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This paper aims to study the mixed convective process due to various dynamics, namely, inner rotating cylinders and upper-wavy wall movement for the first time.

The Galerkin finite element method together with the characteristic-based split scheme is applied to solve the governing system.

The main outcomes revealed that the direction of the rotation of the cylinders, radius and locations of the rotating shapes are beneficial controlling elements for the enhancement of heat transfer. Also, for all the considered cases, values of the Bejan number indicate that the fluid friction irreversibility is dominance compared to the heat transfer irreversibility. Further, average values of the heat transfer entropy, fluid friction entropy and total entropy are minimized in the case of fixed cylinders regardless of the cylinder radius.

The authors are interested in the mixed convection case due to regular boundaries and hence this simulation purposes a first attempt to examine the mixed convective flow due to irregular wavy boundaries. This study considered various dynamics, namely, inner rotating cylinders and wavy-lid driven wall which makes it more attractive to the readers. Various cases based on radius of the cylinder and direction of the rotations together with several locations of the rotating shapes are taken into account which makes the current simulation is comprehensive. Various studies presented in this field are made by commercial software and these treatments need special conditions (having limitation) but the current solution methodology is based on a finite element method home-code. Various important impacts, are, also, examined, namely, inclined geometry, inclined magnetic field, thermal radiation and heat generation/absorption. The entropy of the current complex system is analyzed based on the second law of thermodynamics.