Narrow Results

This paper deals with the modeling of the ionospheric plasma. Starting from the two-fluid Euler–Maxwell equations, we present two hierarchies of models. The MHD hierarchy deals with large plasma density situations while the dynamo hierarchy is adapted to lower density situations. Most of the models encompassed by the dynamo hierarchy are classical ones, but we shall give a unified presentation of them which brings a new insight into their interrelations. By contrast, the MHD hierarchy involves a new (at least to the authors) model, the massless-MHD model. This is a diffusion system for the density and magnetic field which could be of great practical interest. Both hierarchies terminate with the "classical" Striation model, which we shall investigate in detail.

Combined effects of forced and natural convection on the occurrence of flow separation and heat transfer on a vertical paraboloid of revolution under the influence of a magnetic field are studied in this investigation. Inside the boundary layer, free convection is established due to the temperature difference between the fluid and the boundary while forced convection happens due to the presence of an external potential flow. The external potential velocity is chosen from the decelerated nature concerning the stream-wise coordinate due to which the flow separation is expected to occur. The influence of natural convection, the applied magnetic field, and the surface transverse curvature on delaying the flow separation and on the rate of heat transfer in the vicinity of the separation point is the aim of the investigation of this study. Regarding these important physical ingredients, the percentage increase in separation length and the rate of heat transfer are calculated. Moreover, their influence on the flow and heat-transfer phenomena has also been discussed in detail and presented through various graphs and tables. An exact numerical solution is obtained with the aid of an implicit finite difference scheme.

We derive a quadratically nonlinear equation that describes the motion of a tangential discontinuity in incompressible magnetohydrodynamics near the onset of a Kelvin–Helmholtz instability. We show that nonlinear effects enhance the instability and give a criterion for it to occur in terms of a longitudinal strain of the fluid motion along the discontinuity.

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L^∞ bound for C¹ solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

Peristaltic flow by a sinusoidal traveling wave in the walls of two-dimensional channel with wall properties is investigated. The channel is filled with incompressible Eyring–Powell fluid. Mathematical modeling is developed through aspects of Hall current, thermal deposition and convection. Long wavelength and low Reynolds number considerations are adopted. Perturbation solutions to the resulting problem for small material parameter of fluid are obtained. Expressions of velocity, temperature, concentration and stream function are derived. Variations of pertinent parameters on the physical quantities of interest are explored in detail. The present analysis is especially important to predict the rheological characteristics in engineering applications by peristalsis.

The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid flow induced by myometrial contractions and it was simulated by asymmetric peristaltic fluid flow in a two-dimensional infinite non-uniform channel. The analysis has been performed under long wavelength and low-Reynolds number assumptions to linearize the governing flow equations. A series solution in respect of a small Weissenberg number is obtained for the stream function, axial pressure gradient and shear stress. Time average of pressure rise and frictional force on the upper wall has also been computed using numerical integration. The results have been presented graphically for the various interested physical parameters. It is observed that for Carreau fluids the peristalsis works as a pump against a greater pressure rise compared with a Newtonian fluid, while there exists no significant difference in free pumping flux for Newtonian and Carreau fluids in the tapered asymmetric channel.

This paper addresses the peristaltic flow of magnetohydrodynamic viscous fluid in an inclined compliant wall channel. Different wave amplitudes and phases ensure asymmetry in the channel flow configuration. Simultaneous effects of heat and mass transfer are also considered. Viscous dissipation effect is present. The flow and heat transfer are investigated under long wavelength and low Reynolds number assumption. The expressions for stream function, axial velocity, temperature and concentration are obtained. The solution expressions for physical quantities are sketched and discussed. It is found that Brinkman and Hartman numbers have reverse effect on the temperature.

The paper provides an analytical investigation, homotopy analysis method (HAM), of the heat and mass transfer for magnetohydrodynamic Oldroyd-B nanofluid flow over a stretching sheet in the presence of convective boundary condition. The PDE governing equations, which consist of equations of continuity, momentum, energy and nanoparticles, are converted to ordinary differential equations using similarity transformations. The current HAM solution demonstrates very good correlation with those of the previously published studies in the special cases. The influences of different flow physical parameters such as the Deborah numbers in terms of relaxation and retardation times (${\beta }_1$, ${\beta }_2$), magnetic parameter (M), Prandtl number (Pr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Lewis number (Le), and Biot number (Bi) on the fluid velocity component $(f^{\prime }(\eta ))$, temperature distribution $(\theta (\eta ))$ and concentration $(\varphi (\eta ))$ as well as the local Nusselt number $({\mathrm{\text{Nu}}}_x/{\mathrm{\text{Re}}}_x^{1/2})$ and the local Sherwood number $({\mathrm{\text{Sh}}}_x/{\mathrm{\text{Re}}}_x^{1/2})$ are discussed in detail.

A numerical analysis has been carried out to investigate the problem of magnetohydrodynamic (MHD) boundary-layer flow and heat transfer of a viscous incompressible fluid over a fixed plate. Convective surface boundary condition is taken into account for thermal boundary condition. A problem formulation is developed in the presence of thermal radiation, magnetic field and heat source/sink parameters. A similarity transformation is used to reduce the governing boundary-layer equations to couple higher-order nonlinear ordinary differential equations. These equations are numerically solved using Keller–Box method. The effect of the governing parameters such as radiation, Prandtl number, Hartman number, heat source/sink parameter on velocity and temperature profile is discussed and shown by plotting graphs. It is found that the temperature is an increasing function of convective parameter A, radiation and heat source parameters. Besides, the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. Finally a comparison with a previously published results on a special case of the problem has done and shows excellent agreement.

The effect of axial magnetic field along with axial temperature gradient, in a confined cylindrical cavity packed with incompressible electrical conducting fluid having a top rotating lid, has been investigated. Due to the presence of axial magnetic field, Joule heating effect is considered in this study. The governing parameters ranges are as follows: $1\le J\le 8$, $1\le \mathrm{\text{Ri}}\le 10$ at Re$=$1000, Pr$=$0.015. It is found that the internal heat generation due to Joule heating in mixed convection is governed by interaction parameter and temperature gradient. However, the Joule heating effect has very less effect on primary flow in comparison to the secondary flow along the meridional plane.

A variety of topics related to our understanding of turbulence and angular momentum transport in astrophysical accretion disks are discussed, including (1) new numerical algorithms for magnetohydrodynamics required to study these processes, (2) turbulence and the decay of vortices in hydrodynamic disks, (3) MHD turbulence driven by the magnetorotational instability (MRI), and (4) studying the MRI through laboratory experiments. A brief outline of some of the outstanding challenges in understanding MHD turbulence in astrophysical disks is given.

Recent observations and theoretical considerations have linked gamma-ray bursts with ultra-bright type Ibc supernovae (‘hypernovae’). We here work out a specific scenario for this connection. Based on earlier work, we argue that especially the longest bursts must be powered by the Blandford–Znajek mechanism of electromagnetic extraction of spin energy from a black hole. Such a mechanism requires a high angular momentum in the progenitor object. The observed association of gamma-ray bursts with type Ibc supernovae leads us to consider massive helium stars that form black holes at the end of their lives as progenitors. In our analysis we combine the numerical work of MacFadyen and Woosley with analytic calculations in Kerr geometry, to show that about 10⁵³ erg each are available to drive the fast GRB ejecta and the supernova. The GRB ejecta are driven by the power output through the open field lines threading the black hole, whereas the supernova can be powered both by the shocks driven into the envelope by the jet, and by the power delivered into the disk via field lines connecting the disk with the black hole. We also present a much simplified approximate derivation of these energetics.

Helium stars that leave massive black-hole remnants can only be made in fairly specific binary evolution scenarios, namely the kind that also leads to the formation of soft X-ray transients with black-hole primaries, or in very massive WNL stars. Since the binary progenitors will inevitably possess the high angular momentum we need, we propose a natural link between balck-hole transients and gamma-ray bursts. Recent observations of one such transient, GRO J1655-40/Nova Scorpii 1994, explicitly support this connection: its high space velocity indicates that substantial mass was ejected in the formation of the black hole, and the overabundance of α-nuclei, especially sulphur, indicates that the explosion energy was extreme, as in SN 1998bw/GRB 980425. Furthermore, X-ray studies of this object indicate that the black hole may still be spinning quite raidly, as expected in our model. We also show that the presence of a disk during the powering of the GRB and the explosion is required to deposit enough of the α nuclei on the companion. © 2000 Elsevier Science B.V. All rights reserved.

This paper presents a computational scheme for compressible magnetohydrodynamics (MHD). The scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and solution-adaptive refinement and coarsening. The pieces of the scheme are described, and the scheme is validated and its accuracy assessed by comparison with exact solutions. A domain-decomposition-based parallelization of the code has been carried out; parallel performance on a number of architectures is presented.

Over the last few decades, developing efficient iterative methods for solving discretized partial differential equations (PDEs) has been a topic of intensive research. Though these efforts have yielded many mathematically optimal solvers, such as the multigrid method, the unfortunate reality is that multigrid methods have not been used much in practical applications. This marked gap between theory and practice is mainly due to the fragility of traditional multigrid methodology and the complexity of its implementation. This paper aims to develop theories and techniques that will narrow this gap. Specifically, its aim is to develop mathematically optimal solvers that are robust and easy to use for a variety of problems in practice. One central mathematical technique for reaching this goal is a general framework called the Fast Auxiliary Space Preconditioning (FASP) method. FASP methodology represents a class of methods that (1) transform a complicated system into a sequence of simpler systems by using auxiliary spaces and (2) produces an efficient and robust preconditioner (to be used with Krylov space methods such as CG and GMRes) in terms of efficient solvers for these simpler systems. By carefully making use of the special features of each problem, the FASP method can be efficiently applied to a large class of commonly used partial differential equations including equations of Poisson, diffusion-convection-reaction, linear elasticity, Stokes, Brinkman, Navier-Stokes, complex fluids models, and magnetohydrodynamics. This paper will give a summary of results that have been obtained mostly by the author and his collaborators on this topic in recent years.

Unsteady mixed convection flow under the influence of gravity modulation and magnetic field has been investigated. The conducting fluid flows past a vertical porous plate of infinite length in a porous medium subjected to oscillating suction and temperature. The solution has been obtained by using regular perturbation method. Velocity profiles, temperature profiles, skin friction and heat transfer coefficients have been derived and shown graphically. It is noted that the fluid flow and heat transfer are significantly affected by gravity modulation.