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.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
- C p :
Specific heat capacity (J kg−1 K−1)
- g :
Gravity (m s−2)
- H :
- k :
Thermal conductivity (W m−1 K−1)
- h :
Convective heat transfer coefficient (W m−2 K−1)
- S T,l :
Local entropy (J K−1)
- T :
- u,v :
Dimensional velocity components in x and y coordinates (m s−1)
- U,V :
Non-dimensional velocity components in X and Y directions
- W :
- x,y :
Cartesian coordinates (m)
- X,Y :
- \(\alpha\) :
Thermal diffusivity (m2 s−1)
- \(\beta\) :
Thermal expansion coefficient (K−1)
- \(\rho\) :
Density (Kg m−3)
Dynamic viscosity (kg m−1 s−1)
- \(\varphi\) :
- \(\upsilon\) :
Kinematic viscosity (m2 s−1)
- \(\theta\) :
- \(\emptyset\) :
Volume fractions of nanoparticles
- \(\eta\) :
Normalized average Bejan Number
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.
Chen S, Doolen GD. Lattice Boltzmann Method For Fluid Flows. Annu Rev Fluid Mech. 1998;30:329–64.
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.
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.
Xia C, Murthy JY. Buoyancy-driven flow transitions in deep cavities heated from below. J Heat Transf. 2002;124(4):650–9.
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.
Shan X. Simulation of Rayleigh–Benard convection using a lattice Boltzmann method. Phys Rev E. 1997;55(3):2780–8.
Cross MC, Hohenberg PC. Pattern formation outside of equilibrium. Rev Mod Phys. 1993;65(3):851–1112.
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.
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.
Choi SUS, Eastman J. Enhancing thermal conductivity of fluids with nanoparticles. Tech Rept: Argonne National Lab, USA; 1995.
Putra N, Roetzel W, Das SK. Natural convection of nanofluids. Heat Mass Transf. 2003;39:775–84.
Wen D, Ding Y. Formulation of nanofluids for natural convective heat transfer Applications. Int J Heat Fluid Flow. 2005;26(6):855–64.
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.
Li CH, Peterson G. Experimental studies of natural convection heat transfer of Al2O3/DI water nanoparticle suspensions (nanofluids). Adv Mech Eng. 2010. https://doi.org/10.1155/2010/742739.
Nnanna AG. Experimental model of temperature-driven nanofluid. J Heat Transf. 2007;129(6):697–704.
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.
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.
Kim J, Kang YT, Choi CK. Analysis of convective instability and heat transfer characteristics of nanofluids. Phys Fluids. 2004;16(7):2395–401.
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. https://doi.org/10.1115/1.4034484.
Park HM. Rayleigh Benard convection of nanofluids based on the pseudo single-phase continuum model. Int J Therm Sci. 2015;90:267–78.
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.
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.
Ashorynejad HR, Shahriari AR. MHD natural convection of hybrid nanofluid in an open wavy cavity. Results in Phys. 2018;9:440–55.
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.
Kefayati GHR. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution. Powder Tech. 2013;243:171–83.
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.
Abu-Nada E. Rayleigh–Bénard convection in nanofluids: effect of temperature dependent properties. Int J of Therm Sci. 2011;50:1720–30.
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.
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.
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.
Mahmud S, Fraser RA. The second law analysis in fundamental convective heat transfer problems. Int J Therm Sci. 2003;42(2):177–86.
Bejan A. A study of entropy generation in fundamental convective heat transfer. J Heat Transf. 1979;101(4):718–25.
Jing CJC, Liu J. The character of entropy production in Rayleigh–Bénard convection. Entropy. 2014;16(9):4960–73.
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.
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.
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. https://doi.org/10.1080/15567036.2020.1800868.
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.
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.
Vijaybabu TR. Influence of permeable circular body and CuO–H2Onanofluid on buoyancy-driven flow and entropy generation. Int J Mech Sci. 2020;166:105240.
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.
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.
Hamilton RL, Crosser OK. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Funda. 1962;1(3):187–91.
Brinkman HC. The viscosity of concentrated suspensions and solution. The J Chem Phys. 1952;20(4):571.
Perumal DA, Dass AK. Lattice Boltzmann Simulation of two- and three-dimensional incompressible thermal flows. Heat Transf Eng. 2014;35:1320–33.
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.
Magherbi M, Abbassi H, Brahim AB. Entropy generation at the onset of natural convection. Int J Heat Mass Transf. 2003;46(18):3441–50.
Oliveski RDC, Macagnan MH, Copetti JB. Entropy generation and natural convection in rectangular cavities. Appl Therm Eng. 2009;29:1417–25.
Clever RM, Busse FH. Transition to time dependent convection. J Fluid Mech. 1974;65:625.
Corcione M. Rayleigh–Bénard convection heat transfer in nanoparticle suspensions. Int J Heat Fluid Flow. 2011;32:65–77.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
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). https://doi.org/10.1007/s10973-020-10496-2
- Rayleigh–Benard (R–B) convection
- Lattice Boltzmann method
- Two-dimensional rectangular cavity