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This work aims to study the conjugate natural convection of micropolar nanofluid within a porous enclosure considering local thermal non-equilibrium model. The Galerkin finite element method is employed to solve the coupled and non-linear equations. The governing parameters are Darcy–Rayleigh number Ra = 10–1000, porosity ε = 0.1–0.9, interface parameter H = 1–1000, Kr = 0.1–10, volume fraction of the nanofluid φnf = 0–0.08, vortex viscosity parameter Δ = 0–3, the width of the solid wall d = 0.1–0.4 and ratio of wall thermal conductivity to that of the base fluid Rk = 0.1–10. It has been revealed that the power of micro-rotations increases with Darcy–Rayleigh number, vortex viscosity parameter, ratio of wall thermal conduction to that of base fluid, interface parameter (Kr and H) in conditions that declines with thickness of the solid wall and porosity. The Nusselt numbers for both phases in the porous medium significantly decline as thickness of the solid wall rises, with the exception of d = 0.35. Also, it can be concluded as the porosity parameter increases for the passing flow, the nanofluid flow is governed by the classic Navier-Stokes equations.