Computational analysis of magnetic induced micropolar flow in a rectangular channel through FreeFem++

In this article, we aim to computationally analyze the magnetic induced micropolar flow in a rectangular channel using a multiphysics finite element solver, FreeFem++. In this respect, a physical model in the framework of the micropolar continuum is taken into consideration with appropriate boundary conditions. The flow is considered laminar and incompressible and moves under the application of an external magnetic field at the boundary of the flow channel. The flow governing equations of momentum, microrotation, and induction are derived, and their weak integral forms in the context of finite elements are presented. The developed finite element model is then implemented in FreeFem++ in order to compute numerical solutions to the corresponding boundary value problem. The effects of different physical parameters are studied and discussed in detail. The main findings of this investigation pertaining to different physical aspects are summarized in the conclusion. It is interesting to find that the present problem becomes unstable with specific choices of material parameters, thereby leading to an unstable solution by the direct solver. However, numerical experimentation suggests that an iterative solver based on the generalized minimum residual method can stabilize the numerical solutions. In this connection, results are shown for varying Hartmann numbers. Moreover, it is worth mentioning that FreeFEM++ provides an efficient platform to compute and analyze magnetic induced flow within the context of a higher order continuum.

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