The second law of thermodynamics for free convection of hybrid nanofluid within the partially open domain with a heated baffle placed at the center is studied computationally. The horizontal surfaces of a chamber are insulated while the right side is partially open and the left border is maintained at fixed temperature (Tc). The control equations are solved employing the finite volume schemes. The emerging parameters, namely, solid volume fraction (ϕ), Hartmann number (Ha = 0 and 50), magnetic field orientation angle (0 < γ < π/2), and dimensionless temperature difference (Ω) are analyzed for a fixed magnitude of the Rayleigh number. The outcomes are demonstrated employing streamlines, isotherms, local and mean Nusselt numbers, and mean entropy generation. The outcomes establish that, for both horizontally or vertically placed heat-generating baffles, the mean Nu and entropy production are raising functions of ϕ. Increasing the Hartmann number suppresses the convective circulation and heat transport, it paradoxically reduces the average entropy production rate. Furthermore, increasing the magnetic field inclination angle from 0 to π/2 generally leads to enlarged thermal stratification, with improved thermal transport for vertical baffles at γ = π/2 but diminished transport for horizontal baffles. The dimensionless temperature difference (Ω) growth leads to a decrease in the entropy generation owing to thermal energy transfer, working material friction, and Lorentz magnetic influence.