This numerical study seeks to inquire the influence of magnetic field (uniform and non-uniform) and uniform absorption/production of heat on entropy generation during hybrid nanofluid conjugate heat transfer. The enclosure cold wall is designed in three shapes: smooth, diagonal and curved, in order to appraise the effect of this parameter on the fluid current. The correctness of the obtained results from the existing simulation via lattice Boltzmann method was checked and confirmed with the outcomes of previous researches. The results of simulation reveal that the flow strength, the amount of heat transfer and entropy production can be reduced by applying magnetic field. A lower reduction of the mean Nusselt number is achieved by non-uniform application of a magnetic field. The influence of changing the type of magnetic field applied becomes more apparent with augmentation of the Hartmann number values. Augmentation of the absorption/production of heat coefficient leads to decline in the mean Nusselt number, which this impact increases with increment of the Hartmann number. In cases where thermal conduction is prevailing, the influence of increment of the nanoparticles volume fraction on the mean Nusselt number growth becomes more apparent. Since heat transfer is a function of the ratio of thermal conductivity and Rayleigh number, enhancement of these two parameters increases the impact of the Hartmann number. By changing the shape of the wall, it is possible to manage the characteristics of the fluid flow significantly. The least effect of the magnetic field and its type changes is related to the diagonal wall. The entropy production decreases with augmentation of the Hartmann number and increases with augmentation of thermal conductivity ratio, Rayleigh number and coefficient of the absorption/production of heat.