In this paper, focusing on the study of entropy generation (EGN), the convection flow of an eco-friendly nanofluid (N-F) in a rectangular enclosure is studied numerically. The nanoparticles (N-Ps) used are silver N-P, which are obtained in an eco-friendly manner from natural materials. By suspending these N-Ps in an equal mixture of water and ethylene glycol (E-G), the N-F has been prepared. There are two constant-temperature triangular obstacles with height w and base H that are placed on the hot wall. There is a magnetic field (M-F) in the x-direction. To simulate the N-F flow, eco-friendly N-P relations are used, and the equations are solved using the volume control method and the SIMPLE algorithm. The variables include Rayleigh number (Ra), Hartmann number (Ha), H, W, and the volume fraction of silver N-Ps. The effect of these parameters is evaluated on the EGN and Bejan number (Be). Finally, a correlation is expressed for the EGN for a range of variables. The most important results of this paper demonstrate that the addition of silver eco-friendly N-Ps intensifies the EGN so that the addition of 3% of N-Ps enhances the EGN by 3.8%. An increment in the obstacle length reduces the Be barrier while increasing the Ha, which enhances the Be when the convection is strong. Increasing the height of the obstacle intensifies entropy generation.