### 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.

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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

S. Chen, G. Doolen, “Lattice Boltzmann Method for Fluid Flows”, Ann. Rev. Fluid Mech., Vol. 30, pp. 329-364, 1998

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

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

O. Filippova, D. Hänel, “Grid refinement for latticeBGK Models”, J. Comput. Phys. Vol. 147, pp. 219- 228, 1998

T. Lee, C. L. Lin, “A Characteristic Galerkin Method for Discrete Boltzmann Equation”, J. Comput. Phys., Vol. 171, pp. 336-356, 2001

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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