In this work entropy generation and heat transfer for magnetohydrodynamic (MHD) forced convection flow in a micro duct filled with a porous medium are investigated using a modified axisymmetric Lattice Boltzmann Method. In modeling the flow, the Brinkman–Forchheimer-extended Darcy model is incorporated in momentum equations. The Local Thermal Non-Equilibrium (LTNE) assumption between fluid and solid phases is adopted to investigate heat transfer. All terms of viscous dissipation effects are included in the energy equation of the fluid phase. Our attention is focused on the effects of different values of Hartmann number Ha, Knudsen number, Kn, Eckert number, Ec, and Biot number, Bi, on the flow, Nusselt number and entropy generation.