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MRT-lattice Boltzmann hybrid model for the double diffusive mixed convection with thermodiffusion effect

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Abstract

The goal of this work is to study numerically the thermodiffusion effect (Soret effect) on double diffusive mixed convection inside a driven cavity. The fluid flow is solved by a multiple relaxation time (MRT) lattice Boltzmann method (LBM), whereas the temperature and concentration fields are computed by finite difference method (FDM). To assess numerical accuracy, the model (MRT-LBM coupled with FDM) are verified and validated using data from the literature. Besides reasonable agreement, satisfactory computational efficiency is also found. Thereafter, the model is applied for the thermal diffusion effect on a double-diffusive mixed convection in a cavity with moving lid. Results are obtained depending on various dimensionless parameters. It is found that upon increasing the Soret number, heat transfer is slightly enhanced whereas the thickness of the concentration boundary layer increases, thereby decreasing the mass transfer rate.

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References

  • All-Amiri AM, Khanafer KM, Pop I (2007) Numerical simulation of combined thermal and mass transport in a square lid-driven cavity. Int J Thermal Sci 46:622–671

    Google Scholar 

  • Alleborn N, Raszillier H, Durst F (1999) Lid-Driven Cavity with Heat and Mass Transport. In J Heat Mass Transf 42:833–853

    Article  Google Scholar 

  • Bahloul A, Boutana N, Vasseur P (2003) Double-diffusive and Soret-induced convection in a shallow horizontal porous layer. J Fluid Mech 491:325–352

    Article  Google Scholar 

  • Béghein C, Haghighat F, Allard F (1992) Numerical study of double diffusive natural convection in a square cavity. Int J Heat Mass Transf 35:833–846

    Article  Google Scholar 

  • Ben Cheikh N, Beya RB (2007) Benchmark solution for time-dependent natural convection flows with an accelerated full-multigrid method. Numer Heat Transf Prat B 52:131–151

    Article  Google Scholar 

  • Bennacer R, Mahidjiba A, Vasseur P, Beji H, Duval R (2003) The Soret effect on convection in a horizontal porous domain under cross-temperature and concentration gradients. Int J Numer Methods Heat Fluid Flow 13:199–215

    Article  Google Scholar 

  • Bettaibi S, Kuznik F, Sediki E (2014) Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity. Phys Lett A 378:2429–2435

    Article  Google Scholar 

  • Bettaibi S, Kuznik F, Sediki E, Succi S (2015) Lattice Boltzmann simulation of mixed convection heat transfer in a driven cavity with non-uniform heating of the bottom wall. Commun Theor Phys 63:91–100

    Article  MathSciNet  Google Scholar 

  • Bettaibi S, Kuznik F, Sediki E (2016) Hybrid LBM-MRT model coupled with finite difference method for double-diffusive mixed convection in rectangular enclosure with insulated moving lid. Physica A 444:311–326

    Article  MathSciNet  Google Scholar 

  • Bettaibi S, Kuznik F, Sediki E, Succi S (2021) Numerical study of thermal diffusion and diffusion thermo effects in a differentially heated and salted driven cavity using MRT-lattice Boltzmann finite difference model. Int J Appl Mech 13:2150049

    Article  Google Scholar 

  • Bhatnagar P, Gross E, Krook M (1954) A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511–525

    Article  Google Scholar 

  • Chen Y, Ohashi H, Akiyama MA (1994) Thermal lattice Bhatnagar–Gross–Krook model without nonlinear deviations in macrodynamic equations. Phys Rev E 50:2776–2783

    Article  Google Scholar 

  • d’Humiéres D, Ginzburg I, Krafczyk M, Lallemand P, Luo L (2002) Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos Trans Roy Soc Math Phys Eng Sci 360:437–451

    Article  MathSciNet  Google Scholar 

  • Filippova O, Hanel D (2000) A novel BGK approach for low Mach number combustion. J Comput Phys 158:139–160

    Article  MathSciNet  Google Scholar 

  • Joly F, Vasseur P, Labrosse G (2000) Soret-driven thermosolutal convection in a vertical enclosure. Int Commun Heat Mass Transf 27:755–764

    Article  Google Scholar 

  • Khadiri A, Amahmid A, Hasnaoui M, Rtibi A (2010) Soret effect on double-diffusive convection in a square porous cavity heated and salted from below. Numer Heat Transf A 57:848–868

    Article  Google Scholar 

  • Kuznik F, Rusaouen G (2007) Numerical prediction of natural convection occurring in building components: a double-population lattice Boltzmann method. Numer Heat Tr A Appl 52:315–335

    Article  Google Scholar 

  • Kuznik F, Vareilles J, Rusaouen G, Krauss G (2007) A double-population lattice Boltzmann method with non-uniform mesh for the simulation of natural convection in a square cavity. Int J Heat Fluid Flow 28:862–870

    Article  Google Scholar 

  • Kuznik F, Obrecht C, Rusaouen G, Roux JJ (2010) LBM based flow simulation using GPU computing processor. Comput Math Appl 59:2380–2392

    Article  Google Scholar 

  • Lallemand P, Luo L-S (2003a) Hybrid finite-difference thermal lattice Boltzmann equation. Int J Mod Phys B 17:41–47

    Article  Google Scholar 

  • Lallemand P, Luo L-S (2003b) Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E 68:036706

    Article  MathSciNet  Google Scholar 

  • Makayssi T, Lamsaadi M, Naimi M, Hasnaoui M, Raji A, Bahlaoui A (2008) Natural double diffusive convection in a shallow horizontal rectangular cavity uniformly heated and salted from the side and filled with non-Newtonian power-law fluids: the cooperating case. Energy Convers Manag 49:2016–2025

    Article  Google Scholar 

  • Mansour A, Amahmid A, Hasnaoui M, Bourich M (2004) Soret effect on double diffusive multiple solutions in a square porous cavity subject to cross gradients of temperature and concentration. Int Commun Heat Mass Transf 31:431–440

    Article  Google Scholar 

  • Massaioli F, Benzi R, Succi S (1993) Exponential tails in two-dimensional Rayleigh–Bénard convection. Europhys Lett 21:305–310

    Article  Google Scholar 

  • McNamara GR, Garca AL, Alder BJ (1997) A hydrodynamically correct thermal lattice Boltzmann model. J Stat Phys 97:1111–1121

    Article  MathSciNet  Google Scholar 

  • Mezrhab A, Moussaoui MA, Jami M, Naji H, Bouzidi M (2010) Double MRT thermal lattice Boltzmann method for simulating convective flows. Phys Lett A 374:3499–3507

    Article  Google Scholar 

  • Morega A, Nishimura T (1996) Double diffusive convection by Chebyshev collocation method. Technol Rep Univ 5:259–276

    Google Scholar 

  • Nasreddine O, Nader BC, Brahim BBa, Taieb L (2008) Numerical simulation of two-dimensional Rayleigh–Bénard convection in an enclosure. Comptes Rendus Mécanique 336(5):464–470

  • Pavlo P, Vahala G, Vahala L, Soe M (1998) Linear stability analysis of Thermo–Lattice Boltzmann models. J Comput Phys 139:79–91

    Article  MathSciNet  Google Scholar 

  • Rebai LK, Mojtabi A, Safi MJ, Mohamad AA (2008) Numerical study of thermosolutal convection with soret effect in a square cavity. Int J Numer Methods Heat Fluid Flow 18:561–574

    Article  MathSciNet  Google Scholar 

  • Succi S (2001) The lattice Boltzmann for fluid dynamics and beyond. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Teamah MA, El-Maghlany WM, lany (2010) Numerical simulation of double-diffusive mixed convective flow in rectangular enclosure with insulated moving lid. Int J Thermal Sci 49:1625–1638

    Article  Google Scholar 

  • Tsai R, Huang JS (2009) Numerical study of Soret and dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes. Computat Mater Sci 47:23–30

    Article  Google Scholar 

  • Wolf-Gladrow DA (2000) Lattice-gas cellular automata and lattice Boltzmann models: an introduction. Springer, Berlin, 308p

    Book  Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire de Recherche en Mécanique Appliquée et Systémes (LASMAP), École Polytechnique de Tunis, Université de Carthage, B.P. 743-2078, La Marsa, Tunisie

    Bouthayna Mhamdi & Moez Chafra

  2. Laboratoire des Energies Renouvelable et Matériaux Avancés (LERMA), Université Internationale de Rabat (UIR), Rocade Rabat-Salé, Rabat-Sala El Jadida, 11100, Maroc

    Soufiene Bettaibi & Omar Jellouli

Authors
  1. Bouthayna Mhamdi
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  2. Soufiene Bettaibi
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  3. Omar Jellouli
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  4. Moez Chafra
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Correspondence to Soufiene Bettaibi.

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Mhamdi, B., Bettaibi, S., Jellouli, O. et al. MRT-lattice Boltzmann hybrid model for the double diffusive mixed convection with thermodiffusion effect. Nat Comput 21, 393–405 (2022). https://doi.org/10.1007/s11047-022-09884-4

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  • DOI: https://doi.org/10.1007/s11047-022-09884-4

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