We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically...

We prove the global well-posedness and regularity of the (isotropic) Lagrangian averaged Navier{Stokes (LANS-¬ ) equations on a three-dimensional bounded domain with a smooth boundary with no-slip boundary conditions for initial data in the set fu 2 Hs \H1 0 j Au = 0 on @« ; div u = 0g, s 2 [3; 5), where A is the Stokes operator. As with the Navier{Stokes equations, one has parabolic-type regul...

A two dimensional numerical simulation has been performed for incompressible and compressible fluid flow through microchannels in slip flow regime. The Navier-Stokes equations have been solved in conjunction with Maxwell slip conditions for modeling flow field associated with slip flow regime. The wall roughness is simulated with triangular microelements distributed on wall surfaces to study th...

For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The la...

Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of motion leaves a Poisson equation for the pressure to be solved. But Poisson equations require boundary conditions. For the case of rectangular periodic boun...

The general form of Maxwell’s velocity slip boundary condition for rarefied gas flows depends on both the geometry of the surface and the constitutive relations used to relate the viscous stress to rate of strain. The dependence on geometry is often overlooked in current rarefied flow calculations, and the generality of the constitutive dependence means the condition can also be usefully applie...

The aim of this work is to show the local null controllability a fluid–solid interaction system by using distributed control located in fluid. fluid modeled incompressible Navier–Stokes with Navier slip boundary conditions and rigid body governed Newton laws. Our main result yields that we can drive velocities structure 0 exactly position body. One important ingredient consists new Carleman est...