The present numerical study scrutinizes the effect of uniform Lorentz force on the thermogravitational energy transport and entropy production of nanosuspension in an open domain with a heat-generating solid element. The left border is kept at low temperature (Tc) whilst the horizontal borders are assumed to be adiabatic. Finite volume method (FVM) is employed to work out the heat and mass transfer equations. For fixed value of Rayleigh number (Ra = 107), numerical analysis was optimized for wide ranges of nanoparticle volume fraction (ϕ = 1%–4%), thermal conductivity ratio of a heat generating body (k⁎ = 0.1–5), Hartmann parameter (Ha = 0–100), angle of inclined magnetic field (γ = 0°–90°) and non-dimensional temperature drop (Ω = 0.001–0.1). The numerical solutions were analyzed employing patterns of temperature and stream function as well as average Nusselt number and entropy lines. The outcomes indicated that, an increasing magnetic parameter Ha leads to reduction of mean Nu and the rate of entropy production. An addition of nano-sized particles enhances the energy transport and average entropy production for the system. It is also revealed that the maximum energy transport strength occurs at high thermal conductivity ratio (k⁎ = 5).