Numerical Investigation of Fluid Flow and Heat Transfer Inside a 2D Enclosure with Three Hot Obstacles on the Ramp under the Influence of a Magnetic Field
Abstract
This paper focuses on solving the fluid flow and heat transfer equations inside a two-dimensional square enclosure containing three hot obstacles affected by gravity and magnetic force placed on a ramp using Boltzmann method (LBM) applying multiple relaxation times (MRT). Although, the Lattice Boltzmann with MRT is a complex technique, it is a relatively new, stable, fast and high-accurate one. The main objective of this research was to numerically model the fluid flow and ultimately obtaining the velocity field, flow and temperature contour lines inside a two-dimensional enclosure. The results and their comparisons for different types of heat transfer revealed that free or forced heat transfer has a considerable impact on the heat transfer and stream lines. This can be controlled by modifying the Richardson number. It is revealed that changing the intensity of the magnetic field (Hartman number) has an appreciable effect on the heat transfer.
Keywords:
Lattice Boltzmann, multiple relaxation times, two-dimensional enclosure, hot obstacles, ramp, Hartmann numberDownloads
References
D. H. Rothman,S. Zaleski, “Lattice-gas Model of Phase Separation: Interfaces, Phase Transitions, and Multiphase Flow”, Rev. Mod. Phys., Vol. 66, No. 4, pp. 1417-1479, 1994 DOI: https://doi.org/10.1103/RevModPhys.66.1417
S. Chen, G. Doolen, “Lattice Boltzmann Method for Fluid Flows”, Ann. Rev. Fluid Mech., Vol. 30, pp. 329-364, 1998 DOI: https://doi.org/10.1146/annurev.fluid.30.1.329
S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon, Oxford, 2001
G. Bella, S. Ubertini, M. Bertolino, “Computational Fluid Dynamics for Low and Moderate Reynolds Numbers through the Lattice Boltzmann Method”, Int. J. Comp. Num. Analysis Applications, Vol. 3, No. 1, pp. 83-115, 2003
G. Bella, M. Presti, S. Succi, “Mass Transfer Improvements in Catalytic Converter Channels:a Hybrid BGK-Finite Volume Numerical Simulation Method”, Society Automotive Engineers, Paper, No. 972907, 1997 DOI: https://doi.org/10.4271/972907
Q. Zah, X. He, “On Pressure and Velocity Flow Boundary Conditions and Bounceback for the Lattice Boltzmann BGK Model”, Physics of Fluids, Vol. 9, pp. 1591-1598, 1997 DOI: https://doi.org/10.1063/1.869307
O. Filippova, D. Hänel, “Grid refinement for latticeBGK Models”, J. Comput. Phys. Vol. 147, pp. 219- 228, 1998 DOI: https://doi.org/10.1006/jcph.1998.6089
T. Lee, C. L. Lin, “A Characteristic Galerkin Method for Discrete Boltzmann Equation”, J. Comput. Phys., Vol. 171, pp. 336-356, 2001 DOI: https://doi.org/10.1006/jcph.2001.6791
N. Rudraiah, R. Barron, M. Venkatachalappa, C. Subbaraya, “Effect of magnetic field on free convection in rectangular enclosure”, International Journal of Engineering Science, Vol. 33, No. 8, pp. 1075-1084, 1995 DOI: https://doi.org/10.1016/0020-7225(94)00120-9
H. Nemati, M. Farhadi, K. Sedighi, H. Ashorynejad, E. Fattahi, “Magneticfield effects on natural convection flow ofnanofluid in rectangular cavity using the Lattice Boltzmann model”, Scientia Iranica, Vol. 19, No. 2, pp. 303-310, 2012 DOI: https://doi.org/10.1016/j.scient.2012.02.016
A. Ghofrani, M. Dibaei, A. Hakim Sima, M. Shafii, “Experimental Investigation on laminar forced convection heat transfer of ferro fluids under an alternating magnetic field”, Experimental Thermal and Fluid Science, Vol. 49, pp. 193-200, 2013 DOI: https://doi.org/10.1016/j.expthermflusci.2013.04.018
I. Mejri, A. Mahmoudi, M. A. Abbassi, A. Omri, “Lattice Boltzmann Simulation of MHD Natural Convection in Nanofluid-Filled EnclosureWith Non-Uniform Heating on Both SideWalls”, International Journal of Mathematical, Computational, Natural and Physical Engineering, Vol. 8,No. 1, pp. 75-91, 2014 DOI: https://doi.org/10.1109/ICCMREA.2014.6843796
M. Hemmat Esfe, M. Akbari, A. Karimipour, “Mixed Convection in a Lid-Driven Cavity with an Inside Hot Obstacle Filled by an Al2O3–Water Nanofluid”, J. Applied Mechanic and Thermal Physics, Vol. 56, No. 3, pp. 443–453, 2015 DOI: https://doi.org/10.1134/S0021894415030141
T. Zhang, D. Che, “Double MRT thermal lattice Boltzmann simulation for MHD naturalconvection of nanofluids in an inclined cavity with four square heatsources”, J. Heat and Mass Transfer, Vol. 94, pp. 87–100, 2016 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2015.11.071
M. Amani, M. Ameri, A. Kasaeian, “Investigating the convection heat transfer of Fe3O4 nanofluid in a porous metal foam tube under constant magnetic field”, Experimental Thermal and Fluid Science, Vol. 82, pp. 439–449, 2016 DOI: https://doi.org/10.1016/j.expthermflusci.2016.12.003
E. Esmaeili, R. Ghazanfar Chaydareh, S. A. Rounaghi, “The influence of the alternating magnetic field on the convective heat transfer properties of Fe3O4-containing nanofluids through the Neel and Brownian mechanisms”, Applied Thermal Engineering, Vol. 110, pp. 1212–1219, 2017 DOI: https://doi.org/10.1016/j.applthermaleng.2016.09.014
T. Hayat, S. Farooq, A. Alsaedi, B. Ahmad, “Hall and radial magnetic fi eld effects on radiative peristaltic fl ow of Carreau – Yasuda fl uid in a channel with convective heat and mass transfer”, Journal of Magnetism and Magnetic Materials, Vol. 412, pp. 207–216, 2016 DOI: https://doi.org/10.1016/j.jmmm.2016.03.046
M. M. Larimi, A. Ghanaat, A. Ramiar, A. A. Ranjbar, “Forced convection heat transfer in a channel under the influence of various non-uniform transverse magnetic field arrangements”, International Journal of Mechanical Sciences, Vol. 118, pp. 101–112, 2016 DOI: https://doi.org/10.1016/j.ijmecsci.2016.09.023
M. Mehrali, E. Sadeghinezhad, A. R. Akhiani, S. Tahan Latibari, H. S. C. Metselaar, A. S. Kherbeet, M. Mehrali, “Heat transfer and entropy generation analysis of hybrid graphene/Fe3O4 ferro-nanofluid flow under the influence of a magnetic field”, Powder Technology, Vol. 308, pp. 149–157, 2016 DOI: https://doi.org/10.1016/j.powtec.2016.12.024
S. V. Mousavi, M. Sheikholeslami, M. Gorji Bandpy, M. Barzegar Gerdroodbary, “The Influence of magnetic field on heat transfer of magnetic nanofluid in a sinusoidal double pipe heat exchanger”, Chemical Engineering Research and Design, Vol. 113, pp. 112–124, 2016 DOI: https://doi.org/10.1016/j.cherd.2016.07.009
E. Sadeghinezhad,M. Mehrali, A. R. Akhiani, S. Tahan Latibari, A. Dolatshahi-Pirouz, H. S. C. Metselaar, M. Mehrali, “Experimental study on heat transfer augmentation of graphene based ferrofluids in presence of magnetic field”, Applied Thermal Engineering, Vol. 114, pp. 415–427, 2017 DOI: https://doi.org/10.1016/j.applthermaleng.2016.11.199
F. Selimefendigil, H. F. Oztop, N. Abu-Hamdeh, “Natural convection and entropy generation in nanofluid filled entrapped trapezoidal cavities under the influence of magnetic field”, Entropy, Vol. 18, No. 2, pp. 1–22, 2016 DOI: https://doi.org/10.3390/e18020043
L. Sha, Y. Ju, H. Zhang, J. Wang, “Experimental investigation on the convective heat transfer of Fe3O4/water nanofluids under constant magnetic field”, Applied Thermal Engineering, Vol. 113, pp. 566–574, 2017 DOI: https://doi.org/10.1016/j.applthermaleng.2016.11.060
M. Sheikholeslami, I. Hashim, S. Soleimani, “Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape, Vol 34, pp. 56-64, 2013 DOI: https://doi.org/10.1155/2013/831725
M. Sheikholeslami, K. Vajravelu, “Nanofluid flow and heat transfer in a cavity with variable magnetic field”, Applied Mathematics and Computation, Vol. 298, pp. 272–282, 2017 DOI: https://doi.org/10.1016/j.amc.2016.11.025
J. Wanga, D. Wanga, P. Lallemand, L. Luoc, “Lattice Boltzmann simulations of thermal convective flows in two dimensions”, Computers and Mathematics with Application, Vol. 65, pp. 262–286, 2013 DOI: https://doi.org/10.1016/j.camwa.2012.07.001
C. Rettinger, Fluid flow simulations using the lattice Boltzmann method with multiple relaxation times, Bachelor Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, 2013
K. Khanafer, K. Vafai, M. Lightstone, “Buoyancy-driven heat transfer enhancement in two-dimensional enclosure utilizing nanofluids”, International Journal of Heat and Mass Transfer, Vol. 46, No. 19, pp. 162–186, 2003 DOI: https://doi.org/10.1016/S0017-9310(03)00156-X
M. Nazari, S. Ramzani, “Natural Convection in a Square Cavity with a Heated Obstacle Using Lattice Boltzmann Method”, J. Heat and Mass Transfer , Vol. 32, pp. 127–133, 2011
Downloads
How to Cite
License
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
