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We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid…
The unsteady motion of a two-layer fluid induced by oscillatory motion of a flat plate along its length is mathematically analyzed. Two cases are considered: (i) the two-layer fluid is bounded only by the oscillating plate (Stokes' second…
We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to…
This article is focused on the dynamics of a rotating electrically conducting fluid in a turbulent state. As inside the Earth's core or in various industrial processes, a flow is altered by the presence of both background rotation and a…
We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier-Stokes equations and the motion of the…
We study the stationary flow of incompressible micropolar fluid in a thin three-dimensional domain under Navier slip boundary condition for the velocity and no-spin condition for microrotation. After rescaling the governing equations, we…
We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system consisting of equation of continuity, momentum balance, entropy…
A new theory for the dynamics of the magnetic particles and their magnetic moments in ferrofluids is developed. Based on a generalized Lagrangian formulation for the equations of motion of the colloidal particle, we introduce its…
Many practical applications exploit an external local magnetic field -- magnetic obstacle -- as an essential part of their constructions. Recently, it has been demonstrated that the flow of an electrically conducting fluid influenced by an…
The rheology of 2D steady surface flow of cohesionless cylinders in a rotating drum is investigated through {\em Non Smooth Contact Dynamics} simulations. Profile of volume fraction, translational and angular velocity, rms velocity, strain…
We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the…
The rotation profile of a magnetized plasma cylinder composed of multiple fluids is investigated analytically, expanding on previous results. The analytic steady-state solution is used as a benchmark for a time-dependent multiple-fluid…
We study the nonlinear evolution of the magnetic buoyancy instability in rotating and non-rotating gas layers using numerical solutions of non-ideal, isothermal MHD equations. The unstable magnetic field is either imposed through the…
The present investigation discusses the flow and heat transfer characteristics of a steady three dimensional Sisko fluid. The flow is induced due to bidirectional stretching sheet. The influence of power-law index and stretching ratio on…
We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…
We discuss the effects of nonhomogeneous magnetic fields in liquid metal flows in two different configurations. In the first configuration, we briefly report the impact of fringing magnetic fields in a turbulent Rayleigh-B{\'e}nard…
The flow of an electrically conducting fluid driven by a traveling magnetic field imposed at the endcaps of a cylindrical annulus is numerically studied. At sufficiently large magnetic Reynolds number, the system undergoes a transition from…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…
A qualitative explanation for the scaling of energy dissipation by high Reynolds number fluid flows in contact with solid obstacles is proposed in the light of recent mathematical and numerical results. Asymptotic analysis suggests that it…
We examine the effects of plastic flow that appear in a neutron-star crust when a magnetic stress exceeds the threshold. The dynamics involved are described using the Navier--Stokes equation comprising the viscous-flow term, and the…