14.

    Ho C, Liu W, Chang Y, Lin C. Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. Int J Therm Sci. 2010;49(8):1345–53.

    CAS  Article  Google Scholar 

  15. 15.

    Li CH, Peterson G. Experimental studies of natural convection heat transfer of Al2O3/DI water nanoparticle suspensions (nanofluids). Adv Mech Eng. 2010.

    Article  Google Scholar 

  16. 16.

    Nnanna AG. Experimental model of temperature-driven nanofluid. J Heat Transf. 2007;129(6):697–704.

    CAS  Article  Google Scholar 

  17. 17.

    Abu-Nada E, Oztop HF. Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid. Int J Heat Fluid Flow. 2009;30(4):669–78.

    CAS  Article  Google Scholar 

  18. 18.

    Khanafer K, Vafai K, Lightstone M. Buoyancy driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf. 2003;46(9):3639–53.

    CAS  Article  Google Scholar 

  19. 19.

    Kim J, Kang YT, Choi CK. Analysis of convective instability and heat transfer characteristics of nanofluids. Phys Fluids. 2004;16(7):2395–401.

    CAS  Article  Google Scholar 

  20. 20.

    Siddheshwar PG, Kanchana C, Kakimoto Y, Nakayama A. Steady finite-amplitude Rayleigh-Benard convection in nanoliquids using a two-phase model: Theoretical answer to the phenomenon of enhanced heat transfer. J Heat Transf. 2017.

    Article  Google Scholar 

  21. 21.

    Park HM. Rayleigh Benard convection of nanofluids based on the pseudo single-phase continuum model. Int J Therm Sci. 2015;90:267–78.

    Article  Google Scholar 

  22. 22.

    Zhang L, Li YR, Zhang JM. Numerical simulation of Rayleigh-Bénard convection of nanofluids in rectangular cavities. J Mech Sci Tech. 2017;31(8):4043–50.

    Article  Google Scholar 

  23. 23.

    Eslamian M, Ahmed M, El-Dosoky MF, Saghir MZ. Effect of thermophoresis on natural convection in a Rayleigh–Benard cell filled with a nanofluid. Int J Heat Mass Transf. 2015;81:142–56.

    CAS  Article  Google Scholar 

  24. 24.

    Ashorynejad HR, Shahriari AR. MHD natural convection of hybrid nanofluid in an open wavy cavity. Results in Phys. 2018;9:440–55.

    Article  Google Scholar 

  25. 25.

    Kefayati GHR. Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method. Int Commun Heat Mass Transf. 2013;40:67–77.

    CAS  Article  Google Scholar 

  26. 26.

    Kefayati GHR. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution. Powder Tech. 2013;243:171–83.

    CAS  Article  Google Scholar 

  27. 27.

    Bilal E, Bachir G, Mojtabi A, Fakih C, Catherine M, Mojatabi C. Modeling of Rayleigh–Bénard natural convection heat transfer in nanofluids. Comptes Rendus Mécanique. 2010;338:350–4.

    Article  CAS  Google Scholar 

  28. 28.

    Abu-Nada E. Rayleigh–Bénard convection in nanofluids: effect of temperature dependent properties. Int J of Therm Sci. 2011;50:1720–30.

    CAS  Article  Google Scholar 

  29. 29.

    Savithiri S, Pattamatta A, Das SK. Rayleigh–Benard convection in water-based alumina nanofluid: a numerical study. Numer Heat Transf Part A Appl. 2017;71(2):202–14.

    CAS  Article  Google Scholar 

  30. 30.

    Hwang KS, Lee JH, Jang SP. Buoyancy-driven heat transfer of water-based Al2O3nanofluids in a rectangular cavity. Int J Heat Mass Transf. 2007;50:4003–10.

    CAS  Article  Google Scholar 

  31. 31.

    Haddad Z, Nada EA, Oztop HF, Mataoui A. Natural convection in nanofluids: are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement? Int J Therm Sci. 2012;57:152–62.

    CAS  Article  Google Scholar 

  32. 32.

    Mahmud S, Fraser RA. The second law analysis in fundamental convective heat transfer problems. Int J Therm Sci. 2003;42(2):177–86.

    Article  Google Scholar 

  33. 33.

    Bejan A. A study of entropy generation in fundamental convective heat transfer. J Heat Transf. 1979;101(4):718–25.

    Article  Google Scholar 

  34. 34.

    Jing CJC, Liu J. The character of entropy production in Rayleigh–Bénard convection. Entropy. 2014;16(9):4960–73.

    Article  Google Scholar 

  35. 35.

    Wei Y, Wang Z, Qian Y. A numerical study on entropy generation in two- dimensional Rayleigh Benard convection at different Prandtl number. Entropy. 2017;19(9):19–22.

    Article  CAS  Google Scholar 

  36. 36.

    Xu A, Shi L, Xi HD. Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection. Phys Fluids. 2019;31:125101.

    Article  CAS  Google Scholar 

  37. 37.

    Fattahi A. LBM simulation of thermo-hydrodynamic and irreversibility characteristics of a nanofluid in microchannel heat sink under affecting a magnetic field. Energy Sour Part A Recovery Util Environ Effects. 2020.

    Article  Google Scholar 

  38. 38.

    Aghakhani S, Pordanjani AH, Afrand M, Sharifpur M, Meyer JP. Natural convective heat transfer and entropy generation of alumina/water nanofluid in a tilted enclosure with an elliptic constant temperature: applying magnetic field and radiation effects. Int J Mech Sci. 2020;174:105470.

    Article  Google Scholar 

  39. 39.

    Tayebi T, Chamkha AJ. Entropy generation analysis due to MHD natural convection flow in a cavity occupied with hybrid nanofluid and equipped with a conducting hollow cylinder. J Therm Anal Calorim. 2020;139:2165–79.

    CAS  Article  Google Scholar 

  40. 40.

    Vijaybabu TR. Influence of permeable circular body and CuO–H2Onanofluid on buoyancy-driven flow and entropy generation. Int J Mech Sci. 2020;166:105240.

    Article  Google Scholar 

  41. 41.

    Vijaybabu TR, Dhinakaran S. MHD Natural convection around a permeable triangular cylinder inside a square enclosure filled with Al2O3–H2O nanofluid: an LBM study. IntJ Mech Sci. 2019;153–154:500–16.

    Article  Google Scholar 

  42. 42.

    Baghsaz S, Rezanejad S, Moghimi M. Numerical investigation of transient natural convection and entropy generation analysis in a porous cavity filled with nanofluid considering nanoparticles sedimentation. J Mol Liq. 2019;279:327–41.

    CAS  Article  Google Scholar 

  43. 43.

    Hamilton RL, Crosser OK. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Funda. 1962;1(3):187–91.

    CAS  Article  Google Scholar 

  44. 44.

    Brinkman HC. The viscosity of concentrated suspensions and solution. The J Chem Phys. 1952;20(4):571.

    CAS  Article  Google Scholar 

  45. 45.

    Perumal DA, Dass AK. Lattice Boltzmann Simulation of two- and three-dimensional incompressible thermal flows. Heat Transf Eng. 2014;35:1320–33.

    CAS  Article  Google Scholar 

  46. 46.

    Karki P, Yadav AK, Perumal DA. Study of adiabatic obstacles on natural convection in a square cavity using Lattice Boltzmann method. J Therm Sci Eng Appl. 2019;11:1–16.

    Article  CAS  Google Scholar 

  47. 47.

    Magherbi M, Abbassi H, Brahim AB. Entropy generation at the onset of natural convection. Int J Heat Mass Transf. 2003;46(18):3441–50.

    Article  Google Scholar 

  48. 48.

    Oliveski RDC, Macagnan MH, Copetti JB. Entropy generation and natural convection in rectangular cavities. Appl Therm Eng. 2009;29:1417–25.

    Article  Google Scholar 

  49. 49.

    Clever RM, Busse FH. Transition to time dependent convection. J Fluid Mech. 1974;65:625.

    Article  Google Scholar 

  50. 50.

    Corcione M. Rayleigh–Bénard convection heat transfer in nanoparticle suspensions. Int J Heat Fluid Flow. 2011;32:65–77.

    CAS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Ajay Kumar Yadav.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Karki, P., Perumal, D.A. & Yadav, A.K. Comparative studies on air, water and nanofluids based Rayleigh–Benard natural convection using lattice Boltzmann method: CFD and exergy analysis. J Therm Anal Calorim (2021).

Download citation


  • Rayleigh–Benard (R–B) convection
  • Lattice Boltzmann method
  • Two-dimensional rectangular cavity
  • Irreversibility
  • Nanofluid