A lattice Boltzmann analysis for MHD convection of Graphene-water nanofluid in a channel filled with porous media under local thermal non-equilibrium conditions

Subject Areas : Journal of New Applied and Computational Findings in Mechanical Systems

mostafa ahmadi ¹ , Iman Zahmatkesh ² , Hamid Reza Goshayeshi ³

1 - Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 -
3 - Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Received: 2024-10-05 Accepted : 2024-11-27 Published : 2024-04-23

Keywords: Porous medium, Local thermal-non-equilibrium, Forced convection, Magnetic field, LBM,

Abstract :

This paper considers numerical simulation of MHD forced convection of Graphene-water nanofluid in a channel filled with porous media. To this aim, non-dimensional form of the Darcy-Brinkman-Forchheimer equations in non-equilibrium conditions are adopted and solved through programming in FORTRAN software. Simulations are undertaken according to the thermal lattice Boltzmann method with single relaxation time, adopting three distribution functions for velocity, nanofluid temperature, and temperature of the porous medium. Then, effects of different parameters including the Darcy number, the medium porosity, the nanoparticles fraction, and the Hartmann number on the Nusselt number and the local thermal-non-equilibrium are analyzed. The results show that with increase in the Darcy number, the nanoparticles fraction, and the medium porosity or decrease in the Hartmann number, the Nusselt number increases. It is also found that the local thermal-non-equilibrium has direct relation with the Darcy number and the medium porosity and inverse relation with the Hartmann number and the nanoparticles fraction.

References:

[1] Vafai, K., (2015), Handbook of Porous Media, CRC Press. [2] Kaviany, M., (1995), Principles of Heat Transfer in Porous Media, Second ed., Spring-Verlag, New York.
[3] Nield, D.A., Bejan, A., (2017), Convection in Porous Media, 5th ed, Springer.
[4] Kuznetsov, A., Nield, D.A., (1998), Effect of Local Thermal Non–equilibrium on the Onset of Convection in a
Porous Medium Layer Saturated by a Nanofluid, Transport in Porous Media 83, pp.425–436. [5] Rees, D.A., Pop, I., (2005), Local Thermal Non–Equilibrium in Porous Media Convection, Transport Phenomena in Porous Media III, pp. 147–173.
[6] Abdollahpour, A., Aminian, J., (2019), Analytical Study of the Effect of Intensity of Local Thermal Non– Equilibrium in Porous Foams, Sharif Mechanical Engineering 35, pp.23–32.
[7] Mabrouk, R., Naji, H., Dhahri, H., Hammouda, S., Younsi, Z., (2020), Numerical Investigation of Porosity Effect on a PCM’s Thermal Performance in a Porous Rectangular Channel via Thermal Lattice Boltzmann Method, International Communications in Heat and Mass Transfer 119, 104992.
[8] Parhizi, M., Torabi, M., Jain, A., (2021), Local Thermal Non–Equilibrium (LTNE) Model for Developed Flow in Porous Media with Spatially–Varying Biot number, International Journal of Heat and Mass Transfer 164, 120538.
[9] Choi, SUS., (1998), Nanofluid Technology: Current Status and Future Research, Argonne National Lab, Argonne.
[10] Ebrahimdoust Roodposhti, P., Bani Asadi, H., Ramezani Saadatabadi, A., Akbari Dahoei, I., (2018), Experimental Investigation of the Effect of Adding Graphene on the Improvement of the Convection Heat Transfer Coefficient in the Water/Ethylene Glycol System in Laminar Flow, Applied Researches in Chemical Engineering – polymer 3, pp. 3–19.
[11] Zahmatkesh, I., Ardekani, R., (2020), Effect of Magnetic Field Orientation on Nanofluid Free Convection in a Porous Cavity: A Heat Visualization Study, Journal of Thermal Engineering 6, pp.170–186.
[12] Zahmatkesh, I., Habibi Shandiz, M.R., (2022), MHD Double–Diffusive Mixed Convection of Binary Nanofluids through a Vertical Porous Annulus Considering Buongiorno’s Two–Phase Model, Journal of Thermal Analysis and Calorimetry 147, pp. 173–180.
[13] Fakur, M., Vahabzadeh, A., Ganji, D., (2017), Study of Heat Transfer and Flow of Nanofluid in Permeable Channel in the Presence of Magnetic Field, Propulsion and Power Research 4, pp. 50–62.
[14] Izadi, M., Mohebbi, R., Delouei, A., Sajjadi, H., (2019), Natural Convection of a Magnetizable Hybrid Nanofluid inside a Porous Enclosure subjected to Two Variable Magnetic Fields, International Journal of Mechanical Sciences 151, pp. 154–169.
[15] Zahmatkesh, I., Shandiz M.R.H., (2019), Optimum Constituents for MHD Heat Transfer of Nanofluids within Porous Cavities, Journal of Thermal Analysis and Calorimetry 138, pp. 1669–1681.
[16] Aliu, O., Sakidin, H., Foroozesh, J., Yahya, N., (2020), Lattice Boltzmann Application to Nanofluids Dynamics–A Review, Journal of Molecular Liquids 300, 112284.
[17] Nazari, M., Kayhani, M.H., Mohebbi, R., (2013), Heat Transfer Enhancement in Channel Partially Filled with Porous Block: Lattice Boltzmann Method, International Journal of Modern Physics 24, pp. 1350060.
[18] Fen, X.B., Liu, Q., He, Y.L., (2020), Numerical Simulations of Convection Heat Transfer in Porous Media using a Cascaded Lattice Boltzmann Method, International Journal of Heat and Mass Transfer 151, pp. 119–410.
[19] Moradi, I., D’Orazio, A., (2023), Lattice Boltzmann Method Pore-scale Simulation of Fluid Flow and Heat Transfer in Porous Media: Effect of Size and Arrangement of Obstacles into a Channel, Engineering Analysis with Boundary Elements 152, pp.83–103.
[20] Bazkhane, S., Zahmatkesh, I., (2021), Heat Transfer of Nanofluid in a Channel with Magnetic Field and Porous Obstacle using the Darcy–Brinkman–Forchheimer Model in the LBM Method, Journal of Applied and Computational Sciences in Mechanics 32, pp.153–172.
[21] Sajjadi, H., Delouei, A.A., Izadi, M., Mohebbi, R., (2019), Investigation of MHD Natural Convection in a Porous Media by Double MRT Lattice Boltzmann Method utilizing MWCNT–Fe3O4/Water Hybrid Nanofluid, International Journal of Heat and Mass Transfer 132, pp. 1087–1104.
[22] Zou, Q., He, X., (1997), On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model, Physics of Fluids 9, pp. 1591–1598.
[23] Sukop, M.C., Thorne, D.T.J., (2006), Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, Springer–Verlag, Berlin, Heidelberg.
[24] Ben Ltaifa, K., D’Orazio, A., Naji, H., Hammouda, S., Mabrouk, R., Dhahri, H., (2023), Simulating Nanofluid Forced Convection Flow by Thermal Lattice Boltzmann Approach, Journal of Thermophysics and Heat Transfer 37, pp. 64–78.
[25] Namadchian, H., Zahmatkesh, I., Alavi, S.M.A., (2021), Numerical Simulation of Nanofluid Flow in an Annular Channel with Porous Barriers using Composition Darcy-Brinkman-Frechheimer Model and Two–Phase Mixture Model, Amirkabir Mechanical Engineering Journal 3, pp. 1897–1914.
[26] Zahmatkesh, I., Naghedifar, S.A., (2018), Pulsating Nanofluid Jet Impingement onto a Partially Heated Surface Immersed in a Porous Layer, Jordan Journal of Mechanical and Industrial Engineering 12, pp. 99–107.