A 2D numerical investigation has been carried out to obtain the heat transfer performance of hybrid (Al2O3 + Ag) nanofluid in a lid driven cavity over solid block under the influence of uniform as well as non-uniform magnetic field. The geometrical domain consists of a cavity containing nanofluid that is driven by means of lid moving in one direction. This circulating nanofluid will extract enormous amount of heat from the solid block underneath the cavity resulting in conjugate heat transfer. A homogenous solver based on the finite volume method with conjugate heat transfer was developed and adopted in the existing study. The heat efficient hybrid nanofluid (HyNF) pair (2.4 vol.% Ag + 0.6 vol.% Al2O3) obtained by Nimmagadda and Venkatasubbaiah  is used in the present investigation. Moreover, efficient non-uniform sinusoidal magnetic field identified by Nimmagadda et al.  is also implemented and compared with uniform magnetic field. Furthermore, the magnetic field is applied over the geometrical domain along the two axial directions separately and the effective heat transfer performance is obtained. The significant impact of extensive parameters like Reynolds number, nanoparticle type, nanoparticle concentration, magnetic field type, magnetic field location and the strength of the magnetic field on heat transfer performance are systematically analyzed and presented.