Physics Commons^™

Kinematics Of Fluids, Andrei Ludu

Publications

The goal of this chapter is to discuss the general frame of hydrodynamics, like particle trajectories (path lines), streamlines, streak lines, free surfaces, and fluid surfaces, and to compare their behavior in the Eulerian and Lagrangian frames. The following sections and chapters proceed on the assumption that the fluid is practically continuous and homogeneous in structure. Of course, the concept of continuum is an abstraction that does not take into account the molecular and nuclear structure of matter. In that, we assume that the properties of the fluid do not change if we consider smaller and smaller amounts of matter …

Hydrodynamics, Andrei Ludu

Publications

The mathematical description of the states of a fluid is based on the study of three fields defined on the domain occupied by the fluid: the velocity field V, the density ρ, and the pressure field P. These three “unknowns” are determined by integrating other five scalar equations, namely the mass conservation (continuity equation), the three components of the equation of momentum balance (Euler or Navier–Stokes), and the energy balance. This last equation needs in addition information about the thermodynamics of the fluid, so it may need to be supplied with some equation of state. In addition to these five …

Entropy Analysis Of Sutterby Nanofluid Flow Over A Riga Sheet With Gyrotactic Microorganisms And Cattaneo–Christov Double Diffusion, M. Faizan, F. Ali, K. Loganathan, A. Zaib, C. A. Reddy, Sara I. Abdelsalam

Basic Science Engineering

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. …

A Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Evan Habbershaw, Steven M. Wise

Faculty Publications and Other Works -- Mathematics

In this report we review some preliminary work on the numerical solution of BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for accurate simulation. This requires sophisticated numerical algorithms and efficient code to realize predictions over desired space and time scales. …

3d Flow Field Measurements Outside Nanopores, Jeffrey Mc Hugh, Alice L. Thorneywork, Kurt Andresen, Ulrich F. Keyser

Physics and Astronomy Faculty Publications

We demonstrate a non-stereoscopic, video-based particle tracking system with optical tweezers to study fluid flow in 3D in the vicinity of glass nanopores. In particular, we used the quadrant interpolation algorithm to extend our video-based particle tracking to displacements out of the trapping plane of the tweezers. This permitted the study of flow from nanopores oriented at an angle to the trapping plane, enabling the mounting of nanopores on a micromanipulator with which it was then possible to automate the mapping procedure. Mapping of the voltage driven flow in 3D volumes outside nanopores revealed polarity dependent flow fields. This is …

The Replacement Rule For Nonlinear Shallow Water Waves, A. Ludu, Z. Zong

Publications

When a (1 + 1)-dimensional nonlinear PDE in real function η(x, t) admits localized traveling solutions we can consider L to be the average width of the envelope, A the average value of the amplitude of the envelope, and V the group velocity of such a solution. The replacement rule (RR or nonlinear dispersion relation) procedure is able to provide a simple qualitative relation between these three parameters, without actually solve the equation. Examples are provided from KdV, C-H and BBM equations, but the procedure appears to be almost universally valid for such (1 + 1)-dimensional nonlinear PDE and their …

Thermo-Fluidic Transport Process In A Novel M-Shaped Cavity Packed With Non-Darcian Porous Medium And Hybrid Nanofluid: Application Of Artificial Neural Network (Ann), Dipak Kumar Mandal, Nirmalendu Biswas, Nirmal K. Manna, Dilip Kumar Gayen, Rama S. R. Gorla, Ali J. Chamkha

Faculty Publications

In this work, an attempt has been made to explore numerically the thermo-fluidic transport process in a novel M-shaped enclosure filled with permeable material along with Al₂O₃-Cu hybrid nanoparticles suspended in water under the influence of a horizontal magnetizing field. To exercise the influence of geometric parameters, a classical trapezoidal cavity is modified with an inverted triangle at the top to construct an M-shaped cavity. The cavity is heated isothermally from the bottom and cooled from the top, whereas the inclined sidewalls are insulated. The role of geometric parameters on the thermal performance is scrutinized thoroughly …

On The Coriolis Effect For Internal Ocean Waves, Rossen Ivanov

Conference papers

A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth's rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.

Editorial For The Special Issue On Micromachines For Non-Newtonian Microfluidics, Lanju Mei, Shizhi Qian

Mechanical & Aerospace Engineering Faculty Publications

In lieu of an abstract, this is an excerpt from the first page.

Microfluidics has seen a remarkable growth over the past few decades, with its extensive applications in engineering, medicine, biology, chemistry, etc [...]

On The Implementation And Further Validation Of A Time Domain Boundary Element Method Broadband Impedance Boundary Condition, Fang Q. Hu, Douglas M. Nark

Mathematics & Statistics Faculty Publications

A time domain boundary integral equation with Burton-Miller reformulation is presented for acoustic scattering by surfaces with liners in a uniform mean flow. The Ingard-Myers impedance boundary condition is implemented using a broadband multipole impedance model and converted into time domain differential equations to augment the boundary integral equation. The coupled integral-differential equations are solved numerically by a March-On-in-Time (MOT) scheme. While the Ingard-Myers condition is known to support Kelvin-Helmholtz instability due to its use of a vortex sheet interface between the flow and the liner surface, it is found that by neglecting a second derivative term in the current …

Recent Analytic Development Of The Dynamic Q-Tensor Theory For Nematic Liquid Crystals, Xiang Xu

Mathematics & Statistics Faculty Publications

Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and Q-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the Q-tensor theory in dynamic configurations.