A general class of linear advective PDEs, whose leading order term is of viscous dissipative type, is considered. It is proved that beyond the limit of the essential spectrum of the underlying inviscid operator, the eigenvalues of the viscous operator, in the limit of vanishing viscosity, converge precisely to those of the inviscid operator. The general class of PDEs includes the equations of i...

The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by...

Laminar free convection flow of viscous, incompressible fluid with variable viscosity and viscous dissipation through two horizontal parallel walls embedded in a porous medium is studied. Arrhenius model is used in which the variable viscosity is used to be decreasing exponentially with temperature. An approximation technique is defined to obtain the solution of the coupled non-linear equations...

We consider the evolution of a small rigid body in an incompressible viscous fluid filling whole space. The motion is modelled by Navier-Stokes equations, whereas described conservation law linear and angular momentum. Under assumption that diameter tends to zero density goes infinity, we prove solution fluid-rigid system converges equations full space without body.

Consider a vicous incompressible fluid occupying a bounded domain Ω ⊂ R. In the Eulerean reference system, the motion of the fluid is completely determined by the velocity field u = u(t, x) a vector valued function of the time t and the spatial position x ∈ Ω. Under the hypothesis of impermeability of the boundary, the velocity satisfies u · n|∂Ω = 0, (1.1) where the symbol n stands for the out...

The objective of this paper is to provide a review of recent finite element formulations for immersed methods. In these finite element formulations, independent Lagrangian solid meshes are introduced to move on top of a background Eulerian fluid mesh. This key feature allows the handling, without excessive fluid mesh adaptation, multiple deformable solids immersed in viscous fluid. In particula...

We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes équations. The structure is a collection of rigid moving bodies, The fluid domain dépends on time and is defined by the position of the structure, itself resulting rrom a stress distribution coming from the fluid. The problem is then n...

In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one corresponds to a viscous fluid driven by the Navier-Stokes system. In both cases we investigate the uniqueness of weak solutions, à la Yudovich for the Eule...

A study of magnetohydrodynamics (MHD) axisymmetric stagnation point flow with viscous dissipation and heat transfer in an electrically conducting laminar steady viscous incompressible fluid over a heated axisymmetric shrinking surface is presented. The governing partial differential equations (PDEs) are reduced to non linear ordinary differential equations (ODEs) in dimensionless form using sui...

In this paper we examined the problem of steady flow of a second order slightly thermo-viscous incompressible fluid through a porous slab bounded between two infinitely spread permeable parallel plates. The effects of various material parameters like Darcy’s porosity parameter, Thermo-mechanical stress interaction coefficient, Strain thermal conductivity coefficient and Suction/injection parame...