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The single relaxation D2Q9 lattice Boltzmann method (LBM) is run in the current research beside the generalized power law model for simulation of non‐Newtonian magneto‐hydrodynamics (MHD) laminar flow field inside a channel with local symmetric constriction. Analytical results of non‐Newtonian fluid flow in a channel without magnetic field, as well as Newtonian fluid flow at various Hartmann No., are used to validate the numerical model. Then, fluid flow simulation is performed for non‐Newtonian fluid with different power law index at various Hartmann No. (Ha) whereas Reynolds No. are set to be constant in all cases. The present non‐Newtonian fluid can be achieved by adding various nanoparticles such as MWCNT to the base fluid. To explore the effect of magnetic Reynolds No. (Rem), the fluid flows with different magnetic resistivity are also simulated. Results show that the separation can be controlled by a magnetic field with the penalty of larger friction coefficient and pressure loss along the channel length. In fact, for a specified Rem, the higher the Ha, the larger the pressure loss. It is also observed that the pressure loss is larger for fluids flow with higher power law index and lower Rem.

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Rarefied pressure-driven gaseous flow with heat transfer in a microchannel with a backward facing micro-step is investigated in this paper using the lattice Boltzmann method (LBM) in slip and transition flow regimes. In a novel approach, a two-relaxation-time LB equation is used to solve the flow velocity and the single-relaxation-time to handle the heat transfer. The asymmetric relaxation time is determined by equating the analytical second-order slip velocity boundary condition and the slip velocity obtained from applying the implemented bounce back specular boundary condition in the LBM. A second-order implicit temperature jump boundary condition is also implemented to capture the rarefaction effect on the fluid temperature at walls. Velocity slip, temperature jump, centerline temperature, and Nusselt number variations are evaluated for channels with and without the micro-step for a wide range of the Knudsen number. Effects of the micro-step on the rarefied gaseous flow and convective heat transfer are evaluated and discussed. The numerical model is verified by comparing with direct simulation Mont Carlo results.