The entropy generation due to steady, incompressible micropolar fluid flow in a rectangular duct with slip and convective boundary conditions is calculated. An external uniform magnetic field is applied which is directed arbitrarily in a plane perpendicular to the flow direction. The governing partial differential equations of momentum, angular momentum and energy are solved numerically using finite difference method. The obtained velocity, microrotation and temperature distributions are then used to evaluate the entropy generation and Bejan number. The effects of various parameters on the entropy generation and Bejan number are discussed through graphs.