Entropy generation and mixed convection flow inside a wavy-walled enclosure containing a rotating solid cylinder and a heat source

The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length h is placed in the middle of the left vertical surface in which its temperature is fixed at T_h. The temperature of the right vertical surface, however, is maintained at lower temperature T_c. The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number Ra = 10³ and 10⁵, number of oscillations: 1 ≤ N ≤ 4, angular rotational velocity:-1000 ≤ W ≤ 1000, and heat source length: 0.2 ≤ H ≤ 0.8. A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder.