We investigate the Navier-Stokes-Fourier system describing the motion of a compressible, viscous and heat conducting fluid on large class of unbounded domains with no slip and slip boundary conditions. We propose a definition of weak solutions, that is particularly convenient for the treatment of the Navier-Stokes-Fourier system on unbounded domains. We prove existence of weak solutions for arb...

Interest in microelectromechanical systems (MEMS) has experienced explosive growth during the past few years. Such small devices typically have characteristic size ranging from 1 mm down to 1 micron, and may include sensors, actuators, motors, pumps, turbines, gears, ducts and valves. Microdevices often involve mass, momentum and energy transport. Modeling gas and liquid flows through MEMS may ...

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible ...

<p style='text-indent:20px;'>This paper is concerned with the existence and uniqueness of strong solution to incompressible Navier-Stokes equations Navier-slip boundary conditions in a two-dimensional strip domain where slip coefficients may not have defined sign. In meantime, we also establish number Gagliardo-Nirenberg inequalities corresponding Sobolev spaces which will be applicable o...

The flow of viscous incompressible fluid over a periodically corrugated surface is investigated numerically by solving the Navier–Stokes equation with the local slip and no-slip boundary conditions. We consider the effective slip length which is defined with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective no-slip boundary pla...

The two-level penalty finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a St...

We consider the Euler system of gas dynamics endowed with incomplete equation state relating internal energy to mass density and pressure. show that any sufficiently smooth solution can be recovered as a vanishing viscosity - heat conductivity limit Navier--Stokes--Fourier properly defined temperature. The result is unconditional in case Navier type (slip) boundary conditions extends no-slip co...

A new exact solution to the problem of Marangoni layered convection is obtained. This describes a steady-state flow viscous incompressible fluid at varying gradients temperature and pressure. The velocity components depend only on transverse coordinate; pressure fields are three-dimensional. effect observed upper free surface layer. On lower solid layer, three different cases defining boundary ...

In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness δ is so small that some non-negligible slip may occur at the fluid-solid interface. The classical problem of steady acoustic streaming over a flat boundary is therefore revisited to include the effect of slip modelled using the Navier boundary condition u|y=0 = Ls∂yu|y...

We study the flow-field generated in a one-dimensional wall-bounded gas layer due to an arbitrary small-amplitude time variation in the temperature of its boundaries. Using the Fourier transform technique, analytical results are obtained for the slip-flow/Navier–Stokes limit. These results are complemented by low-variance simulations of the Boltzmann equation, which are useful for establishing ...