In this contribution, effect of micromagnetorotation is studied in a micropolar flow within a lid-driven cavity. The governing dynamics of the flow is based on the theory of a non-classical continuum, specifically the micropolar continuum. Micromagnetorotation is a phenomenon that is related to the externally applied magnetic field in which the magnetic particles experience microrotations at the micro-scale within the flow. To date, the literature presented on the topic does not discuss the model description in three-dimension and its analysis in a two-dimensional domain. The aim of this investigation is to present three-dimensional model with analysis of micromagnetorotation in a two-dimensional domain with velocity driven flow. To this end, the theory of micropolar continuum is employed to derive a two-dimensional boundary value problem in PDEs. The obtained model problem is implemented through finite elements using FreeFem++ as a programming language. The code is validated through a reduced one-dimensional model with analytical solution. $L^2$ and $H^1-$error norms are calculated and it is found that the numerical results through the implemented code are in strong agreement with the analytical results in reduced model case. Simulations are performed on a square domain with different physical parameter of interests. The results obtained in the presence and absence of MMR effect are described for micro-inertial coupling parameter, micropolar viscosity ratio, magnetization relaxation time, size effect parameter, magnetization parameter and Hartmann number. This study, the first of its kind, explores new flow features in the presence of micromagnetorotation, providing valuable insights in the field of fluidized materials, thermal and biochemical processes.
Hameed, I. and Khan, M. Sabeel (2026). Effect of micromagnetorotation within a micropolar flow in a lid-driven cavity through finite element method. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.67287.3196
MLA
Hameed, I. , and Khan, M. Sabeel. "Effect of micromagnetorotation within a micropolar flow in a lid-driven cavity through finite element method", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2025.67287.3196
HARVARD
Hameed, I., Khan, M. Sabeel (2026). 'Effect of micromagnetorotation within a micropolar flow in a lid-driven cavity through finite element method', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.67287.3196
CHICAGO
I. Hameed and M. Sabeel Khan, "Effect of micromagnetorotation within a micropolar flow in a lid-driven cavity through finite element method," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2025.67287.3196
VANCOUVER
Hameed, I., Khan, M. Sabeel Effect of micromagnetorotation within a micropolar flow in a lid-driven cavity through finite element method. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2025.67287.3196
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