Numerical investigation is presented for mixed convection problem in a concentric inner sinusoidal (soft, semi- circular and square) cylinder and an outer rotating circular cylinder, which were kept at constant hot and cold temperature respectively. The governing equations are formulated and modeling in ANSYS-Fluent.21R1, a partial differential equation solver based on (FVM). The governing parameter considered are Reynolds number (50,75,100,119.5,150 and 350) for each Rayleigh number (50000,100000 and 150000) and the inner cylinder corrugation varied as (N0, SWA10, SW, SC and SQ) this study investigate the effect of varying cylindrical surface geometric –  from smooth to sinusoidal soft, semi – circular, and square wave – on thermal performance as wave amplitude increases. The results revealed that gentle undulation with low Rayleigh number enhanced heat transfer by 12.6%, as a result of shear retardation and forced convection at (Re=150). When the wave amplitude was increased to 22.96 mm, the enhancement reached 32% at (Re=350). Specifically, the transition from deep undulation soft to semicircular ripple contributed to remarkable enhancements of 138% at high Rayleigh number under (Re=150). In addition, the study demonstrated that the square ripple consistently provided the most effective thermal insulation under all examined conditions.