In this paper, the effects of radiation and magnetic field on the convection heat transfer rate and the nanofluid entropy generation in a diagonal square cavity with a conductor fin have been numerically investigated. A fin with a thermal conductivity coefficient of k* = 100 is located on one of the walls of the cavity. A volumetric heat source is considered in the fluid that is producing heat in the form of radiation. The effect of this source is added as a source to the energy equation and its value is shown by the Rd radiation parameter. Mass, momentum, and energy conservation equations in two-dimensional mode are discretization with finite difference method based on the control volume and solved using the simple algorithm. The model used for the thermal conductivity coefficient is the phenomenon model, taking into account the Brownian motion of the particles. In this paper, the effects of Rayleigh numbers, Hartmann numbers, radiation parameter and volume percentages of nanoparticles on the entropy generation and heat transfer have been investigated. The results show that increasing the Rayleigh number and reducing the Hartmann number increases the Nusselt number. Alternatively, adding 6% of the nanoparticles to the base fluid in the absence of radiation increases the heat transfer rate and entropy generation by 5.9% and 16.6%, respectively. By adding the radiation parameter, Rd = 3, and the volume percentage of nanopartides of 6%, the heat transfer rate and total entropy generation increased by 3.4% and 11.2%, respectively. It was also observed that increasing the radiation parameter at high Rayleigh numbers increases the Nusselt number and entropy generation and decreases the Bejan number. Increasing the heat transfer rate is more significant by increasing the radiation parameter at higher Rayleigh numbers. (C) 2018 Elsevier Ltd. All rights reserved.