Conjugate heat transfer problems are of importance in many engineering applications, since flows are usually confined by some material with heat transfer properties. Whenever there is a temperature difference between the fluid and solid, heat will be transfered and change the flow properties in a non-trivial way (Giles 1997; Henshaw & Chand 2009; Lindström & Nordström 2010; Roe et al. 2008). Th...

Following earlier work for Stokes equations, a least-squares functional is developed for twoand three-dimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen equations examined here is obtained by linearizing the incompressible Navier-Stokes equations. An algorithm ...

Stokes Paradox, Fluid dynamics, Stokes flow, Stream function, Biharmonic equation, Helmholtz equation, Low Reynolds number This paper proposes a solution to Stokes’ paradox for asymptotically uniform viscous flow around a cylinder. The existence of a global stream function satisfying a perturbative form of the two-dimensional Navier–Stokes equations for low Reynolds number is established. This ...

We study how the inertial term in the steady state Navier-Stokes flow can drive transitions in the optimal topology of a microfluidic network. Our method is a generalization of the work by Borrvall and Petersson on topology optimization of fluids in Stokes flow [Int. J. Num. Meth. Fluids 41, 77 (2003)]. We state the Navier-Stokes flow problem in a generic divergence form that allows the problem...

We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equa...

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically alm...

The Kármán–Howarth theorem is derived for the Lagrangian averaged Navier-Stokes alpha (LANS−α) model of turbulence. Thus, the LANS−α model’s preservation of the fundamental transport structure of the Navier-Stokes equations also includes preservation of the transport relations for the velocity autocorrelation functions. This result implies that the alpha-filtering in the LANS−α model of turbule...

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle interactions) to ones that are essentially indistinguishable from the simple rel-ativistic Navier-Stokes descriptions of these states. Thus, for example, in t...

Abstract. In this paper we prove a local exact controllability of the Navier–Stokes equations with the condition on the pressure on parts of the boundary. The local exact controllability is proved by using a global Carleman inequality and an estimate of an equation adjoint to a linearized Navier– Stokes equation with the nonstandard boundary condition. We also obtain the null controllability of...