1,217,617 research outputs found
Reduced formulation of a steady fluid-structure interaction problem with parametric coupling
We propose a two-fold approach to model reduction of fluid-structure
interaction. The state equations for the fluid are solved with reduced basis
methods. These are model reduction methods for parametric partial differential
equations using well-chosen snapshot solutions in order to build a set of
global basis functions. The other reduction is in terms of the geometric
complexity of the moving fluid-structure interface. We use free-form
deformations to parameterize the perturbation of the flow channel at rest
configuration. As a computational example we consider a steady fluid-structure
interaction problem: an incmpressible Stokes flow in a channel that has a
flexible wall.Comment: 10 pages, 3 figure
Radiation and viscous dissipation effects for the Blasius and Sakiadis flows with a convective surface boundary condition
This study is devoted to investigate the radiation and viscous dissipation effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow) both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique along side with the sixth order of Runge-Kutta integration scheme and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Prandtl number Pr, radiation parameter NR, parameter a and the Eckert number Ec, which characterizes our convection processes are graphed and tabulated. Quite different and interesting behaviours were encountered for Blasius flow compared with a Sakiadis flow. A comparison with previously published results on special cases of the problem shows excellent agreement
Buoyancy and thermal radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition
This study is devoted to investigate the Buoyancy and thermal radiation effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow) both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique along side with the sixth order of Runge-Kutta integration scheme and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Prandtl number Pr, radiation parameter NR, parameter a and the local Grashof number Grx, which characterizes our convection processes are graphed and tabulated. Quite different and interesting behaviours were encountered for Blasius flow compared with a Sakiadis flow. A comparison with previously published results on special cases of the problem shows excellent agreement
Flow in a slowly-tapering channel with oscillating walls
The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou \cite{HP}. A careful study of the governing partial differential system for the first order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry-breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window stability is again lost to exponentially growing solutions as the Reynolds number is increased
UNSTEADY MIXED CONVECTION WITH SORET AND DUFOUR EFFECTS PAST A POROUS PLATE MOVING THROUGH A BINARY MIXTURE OF CHEMICALLY REACTING FLUID
This study investigates the unsteady mixed convection flow past a vertical porous
flat plate moving through a binary mixture in the presence of radiative heat transfer
and nth-order Arrhenius type of irreversible chemical reaction by taking into account
the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an
optically thin radiating fluid and using a local similarity variable, the governing
nonlinear partial differential equations have been transformed into a set of coupled
nonlinear ordinary differential equations, which are solved numerically by applying
shooting iteration technique together with fourth-order Runge-Kutta integration
scheme. Graphical results for the dimensionless velocity, temperature, and concentration
distributions are shown for various values of the thermophysical parameters
controlling the flow regime. Finally, numerical values of physical quantities, such as
the local skin-friction coefficient, the local Nusselt number, and the local Sherwood
number are presented in tabular form
Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms
We present the fifth-order equation of the nonlinear Schrodinger hierarchy. This integrable partial differential ¨
equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use
Darboux transformations to derive exact expressions for the most representative soliton solutions. This set
includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures
composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard
nonlinear Schrodinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated ¨
flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons,
which cannot exist for the standard NLSE.The authors acknowledge the support of the Australian
Research Council (Discovery Project No. DP140100265).
N.A. and A.A. acknowledge support from the Volkswagen
Stiftung and A.C. acknowledges Endeavour Postgraduate
Award support
Effects of Soret, Dufour, chemical reaction, thermal radiation and volumentric heat generation/absorption on mixed convection stagnation point flow on an Iso-thermal vertical plate in porous media
A mathematical model is analyzed in order to study the effects of Soret, Dufour, chemical reaction, thermal radiation and volumentric heat generation/absorption on mixed convection stagnation point flow on an Iso-thermal vertical plate in a porous media. The governing partial differential equations are transformed into set of coupled ordinary differential equations, which are solved numerically using Runge-Kutta sixth order method along with shooting technique. The physical interpretation to this expression is assigned through graphs and tables for the wall shear stress , Nusselt number and Sherwood number . Results were compared with the existing literature and showed a perfect agreement. Similarly, results showed that the fields were influenced appreciably by the effects of the governing parameters: Soret number Sr, Dufour number Df, chemical reaction parameter γ, thermal radiation parameter Ra, order of reactions n, thermal Grashof number GT, solutal Grashof number GC, Prandtl number Pr, permeability parameter K, rate of heat generation/absorption parameter S, and magnetic field strength parameter M. It was evident that for some kind of mixtures such as the light and medium molecular weight, the Soret and Dufour’s effects should be considered as well
Steady-state rarefaction waves in magnetized flows and their application to gamma-ray burst outflows
We investigate the characteristics of a relativistic magnetized fluid flowing around a corner. If the flow is faster than the fast-magnetosonic speed the non-smooth boundary induces a rarefaction wave propagating in the body of the flow. The subsequent expansion is accompanied with a very efficient increase of the flow speed and bulk Lorentz factor γ. We apply this ”rarefaction acceleration mechanism” to the collapsar model of gamma-ray bursts, in which a relativistic jet initially propagates in the interior of the progenitor star, before crossing the stellar surface with a simultaneous drop in the external pressure support. We integrate the steady-state equations using a special set of partial (r self-similar) solutions. The use of these solutions degrades the system of the complex, non-linear, 2nd order partial differential equations into a system of two 1st order ordinary differential equations whose integration is straightforward. For the conditions expected in a gamma-ray burst, a fully analytical solution can be obtained. The aim of this work is to better understand the results of recent timedepended numerical simulations and show that rarefaction acceleration is a plausible mechanism in gamma-ray burst outflows
Wide partitions, Latin tableaux, and Rota's basis conjecture
Say that mu is a ``subpartition'' of an integer partition lambda if the
multiset of parts of mu is a submultiset of the parts of lambda, and define an
integer partition lambda to be ``wide'' if for every subpartition mu of lambda,
mu >= mu' in dominance order (where mu' denotes the conjugate or transpose of
mu). Then Brian Taylor and the first author have conjectured that an integer
partition lambda is wide if and only if there exists a tableau of shape lambda
such that (1) for all i, the entries in the ith row of the tableau are
precisely the integers from 1 to lambda_i inclusive, and (2) for all j, the
entries in the jth column of the tableau are pairwise distinct. This conjecture
was originally motivated by Rota's basis conjecture and, if true, yields a new
class of integer multiflow problems that satisfy max-flow min-cut and
integrality. Wide partitions also yield a class of graphs that satisfy
``delta-conjugacy'' (in the sense of Greene and Kleitman), and the above
conjecture implies that these graphs furthermore have a completely saturated
stable set partition. We present several partial results, but the conjecture
remains very much open.Comment: Joined forces with Goemans and Vondrak---several new partial results;
28 pages, submitted to Adv. Appl. Mat
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