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Numerical Investigation of Mixed Convection Heat Transfer in a Lid-Driven Cavity with Two Embedded Rotating Cylinders Based on Immersed Boundary-Lattice Boltzmann Method

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Advances in Thermal Science and Energy (JITH 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

In this study, laminar mixed convection flow in a lid-driven cavity with two embedded rotating cylinders maintained at a hot temperature is examined. The upper wall of the enclosure is in motion and maintained at a cold temperature when the vertical walls are insulated. In this paper, the numerical method used is the lattice Boltzmann method (LBM). The numerical simulations are performed to investigate the Richardson number's effect on temperature/velocity fields and the rate of heat transfer. The immersed boundary method (IBM) is used to deal with the boundary conditions in complex geometries. It is found that for low Richardson number values, the natural convection mode is dominated by forced convection mode. In addition, increasing the Richardson number leads to a decrease in the rate of heat transfer.

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Abbreviations

\({\varvec{c}}_{{\varvec{i}}}\):

Discrete lattice velocity in the direction \(i\)

c:

Microscopic velocity fluid particle

\(f_{i}\):

Distribution function of the velocity field

\(f_{i}^{eq}\):

Equilibrium distribution function of velocity field

\(F_{i}\):

External force

\(g_{i}\):

Distribution function of thermal field

\(g_{i}^{eq}\):

Equilibrium distribution function of thermal field

g:

Gravitational acceleration

L:

Characteristic length

Pr:

Prandtl number \({\text{Pr}} = \frac{\vartheta }{\alpha }\)

Ra:

Rayleigh number \(Ra = g\beta \Delta TL^{3} /\alpha \upsilon\)

Re:

Reynolds number \({\text{Re}} = \frac{U \times L}{\upsilon }\)

Ri:

Richardson number \({\text{Ri}} = \frac{Ra}{{Re^{2} Pr}}\)

T:

Dimensionless temperature

Th:

Hot temperature

Tc:

Cold temperature

T0:

Reference temperature

U:

Characteristic velocity

u,v:

Vertical and horizontal components of velocity

u = (u, v):

Macroscopic fluid velocity

α:

Thermal diffusivity

β:

Thermal expansion coefficient

∆t:

Lattice time step

∆x:

Lattice space step

ωi:

Weighting factor in the direction i

ρ:

Fluid density

ϑ:

Fluid viscosity

τf:

Flow relaxation time

τg:

Energy relaxation time

b:

Boundary

c:

Cold

eq:

Equilibrium

h:

Hot

i:

Direction i

w:

Wall

f:

Density distribution function

g:

Internal energy distribution function

BGK:

Bhatnagar, Gross and Krook

CFD:

Computational Fluid Dynamics

LBM:

Lattice Boltzmann Method

SRT:

Simple Relaxation Time

References

  1. Purusothaman, A.: Investigation of natural convection heat transfer performance of the QFN-PCB electronic module by using nanofluid for power electronics cooling applications. Adv. Powder Technol. 29(4), 996–1004 (2018)

    Article  CAS  Google Scholar 

  2. Ratzel, A.C., Hickox, C.E., Gartling, D.K.: Techniques for reducing thermal conduction and natural convection heat losses in annular receiver geometries (1979)

    Google Scholar 

  3. Iwatsu, R., Hyun, J.M., Kuwahara, K.: Mixed convection in a driven cavity with a stable vertical temperature gradient. Int. J. Heat Mass Transf. 36(6), 1601–1608 (1993)

    Article  CAS  Google Scholar 

  4. Msaad, A.A., et al.: Numerical simulation of thermal chaotic mixing in multiple rods rotating mixer. Case Stud. Therm. Eng. 10, 388–398 (2017)

    Article  Google Scholar 

  5. Farkach, Y., Derfoufi, S., Ahachad, M., Bahraoui, F., Mahdaoui, M.: Numerical investigation of natural convection in concentric cylinder partially heated based on MRT-lattice Boltzmann method. Int. Commun. Heat Mass Transf. 132, 105856 (2022)

    Article  Google Scholar 

  6. Derfoufi, S., Moufekkir, F., Mezrhab,A.: Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM. Int. J. Numer. Methods Heat Fluid Flow (2018)

    Google Scholar 

  7. Dalvi, S., Bali, S., Nayka, D., Kale, S.H., Gohil, T.B.: Numerical study of mixed convective heat transfer in a lid-driven enclosure with rotating cylinders. Heat Transf. Res. 48(4), 1180–1203 (2019)

    Article  Google Scholar 

  8. Keya, S.T., Yeasmin, S., Rahman, M.M., Karim, M.F., Amin, M.R.: Mixed convection heat transfer in a lid-driven enclosure with a double-pipe heat exchanger. Int. J. Thermofluids 13, 100131 (2022)

    Article  Google Scholar 

  9. Kashyap, D., Dass, A.K.: Influence of cavity inclination on mixed convection in a double-sided lid-driven cavity with a centrally inserted hot porous block. Int. J. Therm. Sci. 181, 107732 (2022)

    Article  Google Scholar 

  10. Selimefendigil, F., Öztop, H.F.: Numerical study of MHD mixed convection in a nanofluid filled lid driven square enclosure with a rotating cylinder. Int. J. Heat Mass Transf. 78, 741–754 (2014)

    Article  Google Scholar 

  11. Chen, H., Chen, S., Matthaeus, W.H.: Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A 45(8), R5339 (1992)

    Article  CAS  PubMed  Google Scholar 

  12. Boussinesq, J.: Thōrie analytique de la chaleur mise en harmonie avec la thermodynamique et avec la thōrie mc̄anique de la lumi_re: Refroidissement et c̄hauffement par rayonnement, conductibilit ̄des tiges, lames et masses cristallines, courants de convection, thōrie mc̄, vol. 2. Gauthier-Villars (1903)

    Google Scholar 

  13. Girimaji, S.: Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. American Institute of Aeronautics and Astronautics (2013)

    Google Scholar 

  14. Guo, Z., Zheng, C., Shi, B.: Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65(4), 46308 (2002)

    Article  Google Scholar 

  15. Feng, Z.-G., Michaelides, E.E.: The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems. J. Comput. Phys. 195(2), 602–628 (2004)

    Article  Google Scholar 

  16. Delouei, A.A., Nazari, M., Kayhani, M.H., Succi, S.: Immersed boundary—thermal lattice Boltzmann methods for non-Newtonian flows over a heated cylinder: a comparative study. Commun. Comput. Phys. 18(2), 489–515 (2015)

    Article  Google Scholar 

  17. Tao, S., He, Q., Chen, B., Qin, F.G.F.: Distribution function correction-based immersed boundary lattice Boltzmann method for thermal particle flows. Comput. Part. Mech. 8(3), 459–469 (2021)

    Article  Google Scholar 

  18. Shu, C., Xue, H., Zhu, Y.D.: Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method. Int. J. Heat Mass Transf. 44(17), 3321–3333 (2001)

    Article  Google Scholar 

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Authors and Affiliations

  1. ETTE, FSTT, Université de Abdelmalek Essaadi Tetouan, Tetouan, Morocco

    Younes Farkach, Soufiane Derfoufi & Mustapha Mahdaoui

Authors
  1. Younes Farkach
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  2. Soufiane Derfoufi
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  3. Mustapha Mahdaoui
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Corresponding author

Correspondence to Younes Farkach .

Editor information

Editors and Affiliations

  1. ENSA Paris-Val de Seine, Paris, France

    Fazia Ali-Toudert

  2. Faculty of Science and Techniques, Abdelmalek Essaâdi University, Tétouan, Morocco

    Abdeslam Draoui

  3. IPEIS, University of Sfax, Sfax, Tunisia

    Kamel Halouani

  4. Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

    Mohammed Hasnaoui

  5. National Engineering School of Monastir, University of Monastir, Monastir, Tunisia

    Abdelmajid Jemni

  6. IUSTI, Aix-Marseille University, Marseille, France

    Lounès Tadrist

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Farkach, Y., Derfoufi, S., Mahdaoui, M. (2024). Numerical Investigation of Mixed Convection Heat Transfer in a Lid-Driven Cavity with Two Embedded Rotating Cylinders Based on Immersed Boundary-Lattice Boltzmann Method. In: Ali-Toudert, F., Draoui, A., Halouani, K., Hasnaoui, M., Jemni, A., Tadrist, L. (eds) Advances in Thermal Science and Energy. JITH 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-43934-6_16

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  • DOI: https://doi.org/10.1007/978-3-031-43934-6_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43933-9

  • Online ISBN: 978-3-031-43934-6

  • eBook Packages: EngineeringEngineering (R0)

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