The current study presents a computational investigation of mixed convective heat transfer in a square enclosure containing power‐law fluid. An active flow modulator is employed in the form of a flat plate with negligible thickness, and the mixed convection is achieved through clockwise rotation of the plate. The rotation of the plate is modeled by incorporating a moving mesh technique. The solution is then obtained by applying the Finite Element Technique under the arbitrary Lagrangian–Eulerian framework. Numerical validation is performed with contemporary research studies consisting of rotating plates to justify the accuracy of the present study. The study is conducted at constant Prandtl number Pr = 1.0 and Reynolds number Re = 500 while varying the power‐law index (0.6 ≤ n ≤ 1.4) and the Richardson number (0.1 ≤ Ri ≤ 10.0). The results have been presented in terms of the flow and thermal fields, spatially averaged Nusselt number, spatially averaged power consumption by the plate, and the velocity and temperature profile in the enclosure. The numerical findings indicate that a higher Richardson number encourages heat transfer. For the shear‐thinning fluid, a 37% thermal augmentation is observed in comparison to the Newtonian fluid at Ri = 10. However, in the case of shear‐thickening fluid, thermal performance was reduced by 21.13%. Small thermal oscillations are observed in naturally dominated mixed convection for shear‐thinning fluids, but none are observed for shear‐thickening or Newtonian fluids. In addition, the findings demonstrate that the flow modulator has a positive impact on heat transfer for the shear‐thickening fluids (n > 1) and an adverse effect for the shear‐thinning fluids (n < 1). Furthermore, the power consumption decreases as Ri increases, and it becomes negative beyond Ri = 1.0 due to the increase in natural convection strength.
