The purpose of this paper is to study numerically the mixed convection between two rotating circular cylinders under horizontal arrangement. The cylinders have a concentric position with a blockage ratio of d/D = 2.5. The annular space is completely filled with non-Newtonian power-law fluid. The surface of the inner cylinder is hot whereas the surface of the outer one is cold. Three cases are studied: in the first one, the inner cylinder has a constant rotational speed, while the outer cylinder is completely fixed; the second case: both cylinders are rotating in the same direction and at the same rotational speed; in the last case, both cylinders are rotating in opposite directions at a similar rotational speed. All studied cases are examined for various values of Reynolds number (Re = 1–10), Richardson number (Ri = 0–3), and power-law index (n = 0.6–1.6) at Prandtl number Pr = 50.