This study deals with the influence of a rotating cylinder inside the square cavity and multiwalled carbon nanotube–iron oxide () hybrid nanofluid with water. 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 has been implemented to compute for velocity, temperature, and concentration fields, while the pressure is approximated by quadratic finite element space of functions. The adaptive Newton method is implemented to solve the discrete system of nonlinear equations. Numerical simulations are performed for different ranges of pertinent parameters such as the nanoparticles volume fraction (between 0 and 0.3%), angular velocity (between and ), Richardson number (between 0.01 and 3), and rotating cylinder sizes (between 0.2 and 0.4), and three different thermal conditions on the cylinder are investigated: namely, the adiabatic cylinder, cold cylinder, and hot cylinder. It is inferred that the average Nusselt number increases, when the cylinder rotates clockwise. On the contrary, the average Nusselt temperature increases, when the cylinder rotates counterclockwise. Moreover, the local Nusselt number increasing instead of enhancing the rotational speed of the circular cylinder toward the clockwise rotation. The flow philosophy is presented in the form of isotherms, streamlines, and some appropriate plots.