An analysis of slippage effects on a solid sphere enclosed by a non-concentric cavity filled with a couple stress fluids.

This investigation shows the effect of slippage on the slow spinning of a rigid sphere covered by a non-concentric spherical hollow full of an incompressible couple stress fluid. Moreover, the velocity slip conditions are employed on surfaces of both the rigid sphere and the cavity. In addition, the solid sphere and the cavity are rotating axially at various angular speeds. The solution is obtained semi-analytically at low Reynolds numbers utilizing the superposition with the numerical collocation approach. This paper discusses the hydrodynamic couple exerted by the fluid on the internal particle. The dimensionless torque increases as the slip and spin slip increase by 99%, the couple stress parameter by 49%, and the separation parameter by 79%. Additionally, the non-dimensional torque decreases with the increase of the size ratio by 89%. Consequently, it is found that all the results agreed with the corresponding numerical analysis in the traditional viscous liquids and the revolving of two eccentric rigid spheres with no slippage (Al-Hanaya et al. in J. Appl Mech Tech Phys 63(5):1-9, 2022).

Thermal-optical mechanical waves of the microelongated semiconductor medium with fractional order heat time derivatives in a rotational field.

Outlined here is an innovative method for characterizing a layer of microelongated semiconductor material under excitation. Fractional time derivatives of a heat equation with a rotational field are used to probe the model during photo-excitation processes. Micropolar-thermoelasticity theory, which the model implements, introduces the microelongation scalar function to characterize the processes occurring inside the microelements. When the microelongation parameters are considered following the photo-thermoelasticity theory, the model investigates the interaction scenario between optical-thermo-mechanical waves under the impact of rotation parameters. During electronic and thermoelastic deformation, the key governing equations have been reduced to dimensionless form. Laplace and Fourier's transformations are used to solve this mathematical problem. Isotropic, homogeneous, and linear microelongated semiconductor medium's general solutions to their respective fundamental fields are derived in two dimensions (2D). To get complete solutions, several measurements must be taken at the free surface of the medium. As an example of numerical modeling of the important fields, we will use the silicon (Si) material's physicomechanical characteristics. Several comparisons were made using different values of relaxation time and rotation parameters, and the results were graphically shown.

Effect of the permeability on the interaction between two spheres oscillating through Stokes-Brinkmann medium.

The effect of permeability on the rectilinear oscillations of two rigid spheres moving through an unbounded viscous fluid about their axis of symmetry with no slip is investigated. A collocation technique was employed to execute the conditions on the surfaces of the rigid spheres. The in-phase and out-phase forces are obtained and expressed graphically for various parameters. In addition, the streamlines are plotted for different relevant parameters. The limiting cases of Stokes and Darcy's flows are discussed.

Effect of magnetic field on the motion of two rigid spheres embedded in porous media with slip surfaces.

A semi-analytical study for the Stokes flow approximation caused by two solid spheres of different sizes with slip surfaces, immersed in a porous medium in the presence of a transverse magnetic field, is investigated. The two spheres are translating with different velocities along the line joining their centers. A general solution is developed from the superposition of the essential solutions in two spherical frameworks with origins located at the centers of the two spheres. Numerical results for the normalized hydrodynamic drag force acting on each sphere are obtained with good convergence for various values of the Hartmann number which characterizes the presence of magnetic field, the permeability parameter which characterizes the porous medium, separation parameter, and velocity and size ratios of the spheres. Our drag results are in good agreement with the available solutions in the literature in the cases of no-slip surfaces and when the porous medium turns into a pure fluid.

Settling slip velocity of a spherical particle in an unbounded micropolar fluid.

The gravitational settling of small spherical particles in an unbounded micropolar fluid with slip surfaces is considered. The motion is studied under the assumption of low Reynolds number. The slip boundary conditions on velocity and microrotation at the surface of the spherical particle is used. The solution for the stream function of the fluid flow is obtained analytically. The settling velocity is obtained and is plotted against the Knudsen number for various values of the micropolarity parameter and constants depending on the material of the solid surface. The problem of rotational motion of a particle with slip surface is also solved and the torque coefficient acting on the spherical particle is obtained and is plotted against Knudsen number for different values of micropolarity parameter, spin parameter, and the material constants. The correction to the Basset equation for settling velocity under gravity for slip particle in micropolar fluids is discussed with the range of Knudsen number which has been proven with known results available in the literature.