Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for d = 2, 3) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity u0 ∈ H (R) for s > 0 in 2-D, or u0 ∈ H (R) satisfying ‖u0‖L2‖∇u0‖L2 being sufficiently small in 3-D. This in particular improves t...

Chaotic advection in three-dimensional unsteady incompressible laminar flow By J U L Y A N H. E. C A R T W R I G H T1;2y , M A R I O F E I N G O L D3z , AND O R E S T E P I R O1;4{ 1Departament de Fı́sica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain. 2Centre de Càlcul i Informatització, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain. 3Department of Physics,...

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first ...

In the present paper, we have studied MHD free convective two dimensional unsteady viscous incompressible flows through a porous effect bounded by an infinite vertical porous plate with constant suction. The permeability of the porous medium fluctuates in time about a constant mean, and the viscosity of fluid is assumed to vary as a linear function of temperature. The flow is permitted under th...

In this work, rising of a single bubble in a quiescent liquid under microgravity condition was simulated. The related unsteady incompressible full Navier-Stokes equations were solved using a conventional finite difference method with a structured staggered grid. The interface was tracked explicitly by connected marker points via hybrid front capturing and tracking method. One field approximatio...

The purpose of this work is to examine the flow of a binary mixture including chemically inert incompressible Newtonian fluids in a duct of semicircular cross-section. Such a flow model has great significance not only of its own theoretical interest, but also for application to various engineering processes. The governing equations have been solved analytically using the finite Fourier sine and...

Abstract: In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain Ω ⊂ R, d = 2, 3. We prove that for a vortex patch initial data the weak Leray solutions of the incompressible Navier-Stokes equations with Navier boundary conditions will converge (locally in time for d = 3 and globally in time for d = 2) to a vo...

The unsteady 2-dimensional flow of electrically conducting, incompressible second grade fluid between two parallel infinite plates approaching or receding from each other symmetrically is studied. A similarity transformation is used to 1 Corresponding author: [email protected] (Muhammad Afzal Rana) 28 A. M. Siddiqui et al reduce the system of partial differential equations to a single fifth-...

We consider the Cauchy problem for incompressible Navier-Stokes equations ut + u∇xu − ∆xu + ∇xp = 0, divu = 0 in Rd×R+ with initial data a ∈ L(R), and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have tD t D n xu ∈ L(R × (0, T )), as long as the ‖u‖Ld+2 x,t (Rd×(0,T )) stays finite.