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Entropy generation with time periodic thermal boundary conditions have numerous applications in heat exchangers, electronic devices, automatic and thermal control systems. The present research focuses on mixed convective hydromagnetic electrically conducting fluid flow in a vertical annulus using thermodynamic concepts, in the presence of induced magnetic field along with entropy generation and time periodic boundary conditions. The governing equations related to the present model are solved using finite element method. Also to predict heat transport features in the vertical annulus, artificial neural network – backpropogated Levenberg Marquardt algorithm is adopted. The steady and periodic profiles of velocity, skin friction, temperature and induced magnetic field are illustrated graphically for specific range of pertinent parameters to demonstrate significant aspects of the results. It is noted that increase in Hartmann number enhances the entropy generation near the outer cylinder, which illustrates that the fluid friction and magnetic field influence is maximum at the outer cylinder surface. The Bejan number in the annulus reduces with increase in viscous heating parameter. Results indicate that raise in the Prandtl number diminishes the thermal boundary layer thickness. As a result of decrease in the intensity of heating the boundary walls, a raise in Strouhal number lowers the fluid temperature profile. The generalized correlation is expressed to predict heat transport features in the annulus using artificial neural network – backpropogated Levenberg Marquardt algorithm. [ABSTRACT FROM AUTHOR]