The Solution of a Coupled Nonlinear System Arising in a Three-Dimensional Rotating Flow Using Spline Method

The behavior of the non-linear-coupled systems arising in axially symmetric hydromagnetics flow between two horizontal plates in a rotating system is analyzed, where the lower is a stretching sheet and upper is a porous solid plate. The equations of conservation of mass and momentum are transformed to a system of coupled nonlinear ordinary differential equations. These equations for the velocity field are solved numerically by using quintic spline collocation method. To solve the nonlinear equation, quasilinearization technique has been used. The numerical results are presented through graphs, in which the effects of viscosity, through flow, magnetic flux, and rotational velocity on velocity field are discussed

Recent Trends in Coatings and Thin Film–Modeling and Application

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value

The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo

A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo -- in some sense the inverse of dynamo quenching. The dynamo is nonhelical, with the mean-field $\alpha$ coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, this paper presents further details of the numerical evidence for the effect, as well as an heuristic description of how magnetic fluctuations can interact with shear flow to produce the required electromotive force. The pressure response of the fluid is fundamental to this mechanism, which helps explain why the magnetic effect is stronger than its kinematic cousin, and the basic idea is related to the well-known lack of turbulent resistivity quenching by magnetic fluctuations. As well as being interesting for its applications to general high Reynolds number astrophysical turbulence, where strong small-scale magnetic fluctuations are expected to be prevalent, the magnetic shear-current effect is a likely candidate for large-scale dynamo in the unstratified regions of ionized accretion disks. Evidence for this is discussed, as well as future research directions and the challenges involved with understanding details of the effect in astrophysically relevant regimes

Stefan blowing, navier slip and radiation effects on thermo-solutal convection from a spinning cone in an anisotropic porous medium

Thermal radiation features in many high temperature materials processing operations. To evaluate the influence of radiative flux on spin coating systems, we consider herein the thermo-solutal (coupled heat and mass transfer) in steady laminar boundary layer natural convection flow from a rotating permeable vertical cone to an anisotropic Darcian porous medium. Surface slip effects are also included in the model presented. The conservation equations are rendered into self-similar form and solved as an ordinary differential two-point boundary value problem with surface and free stream boundary conditions using MAPLE 17 software. The transport phenomena are observed to be controlled by ten parameters, viz primary and secondary Darcy numbers (Dax and Da), rotational (spin) parameter (NR), velocity slip parameter (a), suction/injection parameter (S), thermal slip parameter (b), mass slip parameter (c) buoyancy ratio parameter (N), and conduction-radiation parameter (Rc). Tangential velocity and temperature are observed to be enhanced with greater momentum slip whereas swirl velocity and concentration are reduced. Increasing swirl Darcy number strongly accelerates both the tangential and swirl flow and also heats the regime whereas it decreases concentrations. Conversely a rise in tangential Darcy number accelerates only the tangential flow and decelerates swirl flow, simultaneously depressing temperatures and concentrations. Increasing thermal slip accelerates the swirl flow and boosts concentration but serves to retard the tangential flow and decrease temperatures. With higher radiation contribution (lower Rc values) temperatures are elevated and concentrations are reduced. Verification of the MAPLE 17 solutions is achieved using a Keller-box finite difference method (KBM). A number of interesting features in the thermo-fluid and species diffusion characteristics are addressed. Key words: Stefan blowing; Spinning cone; MAPLE 17; Anisotropi

Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM.

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics

Radiative and magnetohydrodynamics flow of third grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

A mathematical analysis is presented to investigate the nonlinear, isothermal, steady-state, free convection boundary layer flow of an incompressible third grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation and heat generation/absorption. The transformed conservation equations for linear momentum, heat and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller Box Method. The numerical code is validated with previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer materials processing

A unified treatment of mean-field dynamo and angular-momentum transport in magnetorotational instability-driven turbulence

Magnetorotational instability (MRI)-driven turbulence and dynamo phenomena are analyzed using direct statistical simulations. Our approach begins by developing a unified mean-field model that combines the traditionally decoupled problems of the large-scale dynamo and angular-momentum transport in accretion disks. The model consists of a hierarchical set of equations, capturing up to the second-order cumulants, while a statistical closure approximation is employed to model the three-point correlators. We highlight the web of interactions that connect different components of stress tensors -- Maxwell, Reynolds, and Faraday -- through shear, rotation, correlators associated with mean fields, and nonlinear terms. We determine the dominant interactions crucial for the development and sustenance of MRI turbulence. Our general mean field model for the MRI-driven system allows for a self-consistent construction of the electromotive force, inclusive of inhomogeneities and anisotropies. Within the realm of large-scale magnetic field dynamo, we identify two key mechanisms -- the rotation-shear-current effect and the rotation-shear-vorticity effect -- that are responsible for generating the radial and vertical magnetic fields, respectively. We provide the explicit (nonperturbative) form of the transport coefficients associated with each of these dynamo effects. Notably, both of these mechanisms rely on the intrinsic presence of large-scale vorticity dynamo within MRI turbulence.Comment: 32 pages, 25 figures; Comments welcom

Universality of multi-field α\alpha-attractors

We study a particular version of the theory of cosmological $\alpha$-attractors with $\alpha=1/3$, in which both the dilaton (inflaton) field and the axion field are light during inflation. The kinetic terms in this theory originate from maximal $\mathcal{N}=4$ superconformal symmetry and from maximal $\mathcal{N}=8$ supergravity. We show that because of the underlying hyperbolic geometry of the moduli space in this theory, it exhibits double attractor behavior: their cosmological predictions are stable not only with respect to significant modifications of the dilaton potential, but also with respect to significant modifications of the axion potential: $n_s\simeq 1-{2\over N}$, $r\simeq {4\over N^2}$. We also show that the universality of predictions extends to other values of $\alpha \lesssim {\cal O}(1)$ with general two-field potentials that may or may not have an embedding in supergravity. Our results support the idea that inflation involving multiple, not stabilized, light fields on a hyperbolic manifold may be compatible with current observational constraints for a broad class of potentials.Comment: 26 pages, 9 figures; v2: published version with references added and discussion extende

The instability of a viscous sheet floating on an air cushion

The dynamics of a thin sheet of viscous liquid levitating on an air cushion is studied. Experimentally, it is observed that, after an initial settling stage, a local disturbance grows, eventually leading to the sheet blowing up like a viscous balloon. We derive a dynamical model for the levitating sheet and propose a mechanism for the onset of the instability. This instability is driven by the local drainage of the sheet due to a growing disturbance on its lower surface and is moderated by surface tension, the bending stiffness of the sheet and advection in the air layer. The balance between these effects determines the most unstable wavelength and this is illustrated by some numerical simulations