In this study, a fluid flow with an incompressible axisymmetric steady couple stress translated through a porous media is analyzed between a hollow sphere and a concentric rigid sphere. In the permeable region, the flow field is regulated by Brinkman's equation. The slip and spin slip conditions are applied on both the rigid sphere and spherical cavity surfaces. Modified Bessel functions provide a systematic approach to the problem by utilizing the principle of a stream function. On the inner sphere, the wall correction factor that an incompressible couple stress fluid encounters is calculated. The effects of the slip, spin slip, coupling stress parameter, separation distance, and permeability parameter on the field functions and the normalized drag force are also graphically shown. The corresponding results are contrasted with the outcomes reported for particular cases of couple stress fluid and viscous fluid flow in two permeability-free concentric circles. Furthermore, graphs of the streamlines for various values of the relevant parameters have been included.

This study applies the generalized photo-thermoelasticity theory to investigate thermo-hydro-mechanical interactions in a poroelastic half-space elastic semiconductor material with variable properties. The model represents a novel approach, treating the material as a uniform, fully saturated, poroelastic semiconductor half-space in alignment with the principles of dynamic poroelasticity within generalized photo-thermoelasticity. We initially applied time-harmonic loads, encompassing normal or thermal loads and plasma electron distributions to this medium. The study then explores the differences between coupled thermo-hydro-mechanical dynamic models and thermo-elastic dynamic models. We employed two-dimensional normal mode analysis to solve the resulting non-dimensional coupled equations. Subsequently, we examined the impact of non-dimensional displacement, excess pore water pressure, mechanical stress, carrier concentration (density), and temperature distribution on the poroelastic half-space medium. We then visually represented these effects.

This article explores the steady and uniform motion of two spherical particles submerged in an infinite fluid with Brinkman-couple stress properties, where the particles are entirely immersed and surface slippage is disregarded. While the particles may vary in size, they are composed of the same material and move along the line that connects their centers, influenced by different velocities or external forces. The analysis is performed under low Reynolds number conditions, which signify laminar flow dominated by viscous forces. Using boundary collocation methods, semi-analytical solutions to the governing differential equations are derived, facilitating a thorough investigation of the system. The study employs normalized drag force to evaluate the effects of particle interactions, presenting calculated values graphically and discussing them with several key factors, such as particle size and separation distance, thereby enhancing the understanding of particle dynamics in complex fluid environments. The analysis of how varying the permeability parameter affects flow patterns around two spheres in a couple of stress fluids is shown.

In this study, we examine the movement of two hard spheres aligned in a straight line within an incompressible couple stress fluid under the impact of the magnetic field. Both objects have distinct shapes and move along an axis connecting their centers with varying velocities. As a first step, an incompressible analytical analysis is performed on a fluid with couple stress properties around an axially symmetric particle. Using the superposition principle, a general solution is developed for couple stress fluid flows over two moving objects. In order to achieve the boundary conditions, the boundary collocation strategy is applied to the surfaces of the two spheres. A set of tables and graphs illustrates numerical estimates of the dimensionless drag forces acting on two spherical objects. In addition, a drop in Hartmann number or an increase in couple stress viscosity will increase the dimensionless drag force on each spherical particle.