The entropy analysis of the magnetohydrodynamic (MHD) thermal convection flow of a nanofluid past an inverted cone with suction/injection is presented in this article. The Buongiorno's model is adopted for nanofluid transport, considering the Brownian motion and thermophoresis effects. The governing partial differential conservation equations and wall and freestream boundary conditions are rendered into a nondimensional form and solved computationally using the Keller‐Box finite‐difference method. The entropy analysis due to MHD fluid flow and viscous dissipation is also included. The numerical results are presented graphically for the impact of various thermophysical parameters on velocity, temperature, nanoparticle volume fraction, shear stress rate, heat transfer rate, and mass transfer. Validations with earlier solutions in the literature are also included. A comprehensive description of the simulations is included. It is observed that velocity and temperature are enhanced with the increase in Brownian motion parameter values, whereas concentration, entropy, and Bejan number are reduced. An increase in the thermophoresis parameter and buoyancy ratio parameter reduces velocity and entropy, but increases temperature, concentration, and Bejan number. An increase in the magnetic parameter is found to decrease velocity, entropy generation number, and Bejan number, but it increases temperature and concentration. Also, an increase in the suction/injection parameter is seen to reduce velocity, temperature, concentration, and Bejan number, but the entropy generation number is observed to increase. The study finds applications in heat exchangers technology, materials processing, solar energy systems, cooling and heating processes, environmental applications, geothermal energy storage, and so on.