This paper presents a fundamental numerical analysis of flow and heat transfer in a vertical rotating disk reactor. These reactors are commonly used for growing thin films via chemical vapor deposition. Under certain conditions, rotating disk reactors have been found to exhibit multiple steady states, where desirable and undesirable flow patterns co-exist at the same conditions. The focus of th...

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navie...

Natural ventilation of building provides improvement of internal comfort and air quality conditions leading to a significant reduction of cooling energy consumption. Design of natural ventilation systems for many types of building is based on buoyancy forces. However, external wind flow can have significant effects on buoyancydriven natural ventilation. Airflow process across vertical vents ind...

For the Boussinesq and Charny nonlinear diffusion equations we employ the known similarity solutions and derive new ones using the Adomian decomposition method and separation of variables. For a periodic water-drive regime with a heavier fluid sweeping a lighter one from a porous formation we arrive at an explicit analytical expression for the interface and describe the phenomena of “superpropa...

This paper is concerned with numerical methods for twophase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate disc...

We study convection of an incompressible Newtonian fluid heated from below in a two-dimensional domain of height H: the Bénard problem. The lower wall is maintained at a temperature θbottom and the upper wall is maintained at a temperature θtop, where θbottom > θtop . The governing equations are the (2D) Navier–Stokes equations under the Boussinesq approximation, in which all variations in phys...

A new approach for the solution of time-dependent calculations of buoyancy driven currents is presented. The density distribution is not uniform throughout the flow field, however the incompressibility condition and Boussinesq approximation are assumed to be valid because the time variation of density is not significant. This method employs the idea that density variation can be pursued by usin...

The effects of randomly irregular bathymetry on the propagation of interfacial gravity waves are studied. Modelling sea water by a two-layer fluid of different densities, weakly nonlinear waves much longer than the sea depth but comparable to the horizontal scale of bathymetry are treated by Boussinesq approximation and multiplescale analysis. For transient wave pulses, the governing equation f...

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. The proof uses the vorticity transport formula represented in terms of the back to label map. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in R. This result has direct applications to the density depend...

The modeling of convective flows with 3D lattice Boltzmann fluid dynamics is presented using a lattice BGK approach for low Mach number flows with variable density combined with a large eddy turbulence model. The ability to resolve non− Boussinesq density varying problems is depicted for two dimensional Rayleigh−Bénard−convection at a Rayleigh number Ra = 800,000. A complex three−dimensional ex...