A Lattice Boltzmann Study of Nano-Magneto-Hydrodynamic Flow With Heat Transfer and Entropy Generation Over a Porous Backward Facing-Step Channel

Abstract

In this study, a numerical investigation of a magneto-hydrodynamic (MHD) and backward-facing nanofluidic flow was performed using the thermal lattice Boltzmann method (LBM) with multiple distribution functions to handle dynamic and thermal fields, including the magnetic force. The Cu-H<sub>2</sub>O based nanofluid is considered as the working fluid, and the Brinkman-Forchheimer model is adopted to mathematically formulate the porous medium. In addition, heat transfer, pumping power, thermal performance index, and entropy generation within a backward-facing step open-ended channel with adiabatic walls has been investigated. A preliminary comparison of the simulation outcome with available numerical results shows that the in-house built code aptly describes the nanofluid flow behavior and heat transfer process. Afterward, a parametric examination of the impact of Hartmann number (0.0 ≤ <i>Ha</i> ≤ 25), Darcy number (10<sup>-3</sup> ≤ <i>Da</i> ≤ 1.0), Eckert number (0 ≤ <i>Ec</i> ≤ 10), nanoparticles volume fraction (0% ≤ φ ≤ 4%), and magnetic field tilt (0 ≤ γ ≤ π/2) on streamlines, isotherms, friction factor (<i>C<sub>f</sub></i>), pressure drop, pumping power, average Nusselt number (<i>Nu</i><sub>av</sub>), thermal performance index (<i>PI</i>), and average entropy generation ratio (S*) has been conducted. Based on the findings obtained, it can be stated that increases in the nanoparticles' volume fraction and <i>Ha</i> rise <i>Nu</i><sub>av</sub>, pressure drop (Δ<i>P</i>), and pumping power (<i>P<sub>pump</sub></i>) occur. On the other hand, <i>PI</i> and S* drop when φ and <i>Ha</i> rise. Bejan's number has also been shown to increase with <i>Ha</i>. It also turned out that increasing the magnetic field tilt involves a rise in heat transfer, pressure drop, and pumping power, except for <i>PI</i> and entropy generation.