Analytical investigation of Bénard-Marangoni convection heat transfer in a shallow cavity filled with two immiscible fluids

The mechanism of natural and Marangoni convection in a system with two stratified fluid layers without mass transfer at the interface is investigated. The basis of the analytical solution is an assumption of parallel flow over a large portion of the system. The two cases of heat fluxes through horizontal or vertical opposite walls are considered. It is demonstrated that four different patterns of convection can be observed in the present system. The zone of occurrence of these flow patterns are specified in terms of non-dimensional parameters. Velocity and temperature distributions, stream function and Nusselt number are presented over a wide range of the governing parameters. The results obtained are explained in terms of the basic physical mechanisms that govern these flows showing many interesting aspects of the complex interaction between the buoyant and surface tension mechanisms.     

Numerical experiments on a flexible variant of GMRES-DR

The Flexible GMRES (FGMRES [1]) and the GMRES with deflated restarting (GMRES-DR [2]) methods are two algorithms derived from GMRES [3], that are considered as powerful when solving large non hermitian systems of linear equations. GMRES-DR is a variant of GMRES with an improved restarting technique that maintains in the Krylov subspace harmonic Ritz vector from the previous restart. In situations where the convergence of restarted GMRES is slow and where the matrix has few eigenvalues close to the origin, this technique has proved very efficient. The new method that we propose is the Flexible GMRES with deflated restarting (FGMRES-DR [6]), which combines the two above mentioned algorithms in order to yield better performance. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Domain decomposition preconditioners of Neumann-Neumann type for hp-approximations on boundary layer meshes in three dimensions

We develop and analyse Neumann–Neumann methods for hpfinite-element approximations of scalar elliptic problems ongeometrically refined boundary layer meshes in three dimensions.These are meshes that are highly anisotropic where the aspectratio typically grows exponentially with the polynomial degree.The condition number of our preconditioners is shown to be independentof the aspect ratio of the mesh and of potentially large jumpsof the coefficients. In addition, it only grows polylogarithmicallywith the polynomial degree, as in the case of p approximationson shape-regular meshes. This work generalizes our previousone on two-dimensional problems in Toselli & Vasseur (2003a,submitted to Numerische Mathematik, 2003c to appear in Comput.Methods Appl. Mech. Engng.) and the estimates derived here canbe employed to prove condition number bounds for certain typesof FETI methods.     

Thermal instability and natural convection in a fluid layer over a porous substrate

The stability and natural convection in a system consisting of a horizontal fluid layer over a layer of porous medium saturated with the same fluid, with heating from below, are considered. The upper surface is either rigid or dynamically free with surface-tension effects allowed for. The solution is obtained using a parallel flow assumption for constant-flux thermal boundary conditions for which the onset of cellular convection corresponds to a vanishingly small wavenumber. The critical Rayleigh number and Nusselt number are found to depend on the depth ratio, the Darcy number, the viscosity ratio, the thermal conductivity ratio, and the Marangoni number. Results are given for a range of values of each of the governing parameters. The results are compared with limiting cases of the problem for standard terrestrial conditions or microgravity, and are found to be in agreement.Es werden die Stabilität und die freie Konvektion in einem System mit einer horizontalen Fluid-Schicht über einer Schicht mit einem porösen Medium, welches mit diesem Fluid gesättigt ist, untersucht. Das System wird von unten beheizt. Die Oberfläche ist entweder unelastisch oder frei von dynamischen Oberflächenspannungen. Die Lösung wird mit der Annahme einer parallelen Strömung mit konstanten thermischen Randbedingungen erhalten. Für diese Randbedingungen bedeutet das Einsetzen der zellularen Konvektion eine verschwindend kleine Wellenzahl. Die kritische Rayleigh- und Nusselt-Zahl hängen von dem Tiefenverhältnis, der Darcy-Zahl, der Viskosität, der thermischen Leitfähigkeit und von der Marangoni-Zahl ab. Für jeden Parameter werden Ergebnisse für einen bestimmten Wertebereich gegeben. Die Ergebnisse werden mit einigen Fällen mit Standard-Erdbedingungen oder Mikrogravitation verglichen und stehen mit diesen in guter Übereinstimmung.     

Apurinic DNA reactivity: Modelisation of apurinic DNA breakage with phenylhydrazine and formation of a pyrazole adduct

We have elucidated the exact mechanism of apurinic oligodeoxynucleotide d(Tp[AP]pT) cleavage by phenylhydrazine and shown that the final isolated product is in fact a 3-substituted derivative of 1-phenyl-pyrazole.     

Variable permeability effect on convection in binary mixtures saturating a porous layer

The Darcy Model with the Boussinesq approximation is used to study natural convection in a shallow porous layer, with variable permeability, filled with a binary fluid. The permeability of the medium is assumed to vary exponentially with the depth of the layer. The two horizontal walls of the cavity are subject to constant fluxes of heat and solute while the two vertical ones are impermeable and adiabatic. The governing parameters for the problem are the thermal Rayleigh number, R _T, the Lewis number, Le, the buoyancy ratio, φ, the aspect ratio of the cavity, A, the normalized porosity, ε, the variable permeability constant, c, and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The onset of supercritical convection, or subcritical, convection are predicted by the present theory. A linear stability analysis of the parallel flow model is conducted and the critical Rayleigh number for the onset of Hopf’s bifurcation is predicted numerically. Numerical solutions of the full governing equations are found to be in excellent agreement with the analytical predictions.     

Analytical and numerical study of natural convection heat transfer in an inclined composite enclosure

Laminar natural convection heat transfer in inclined fluid layers divided by a partition with finite thickness and conductivity is studied analytically and numerically. The governing equations for the fluid layers are solved analytically in the limit of a thin layered system with constant flux boundary conditions. The study covers of the range of Ra from 10³ to 10⁷, from 0° to 180° and the thermal conductivity ratio of partition to fluid ratioK from 10^–2 to 10⁶. The Prandtl number was 0.72 (for air). Results are obtained in terms of an overall Nusselt number as a function of Rayleigh number, angle of inclination of the system, mid layer thickness, and mid layer thermal conductivity. The critical Rayleigh number for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with the numerical results obtained by solving the complete system of governing equations, using SIMPLER method, as well as with the limiting cases in the literature.     

Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws

We study the contraction properties (up to shift) for admissible Rankine–Hugoniot discontinuities of \({n\times n}\) systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in (Serre and Vasseur, J l’Ecole Polytech 1, 2014), using the spatially inhomogeneous pseudo-distance introduced in (Vasseur, Contemp Math AMS, 2013). Our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems, including the Euler system. Moreover, we introduce necessary conditions for contraction, specifically targeted for intermediate shocks. As an application, we show that intermediate shocks of the two-dimensional isentropic magnetohydrodynamics do not verify any of our contraction properties. We also investigate the contraction properties, for contact discontinuities of the Euler system, for a certain range of contraction weights. None of the results involve any smallness condition on the initial perturbation or on the size of the shock.     

Strong Traces for Solutions of Multidimensional Scalar Conservation Laws

In this paper we consider multidimensional scalar conservation laws without BV estimates defined in a subset Ω??⁺×? ^d . We show that, with a non-degeneracy hypothesis on the flux, we can define a strong notion of trace at the boundary of Ω reached by L ¹ convergence.     

Effect of curvature on interfacial segregation: Electronic contribution to the point defect/interface binding energy

The electronic contribution to the driving force for segregation to a curved interface between a cylindrical fiber of insulator embedded in a metal matrix is calculated. The solute/curved-interface binding energy is shown to vary as the inverse of the radius of curvature of the interface in the limit of a small radius. This result implies that the propensity for segregation of curved interfaces is larger than that of planar interfaces.