In classical continuum mechanics, a monolithic Eulerian formulation is used for numerically solving fluid–structure interaction (FSI) problems in the frame of a physically deformed configuration. This numerical approach is well adapted to large-displacement fluid–structure configurations where velocities of solids and fluids are computed all at once in a single variational equation. In the recent past, a monolithic Eulerian formulation for solving FSI problems of finite deformation to study the different physical features of fluid flow has been employed. Almost all the current studies use a classical framework in their approach. Despite producing decent results, such methods still need to be appropriately configured to generate exceptional results. Recently, a number of researchers have used a non-classical framework in their approach to analyze several physical problems. Therefore, in this paper, a monolithic Eulerian formulation is employed for solving FSI problems in a non-classical framework to study the micro-structural characteristics of fluid flow by validating the results with classical benchmark solutions present in the literature. In this respect, the Cosserat theory of continuum is considered where a continuum of oriented rigid particles has, in addition to the three translational degrees of freedom of classical continuum, three micro-rotational degrees of freedom. The mathematical formulation of model equations is derived from the general laws of continuum mechanics. Based on the variational formulation of the FSI system, we propose the finite element method and semi-implicit scheme for discretizing space and time domains. The results are obtained by computing a well-known classical FSI benchmark test problem FLUSTRUK-FSI-3* with FreeFem++. The results of the study indicate that the increase in micro-rotational viscosity ${\mu }_r$ leads to significantly large micro-rotations in fluid flow at the micro-structural level. Further, it is found that the amplitude of oscillations is related inversely to the material parameters c₁ and ${\mu }_r$ while the increase in c₁ stabilizes the amplitude of oscillations relatively more quickly than increasing ${\mu }_{r.}$ The color snapshots of the numerical results at different times during the computer simulations and general conclusions drawn from the results are presented.

The monolithic Eulerian formulation has widely been employed for solving numerically fluid–structure interaction (FSI) problems of finite structural displacement using the same mathematical variational formulation for fluid and structural dynamics. Recently, different physical features of fluid flow have been analyzed using this approach to such coupling problems by computing the classical benchmark solutions in a non-classical framework. Despite producing decent results, the analysis of micro-structural characteristics of fluid flow by applying the classical benchmark solutions still needs to be enhanced and extended further for such coupling problems. In this paper, the classical benchmark solutions have been enhanced and extended further for analyzing the combined micro-structural effects of linearly increasing Reynolds number $R_e$ and mean inflow velocity $\overline{U}$ on flow fields with mesh independence analysis by employing a monolithic Eulerian formulation in a non-classical framework. To this aim, the Cosserat fluids theory is taken into account for the present coupling problem by considering three micro-rotational degrees of freedom (dof) of fluid particles. The model equations of the proposed Cosserat fluid–structure interaction (CFSI) problem are derived using underlying laws of continuum mechanics. A numerical section presents the implementation of the benchmark problem with test examples followed by a detailed evaluation of the obtained results. The results obtained indicate that a uniform linear increase in Reynolds number $R_e$ and mean inflow velocity $\overline{U}$ produce the significant combined micro-structural effects on the micro-rotation velocity field $\mathsf{\omega }$, and this effect is found increasing on the increase of both parameters. This combined effect of increasing $R_e$ and $\overline{U}$ on the velocity field $u$ is also observed to be very significant in a sense that horizontal and vertical flow velocity profiles experience great variation by maintaining the same pattern on each increasing value of $R_e$ and $\overline{U}$ at any particular location in the computational domain. Further, the mesh independence analysis is employed to verify the convergence of obtained results. The study concludes that the linear increase in Reynolds number and mean inflow velocity affect micro-rotational velocity field significantly at the micro-structural level with mesh independence analysis. Finally, some future recommendations to enhance and extend the study with some of its limitations are presented.

The interplay between microrotation, microinertia, and viscoelastic relaxation significantly influences the hydrodynamic performance of non-Newtonian cavity flows. This study investigates the combined effects of the Eringen number, micropolar coupling constant, and fluid relaxation factor on drag force, microrotation, and flow behavior in a two-dimensional lid-driven cavity. The governing nonlinear partial differential equations are formulated using Eringen’s micropolar theory with relaxation-time-dependent stress, and the characteristic Galerkin finite element method is employed for numerical solution using a custom FreeFEM++ implementation. The results reveal a strong coupling between microrotation and viscoelastic relaxation effects. Increasing the relaxation factor enhances flow elasticity, leading to variations in drag force depending on the flow regime. The Eringen number stabilizes the flow and suppresses drag oscillations, while the micropolar coupling constant modulates shear-layer thickness and vortex intensity. Higher Eringen number increases kinetic energy and produces more ordered streamline patterns, whereas larger values of micropolar constant reduces drag while amplifying microrotation. Overall, tuning Eringen number, micropolar constant and time relaxation provides an effective mechanism for controlling drag and optimizing flow stability. These findings offer valuable insights for the design of advanced microfluidic and rheological systems where microstructural and viscoelastic effects coexist.

A full mathematical analysis of magnetohydrodynamic (MHD) hybrid nanofluid flow over a stretching/shrinking sheet with thermal radiation is presented in this paper. The hybrid nanofluid consists of copper (Cu) and alumina (Al 2 O 3 ) nanoparticles suspended in water as base fluid. By means of similarity transformations the governing partial differential equations are transformed into ordinary differential equations and are solved numerically by the Runge-Kutta-Fehlberg method with a shooting technique. The effects of the significant parameters like magnetic field parameter, radiation parameter, suction/injection parameter, stretching/shrinking parameter and nanoparticle volume fractions on the velocity and temperature profiles, skin friction coefficient and local Nusselt number are discussed . The dual solutions for the cases of shrinking sheet are obtained. The results are given in tables and figures and physical interpretation are made. The results show that hybrid nanofluids significantly enhance the heat transfer compared with mono nanofluids and the thermal radiation further increases the thermal boundary layer thickness.

Brain tumor being one of the major health hazards always needs a prompt diagnosis for the early treatment options to improve the chances of the survival of the patients. Traditional manual assessment of MRI (magnetic resonance imaging) to identify these conditions is a common practice. Hence, automation of the diagnosis practices can considerably improve the quality of the treatment procedures. In recent years almost every method for the automated diagnosis of brain tumor detection uses a deep learning technique. Despite decent works current techniques need a significant improvement to produce better results. Along with failure to produce decent results, the current deep learning models present very complex architectures which sometimes require huge computational resources. Therefore, in this paper we present a novel method that uses a lightweight dual-stream model with dual-input to detect brain tumors on MRI images. Both the inputs use different pre-processing mechanisms based on Contrast Limited Adaptive Histogram Equalization (CLAHE) and White Patch Retinex algorithm in order to enhance the feature learning capabilities of the proposed model. In addition, the proposed method uses a two-fold margin loss to boost training process for better feature learning. The proposed method produces state-of-the-art results for the detection of Glioma, Meningioma and Pituitary tumors. The model presents accuracy of 99%, 98% and 99% respectively for Glioma, Meningioma and Pituitary tumor detection.