In this study, two-component displacement of a time-dependent non-Newtonian fluid by a Newtonian fluid in a two-dimensional inclined channel is simulated. Using a special multi-component model of the lattice Boltzmann method that is called He-Chen-Zhang, made it possible to do the simulations for non-uniform density and very high viscosity ratios. The main focus of this study is altering the flow pattern and displacement efficiency by Applying Electro- and magneto-hydrodynamic fields, using added nanoparticles and heating the channel walls. Displacement efficiency in different cross-sections, thickness of the static wall layer at the top and bottom of the channel, development of interfacial instabilities, magnitude of generated forces and, temperature distribution in the simulation environment are analyzed comprehensively to fully control the fingering structure. Investigation of injected fluid movement in the other one and displacement efficiency showed that enhancement in the power of the electric field is associated with displacement efficiency alteration in various longitudinal sections of the channel. However, removing the residual layer at the top and bottom of the fingering structure doesn’t cause the total efficiency of displacement (Mt) to change significantly since the axial motion of the invading fluid is weakened. In contrast, applying magnetic field, increasing the Hartmann number and changing the rotation angle of the coordinate system (to 180), enhances the axial velocity and displacing ability of this fluid. Furthermore, for Ha = 10 and θ = 0, with the transverse velocity rising, displacement efficiency for longitudinal sections close to the channel axis decreases and the occurrence of interfacial instabilities is inevitable.