Lattice Boltzmann method for MHD natural convection of CuO/water nanofluid in a wavy-walled cavity with sinusoidal temperature distribution

Document Type : Original Research Paper


Department of Mechanical Engineering, University of Zabol, Zabol, Iran


In this paper, natural convection heat transfer of CuO-water Nanofluid within a wavy-walled cavity and subjected to a uniform magnetic field is examined by adopting the lattice Boltzmann model. The left wavy wall is heated sinusoidal, while the right flat wall is maintained at the constant temperature of Tc. The top and the bottom horizontal walls are smooth and insulated against heat and mass. The influence of pertinent parameters such as solid volume fraction of nanoparticles (φ), Rayleigh number (Ra), Hartmann number (Ha) and phase deviation of sinusoidal boundary condition (Φ) are investigated on flow and heat transfer fields. Results show that the heat transfer decreases with the increase of the Hartmann number, but it increases by the increment of Rayleigh number and nanoparticle volume fraction. The magnetic field augments the effect produced by the presence of nanoparticles at Ra = 104 and 105 in contrast with Ra = 103. Moreover, the greatest effects of nanoparticles are observed for different values of the phase deviation with an increase in Rayleigh number. This study can, provide useful insight for enhancing the MHD natural convection heat transfer performance within wavy-walled cavity and sinusoidal temperature distribution.


[1] de Vahl Davis G.Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for numerical methods in fluids. 1983 May 1;3(3):249-64.
[2] Barakos G, Mitsoulis E, Assimacopoulos D. Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions. International Journal for Numerical Methods in Fluids. 1994 Apr 15;18(7):695-719.
[3] Fusegi T, Hyun JM, Kuwahara K, Farouk B.A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure. International Journal of Heat and Mass Transfer. 1991 Jun 1;34(6):1543-57.
[4] Chol SU. Enhancing thermal conductivity of fluids with nanoparticles. ASME-Publications-Fed. 1995 Nov 12;231:99-106.
[5] Kim J, Kang YT, Choi CK. Analysis of convective instability and heat transfer characteristics of nanofluids. Physics of fluids. 2004 Jul;16(7):2395-401.
[6] Putra N, Roetzel W, Das SK. Natural convection of nano-fluids. Heat and Mass Transfer. 2003 Sep 1;39(8-9):775-84.
[7] Khanafer K,Vafai K, Lightstone M.Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International journal of heat and mass transfer. 2003 Sep 30;46(19):3639-53.
[8] Rudraiah N, Barron RM, Venkatachalappa M,Subbaraya CK. Effect of a magnetic field on free convection in a rectangular enclosure. International Journal of Engineering Science. 1995 Jun1;33(8):1075-84.
[9] Kahveci K, Öztuna S. MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure. European Journal of Mechanics-B/Fluids. 2009 Dec 31;28(6):744-52.
[10] Sathiyamoorthy M, Chamkha A. Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall (s). International Journal of Thermal Sciences. 2010 Sep 30;49(9):1856-65.
[11] Saha LK, Hossain MA, Gorla RS. Effect of Hall current on the MHD laminar natural convection flow from a vertical permeable flat plate with uniform surface temperature. International journal of thermal sciences. 2007 Aug 1;46(8):790-801.
[12] Oztop HF, Oztop M, Varol Y. Numerical simulation of magnetohydrodynamic buoyancy-induced flow in a non-isothermally heated square enclosure. Communications in Nonlinear Science and Numerical Simulation. 2009 Mar 31;14(3):770-8.
[13] Succi S. The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford university press; 2001 Jun 28.
[14] Aidun CK, Clausen JR. Lattice- Boltzmann method for complex flows. Annual review of fluid mechanics. 2010;42:439-72.
[15] Gao D, Chen Z. Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media. International Journal of Thermal Sciences. 2011 Apr 30;50(4):493-501.
[16] Filippova O, Hänel D. Boundary-fitting and local grid refinement for lattice-BGK models. International Journal of Modern Physics C. 1998 Dec;9(08):1271-9.
[17] Mei R, Luo LS, Shyy W.An accurate curved boundary treatment in the lattice Boltzmann method. Journal of computational physics. 1999 Nov 1;155(2):307-30.
[18] Guo Z, Zheng C, Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E. 2002 Apr 10;65(4):046308.
[19] Ghasemi B, Aminossadati S , Raisi A. Magnetic field effect on natural convection in a nanofluid-filled square enclosure. International Journal of Thermal Sciences. 2011 Sep 30;50(9):1748-56.
[20] Kefayati GR. Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method. International Communications in Heat and Mass Transfer. 2013 Jan 31;40:67-77.
[21] Kefayati GR. Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with sinusoidal temperature distribution. Powder technology. 2013 Jul 31;243:171-83.
[22] Mliki B, Abbassi MA, Omri A, Zeghmati B. Augmentation of natural convective heat transfer in linearly heated cavity by utilizing nanofluids in the presence of magnetic field and uniform heat generation/absorption. Powder Technology. 2015 Nov 30;284:312-25.
[23] Sheikholeslami M, Gorji-Bandpy M, Ganji D. Investigation of Nanofluid Flow and Heat Transfer in Presence of Magnetic Field Using KKL Model. Arabian Journal for Science & Engineering (Springer Science & Business Media BV). 2014 Jun 1;39(6).
[24] Sheremet MA, Pop I, Roşca NC. Magnetic field effe-ct on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno's mathematical model. Journal of the Taiwan Institute of Chemical Engineers. 2016 Apr 30;61:211-22.
[25] Sabeur-Bendehina A, Imine O, Adjlout L. Laminar free convection in undulated cavity with non-uniform boundary conditions. Comptes Rendus Mécanique. 2011 Jan 1;339(1):42-57.
[26] A. Shahriari: Numerical simulation of free convection heat transfer of nanofluid in a wavy-wall cavity with sinusoidal temperature distribution, using lattice Boltzmann method, Modares Mechanical Engineering 16 (2016) 143-154.
[27] Xuan Y, Roetzel W. Conceptions for heat transfer correlation of nanofluids. International Journal of heat and Mass transfer. 2000 Oct 1;43(19):3701-7.
[28] Brinkman HC. The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics. 1952 Apr;20(4):571-.
[29] Hamilton RL, Crosser OK. Thermal conductivity of heterogeneous two-component systems. Industrial & Engineering chemistry fundamentals. 1962 Aug;1(3):187-91.
[30] Kao PH, Yang RJ. Simulating oscillatory flows in Rayleigh–Benard convection using the lattice Boltzmann method. International Journal of Heat and Mass Transfer. 2007 Aug 31;50(17):3315-28.
[31] Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Annual review of fluid mechanics. 1998 Jan;30(1):329-64.
[32] Sheikholeslami M, Gorji-Bandpy M, Vajravelu K. Lattice Boltzmann simulation of magnetohydrodynamic natural convection heat transfer of Al2O3–water nanofluid in a horizontal cylindrical enclosure with an inner triangular cylinder. International Journal of Heat and Mass Transfer. 2015 Jan 31;80:16-25.
[33] Tiwari RK, Das MK. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. International Journal of Heat and Mass Transfer. 2007 May 31;50(9):2002-18.
[34] Lin KC, Violi A. Natural convection heat transfer of nanofluids in a vertical cavity: Effects of non-uniform particle diameter and temperature on thermal conductivity. International Journal of Heat and Fluid Flow. 2010 Apr 30;31(2):236-45.
[35] Krane RJ, Jessee J. Some detailed field measurements for a natural convection flow in a vertical square enclosure. In1st ASME-JSME thermal engineering joint conference 1983 Mar 20 (Vol. 1, pp. 323-329). ASME New York.
[36] Oztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International journal of heat and fluid flow. 2008 Oct 31;29(5):1326-36.
[37] Cho CC, Chen CL. Natural convection heat transfer performance in complex-wavy-wall enclosed cavity filled with nanofluid. International Journal of Thermal Sciences. 2012 Oct 31;60:255-63.
[38] Kefayati GR. Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field. Theoretical and Computational Fluid Dynamics. 2013 Nov 1:1-9.
[39] Ahrar AJ, Djavareshkian MH. Lattice Boltzmann simulation of a Cu-water nanofluid filled cavity in order to investigate the influence of volume fraction and magnetic field specifications on flow and heat transfer. Journal of Molecular Liquids. 2016 Mar 31;215:328-38.