This study deals the influence of fins and inclined magnetic field with nanofluid in single lid-driven and double lid-driven cavities. The effect of fins length and distance between them is also given attention. A two dimensional system of partial differential equations has been discretized by employing Galerkin finite element method. A finite element method involving the cubic polynomials (IP3) has been implemented to compute for velocity and temperature fields while the pressure is approximated by quadratic (IP2) finite element space of functions. The system of discretized equations is simplified using the adaptive Newton's method. The implemented finite element code is validated with an experimental study. Simulations are performed for various ranges of pertinent parameters such as distance among fins (between 0.2 and 0.5), Hartmann number (between 0 and 100), length of fins (between 0.25 and 0.50), Richardson numbers (between 0.01 and 1), number of fins (between 2 and 5) and magnetic field inclination (between 0 degrees and 90 degrees). Two cases of fins such as adiabatic and isothermal are also discussed in view of average Nusselt number. It is inferred that the fluid flow and heat transfer are significantly affected in the presence of fins comparing to the absence of fins. The smallest convective heat transfer is achieved when the distance between adiabatic fins is 0.3. Fluid flows faster at the angle gamma = 90 degrees than gamma = o degrees in both cases. Also, isotherms form larger red hot zones inside the cavity at gamma = 90 degrees. Isothermal fins have much more weakening effect on convective heat transfer than the adiabatic fins.