Abstract This work studies the thermogravitational transmission and thermal radiation of micropolar nanoliquid within a porous chamber in the presence of the uniform magnetic influence. The model includes the single-phase nanofluid approach, local thermal equilibrium approximation and Darcy law for the processes within the porous structure. The Galerkin finite element method with the structured non-uniform mesh is used to calculate the formulated equations. The key characteristics are the Darcy–Rayleigh number Ra = 10–1000, Darcy number Da = 10−5–10−1, porosity e = 0.1–0.9, nanoparticles concentration φ = 0–0.04, radiation parameter Rd = 0–2, vortex viscosity characteristic Δ = 0–2, and Hartmann number Ha = 0–50. It has been ascertained the energy transport intensification with thermal radiation parameter, Darcy–Rayleigh number, porosity and nanoparticles concentration. Also, the results indicate that the average Nusselt number reduces with an increment of the Hartmann number for high values of the Rayleigh number, while for low magnitudes of the Rayleigh number a weak change of the average Nusselt number can be found.