MHD

The aim of this work was to characterize lipid nanoparticles from a rheological point of view, intended for drug delivery after parenteral administration. The conditions to obtain a re-dispersible powder using freeze-drying and spray-drying have also been investigated. Lipid nanoparticles (179.9 ± 6.2 nm) were prepared with the high pressure homogenization technique, using previously established optimal conditions (lipid volume fraction of 0.121), though particle size increased (285.9 ± 4.3 nm) in suspensions produced with higher lipid volume fractions (0.255). Rheology evidenced an expected increase of viscosity with the volume fraction and Newtonian behaviour was observed for volume fractions up to 0.161, while higher volume fractions showed shear thinning and shear thickening. In the suspension with a volume fraction of 0.255, a change of the complex modulus was observed at low shear stress. Freeze-drying and nano spray-drying were suitable only when trehalose was employed as an additive. In the former case, particle size was increased by 18% (198.7 ± 1.1 nm) using 20 fold water dilution. With spray-drying, the use of 20 fold dilution in water:ethanol (8:2) led to particle dimensions of 207.7 ±10.0 ( size 20%). In conclusion, cetylpalmitate nanoparticles seem to be suitable for parenteral application, up to volume fractions of 0.16, and pharmaceutical operations, which submit suspensions to shear stress, should not be a critical issue.

We use a simple toy-model to discuss global MHD modes of a neutron star, taking into account the magnetic coupling between the elastic crust and the fluid core. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system. All modes excite Alfvén waves in the core. However, we also show that the modes that are most likely to be excited by a fractured crust, eg. during a magnetar flare, are such that the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the "pure crustal" frequencies. In addition, our model provides a natural explanation for the presence of lower frequency (< 30 Hz) quasi-periodic oscillations seen in the December 2004 giant flare of SGR 1806-20.

Aqueous extracts, prepared from dried or fresh roots, stems or leaves of Mikania glomerata, a plant found in Mata Atlântica in Southeastern Brazil, were able to efficiently neutralize different toxic, pharmacological, and enzymatic effects induced by venoms from Bothrops and Crotalus snakes. Phospholipase A2 activity and the edema induced by Crotalus durissus terrificus venom were inhibited around 100 and ∼40%, respectively, although this inhibition was only partial for Bothrops venoms. The hemorrhagic activity of Bothrops venoms (Bothrops altenatus, Bothrops moojeni, Bothrops neuwiedi, and Bothrops jararacussu) was significantly inhibited by this vegetal species, while the clotting activity of Crotalus durissus terrificus, Bothrops jararacussu, and Bothrops neuwiedi venoms was totally inhibited. Although, the mechanism of action of Mikania glomerata extract is still unknown, the finding that no visible change was detected in the electrophoretic pattern of snake venom after incubation with the extract excludes proteolytic degradation as a potential mechanism. Since the extract of Mikania glomerata significantly inhibited the studied snake venoms, it may be used as an alternative treatment to serumtherapy and, in addition, as a rich source of potential inhibitors of PLA2s, metalloproteases and serineproteases, enzymes involved in several physiopathological human and animal diseases.

In this present work the effects of temperature dependent viscosity and thermal conductivity on the coupling of conduction and Joule heating with MHD free convection flow along a semi-infinite vertical flat plate have been analyzed. The governing boundary layer equations with associated boundary conditions for this phenomenon are transformed to non-dimensional form using the appropriate variables. By the help of the implicit finite difference method with Keller-box scheme the resulting non-linear system of partial differential equation is then solved numerically. The purpose of this paper is to study the skin friction coefficient, the surface temperature, the velocity and the temperature profiles over the whole boundary layer for different values of the Prandtl number Pr, the magnetic parameter M, the thermal conductivity variation parameter γ, the viscosity variation parameter ε and the Joule heating parameter J. The results indicate that the flow pattern, temperature field and rate of heat transfer are significantly dependent on the above mentioned parameters. The local skin friction co-efficient and the surface temperature profiles for different values of ε are compared with previously published works and are found to be in good agreement.

The study of MHD and nano effect on the flow over a moving surface in presence
of thermal radiation, vis
Engineering processes can be modeled as flow over a moving surface. Viscous
nanofluid flows play very important role in chemical engineering. So in this paper the
effect of viscous dissipation and chemi
layer region is studied. The governing equations are solved by HAM by considering
plate movement in both the directions. The effects of non
graphically represented and the results

Abstract
Purpose – The purpose of this study is numerical simulation of magnetohydrodynamics (MHD) water–
Al2O3 nanofluid mixed convection in a grooved channel with internal heat generation in solid cylinders.
Simulations were carried out at Reynolds numbers 50#Re#100, Hartmann numbers 0#Ha#15, Grashof
numbers 5,000#Gr#10
4 and volume fraction 0#w #0.04. The effect of Reynolds number and the
influence of magnetic field and pressure drop on convective heat transfer coefficient were studied in different
volume fractions of nanoparticles at different Reynolds numbers.
Design/methodology/approach – The results show that average Nusselt number increases by
increasing Reynolds and Hartman numbers. Also, when Hartman number increases, velocity profile becomes
asymmetric. Pressure distribution shows that magnetic field applies Lorentz force at opposite direction of the
flow, which causes asymmetric distribution of pressure. As a result, pressure in the upper half of the cylinder
is higher than the lower half. Finally, velocity and temperature contours along the channel for different
Hartmann numbers, volume fraction 3 per cent, Re = 50 and 100 and Gr = 10,000, are presented.
Findings – The effect of Reynolds number and the influence of magnetic field and pressure drop on convective
heat transfer coefficientwere studied in different volume fractions of nanoparticles at different Reynolds numbers.
Originality/value – Effect of MHD on the flow and heat transfer characteristics of Water–Al2O3 nanofluid
in a grooved channel with internal heat generation in solid cylinders.

Vipera ammodytes is the most venomous European snake, whose venom has been used as antigen for immunization of antivenom-producing animals. Same as venom of any other snake, it is a complex mixture of proteins, peptides and other compounds which biochemical and pharmacological variability has been demonstrated at interspecies and intraspecies level. In this work we demonstrated intraspecific variability between 8 venom production batches using both the conventional and the new methodology. Moreover, in contrast to the literature on different venoms' variability, for the first time we were able to select those biochemical differences that are related to and give information on the venom's toxicity and immunogenicity. We have shown that methods quantifying ammodytoxin (the most toxic compound identified so far in the Vipera ammodytes ammodytes venom) content of the venom clearly distinguish between high and low immunogenic venoms.

An analysis has been carried out to study the flow and heat transfer characteristics for MHD viscoelastic boundary layer flow over an impermeable stretching sheet with space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink), viscous dissipation, thermal radiation and magnetic field due to frictional heating. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied vertically in the flow region. The governing partial differential equations for the flow and heat transfer are transformed into ordinary differential equations by a suitable similarity transformation. The governing equations with the appropriate conditions are solved exactly. The effects of viscoelastic parameter and magnetic parameter on skin friction and the effects of viscous dissipation, non-uniform heat source/sink and the thermal radiation on heat transfer characteristics for two general cases namely, the prescribed surface temperature (PST) case and the prescribed wall heat flux (PHF) case are presented graphically and discussed. The numerical results for the wall temperature gradient (the Nusselt number) are presented in tables and are discussed.

The boundary-layer flow and heat transfer over a non-isothermal stretching sheet in a nanofluid with the effect of magnetic field and thermal radiation have been investigated. The transport equations used for the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., thermal radiation parameter R, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order nonlinear ordinary differential equations. These equations were numerically solved using a fourth-order Runge-Kutta method with shooting technique. The analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to see the effects of governing parameters for various physical conditions. Numerical results are obtained for distribution of velocity, temperature and concentration, for both cases i.e., prescribed surface temperature and prescribed heat flux, as well as local Nusselt number and Sherwood number. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le. Besides, it is found that the surface temperature increases with an increase in the Lewis number Le for prescribed heat flux case. A comparison with the previous studies available in the literature has been done and we found an excellent agreement with it.

The steady two-dimensional flow of an incompressible non-Newtonian Molybdenum Disulfide nanofluid in the presence of source or sink between two stretchable or shrinkable walls under the influence of thermal radiation is investigated numerically. A generalized transformation is applied to convert the constructed set of partial differential equations (PDEs) into the system of non-linear coupled ordinary differential equations (ODEs). The obtained system of ODEs is solved by using Runge-Kutta 4 th and 5 th order. The influence of physical parameters, shrinking/ stretching parameter, Casson parameter, Hartmann number, Reynolds number, solid volume fraction, opening angle of the channel and radiation parameter on the velocity and temperature distribution are observed for converging and diverging channels. It is noticed that thermal boundary layer thickness is diminished for increased thermal radiation resulting in gradual temperature fall. The results also reveal that velocity and temperature profile both are elevated on raising the stretching parameter and Hartmann number. A comparative analysis is made out to validate the present results.

The problem of the MHD boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is discussed. Using similarity transformation governing equations are transformed in to nonlinear ordinary differential equation. The Implicit finite difference Keller box method is applied to find the numerical solution of nonlinear differential equation. Graphical results of fluid velocity have been presented and discussed for the related parameters.

In this analysis, MHD boundary layer flow and heat transfer of a fluid with variable viscosity through a porous medium towards a stretching sheet by taking in to the effects of viscous dissipation in presence of heat source/sink is considered. The symmetry groups admitted by the corresponding boundary value problem are obtained by using Lie's scaling group of transformations. These transformations are used to convert the partial differential equations of the governing equations into self-similar non-linear ordinary differential equations. Numerical solutions of these equations are obtained by Runge-Kutta fourth order with shooting method. Numerical results obtained for different parameters such as viscosity variation parameter A, permeability parameter k 1 , heat source/sink parameter k, magnetic field parameter M, Prandtl number Pr, and Eckert number Ec are drawn graphically and effects of different flow parameters on velocity and temperature profiles are discussed. The skin-friction coefficient Àf 00 ð0Þ and heat transfer coefficient Àh 0 (0) are presented in tables.

Numerical investigation is carried out to analyze the flow, heat and mass transfer characteristics of gyrotactic microorganisms contained magneto hydrodynamic Casson fluid flow towards a vertical rotating cone/plate in porous medium. In the presence of thermo diffusion and diffusion thermo effects we have presented dual solutions for the flow over a rotating cone and a rotating flat plate. Further, the numerical solutions are elucidated by using Runge–Kutta–Felhberg integration Scheme. Obtained results are validated with open literature and found an excellent agreement. The influence of non-dimensional governing parameters on velocity, temperature, concentration and density of the motile microorganisms along with the friction factor, local Nusselt, Sherwood numbers and the local density of the motile microorganisms was determined and discussed with the help of graphs and tables. Results proved that there is a significant variation of heat and mass transfer in the flow over a rotating cone and a plate. It is also found that the heat and mass transfer performance of the flow over a rotating cone is significantly high while compared with the flow over a rotating plate.

In this paper the problem of two dimensional, unsteady, laminar, magneto hydro
dynamic free convective flow through a porous medium past a vertical plate in the
presence of heat absorption and chemical reaction is considered. The Dufour effect is
taken into account. The free stream velocity is supposed to follow the exponentially
increasing small perturbation law. The non-dimensional governing equations are
solved analytically by two-term harmonic and non-harmonic functions. The velocity,
temperature and concentration distributions are analyzed for different values of
parameters

A plausible scenario for solar dynamo action is that the large-scale organized toroidal magnetic field is generated by the action of strong radial shear at the base of the solar convection zone, whereas the weaker poloidal field is regenerated by cyclonic convection throughout the convection zone. We show, using high-resolution threedimensional numerical simulations, that the required transport of magnetic field from the convection zone to the overshoot region can be achieved on a convective rather than diffusive timescale by a pumping mechanism in turbulent penetrative compressible convection. A layer of magnetic field initially placed in the convection zone is swept down by strong sinking plumes, locally amplified, and deposited in the stable region at the base of the convection zone, despite the opposing action of magnetic buoyancy. The rate of transport is insensitive to the strength of the initial imposed field.

L'effet d'un champ magnétique sur la détermination du nombre de Rayleigh critique Ra Cr et la stabilité des écoulements de convection naturelle dans une configuration cylindrique de type Czochralski contenant un métal liquide, est faite. Dans la limite des faibles nombres de Prandtl, l'instabilité apparaît sous forme d'oscillations régulières pour des valeurs suffisamment élevées du nombre de Rayleigh. Des diagrammes de stabilité montrent la dépendance du nombre de Rayleigh critique (correspondant à la transition oscillante régulière) et de la fréquence critique des oscillations en fonction du nombre de Hartmann, Ha. Une forte dépendance du nombre de Rayleigh critique et de la fréquence critique F Cr avec l'augmentation du champ magnétique de Ha = 10 à 50 pour les trois nombres de Prandtl, Pr= 0.015, 0.019, 0.026, est obtenue. Mots clés : Convection naturelle/transfert de chaleur/ champ magnétique/ instabilité/métal liquide. Nomenclature B champ magnétique, Tesla F fréquence adimensionnelle F r ,F z Forces adimensionnelles de Lorentz suivant r et z r,z coordonnées cylindriques adimensionnelles r * ,z * coordonnées cylindriques dimensionnelles, m r C rayon du cylindre, m r S rayon du cristal, m H hauteur du cylindre, m Ha nombre de Hartmann Ra nombre de Rayleigh p pression adimensionnelle p * pression, Pa Pr nombre de Prandtl T température adimensionnelle T* température, K t temps dimensionnel, s g accélération de la pesanteur, m 2 .s -1 u,v composantes de la vitesse adimensionnelles u * ,v * composantes de la vitesse dimensionnelles, m.s -1 Symboles grecs α diffusivité thermique, m 2 .s -1 β coefficient d'expansion thermique, K -1 υ viscosité cinématique, m 2 .s -1 σ conductivité électrique, Ω -1 .m -1 ρ masse volumique, Kg.m -3 τ temps adimensionnel ω amplitude adimensionnelle Ψ fonction de courant adimensionnelle Indices et exposants Cr valeur critique c froide h chaude max maximale min minimale Congrès Français de Thermique, SFT 2007, Île des Embiez, 29 mai -1 juin 2007

The development of centered heat conducting obstacle effect on combined magnetoconvective flow in a lid driven chamber has been numerically studied. The enclosure considered has rectangular horizontal lower surfaces and vertical side surfaces. The lower and upper surfaces are insulated. The left wall is mechanically lid driven having uniform temperature T i and velocity v 0 while other vertical side is wavy and maintains higher temperature T h than the lid. The governing two-dimensional flow equations have been solved by using Galerkin weighted residual finite element technique. The investigations are conducted for different values of Richardson number (Ri) and physical parameter i.e. diameter (D) of square solid body. Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the mean Nusselt number (Nu), the average temperature (θ av ) of the fluid and temperature of obstacle center (θ c ) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the chamber. Conducting largest obstacle is preferable for effective heat transfer mechanism in presence of magnetic field.

This paper presents an analysis of combined heat and mass transfer MHD flow past an oscillating vertical porous plate under the action of radiation effects and chemical reaction when heat is supplied to the plate at constant rate. The governing equations are solved in two term perturbation method. The results are obtained for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number. The effects of various parameters on flow variables are illustrated graphically, and the physical aspects of the problem are discussed qualitatively.

In this paper an analysis has been made to study the influence of thermal radiation, a firstorder homogeneous chemical reaction and thermal diffusion (Soret) effects on an unsteady two-dimensional flow of a viscous incompressible electrically conducting fluid flowing past an infinite vertical porous plate in a velocity slip-flow region. The plate is immersed in a heat absorbing highly porous media. Due to high viscosity, viscous dissipation term is considered in the energy equation. A uniform transverse magnetic field is applied to the plate, which absorbs the carrying fluid with a suction velocity varying with time, while the free stream velocity is assumed to increase exponentially. Rosseland approximation is adopted to quantify the radiative heat flux. A multi-parameter perturbation scheme is developed to transform the resulting non-linear partial differential equations into a set of ordinary differential equations. The influence of various physical parameters on the fluid velocity, temperature, and concentration fields as well as viscous drag, Nusselt and Sherwood numbers are presented in terms of graphs and tables.

Present analysis is carried out to study the two-dimensional stagnation-point flow of an in-compressible Carreau fluid toward a shrinking surface. The formulation of the Carreau fluid model has been developed first time for boundary layer problem of shrinking sheet and the governing partial differential equations are rehabilitated into ordinary differential equations using similarity transformations. The simplified nonlinear boundary value problem is solved by Runge-Kutta method after converting into the system of initial value problem using shooting method. Dual solutions are obtained graphically and results are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients are also computed.

This research article explores on the steady of the two-dimensional buoyancy effects on MHD Casson fluid flow over a stretching of permeable sheet through a porous medium in the occurrence of suction/injection. The central PDEs are changed into ODEs by applying similarity transformations and the changed equations’ solutions are got by Runge-Kutta fourth order along with a shooting technique. The working fluid flow is considered for numerous different parameters graphically. It has been observed that velocity decreases, temperature and concentration increase when magnetic field and permeability of porous parameter increases

The problem of two-phase unsteady MHD flow between two concentric cylinders of infinite length has been analysed when the outer cylinder is impulsively started. The system of partial differential equations describing the flow problem is formulated taking the viscosity of the particle phase into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving outer cylinder. The problem is solved using a combination of the Laplace transform technique, D'Alemberts and the Riemann-sum approximation methods. The solution obtained is validated by comparisons with the closed form solutions obtained for the steady states which has been derived separately. The governing equations are also solved using the implicit finite difference method to verify the present proposed method. The variation of the velocity and the skin friction with the dimensionless parameters occuring in the problem are illustrated graphically and discussed for both phases. NOMENCLATURE a radius of the inner cylinder b

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented. A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy. The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity. The governing equations are solved by the perturbation technique and a numerical method. The analytical expressions for the velocity field, the temperature field, the induced magnetic field, the skin-friction, and the rate of heat transfer at the plate are obtained. The numerical results are demonstrated graphically for various values of the parameters involved in the problem. The effects of the Hartmann number, the chemical reaction parameter, the magnetic Prandtl number, and the other parameters involved in the velocity field, the temperature field, the concentration field, and the induced magnetic field from the plate to the fluid are discussed. An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values. The induced magnetic field along the x-direction increases with the increase in the Hartmann number, the magnetic Prandtl number, the heat source/sink, and the viscous dissipation. It is found that the flow velocity, the fluid temperature, and the induced magnetic field decrease with the increase in the destructive chemical reaction. Applications of the study arise in the thermal plasma reactor modelling, the electromagnetic induction, the magnetohydrodynamic transport phenomena in chromatographic systems, and the magnetic field control of materials processing. 1218 J. ZUECO and S. AHMED Nomenclature B0, uniform magnetic field; b x , induced magnetic field along the x-

An investigation was carried out on the numerical solution for thermal radiation effect on inclined magnetic field of magneto hydrodynamic (MHD) free convective heat transfer dissipative fluid flow past a moving vertical porous plate with variable suction. The dimensionless governing equations are formulated in (y*, t*) co-ordinates sysytem with appropriate boundary condition s and the radiative heat flux takes the Rosseland approximation. The equations are solved by using an implicit finite difference method of Crank-Nicolson type. The effects of various parameters on the velocity and temperature fields as well as the Coefficient of skin-friction and Nusselt number were presented graphically and in tabulated forms. It was observed that, when the radiation parameter increases, the velocity and temperature increases in the boundary layer. The effect of increasing values of Hartman number (M) which resulted in decrease in velocity distribution, while, increase in temperature across the boundary layer because of the application of transfer magnetic field which resulted in a restrictive type of force (Lorenz force) similar to drag force which tends to resist the fluid and this reducing its velocity. This model finds applications in geophiscs, metallurgic and also in the design of high temperature industrial processing systems.

An E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

In this paper the problem of two dimensional, unsteady, laminar, magneto hydro
dynamic free convective flow through a porous medium past a vertical plate in the
presence of heat absorption and chemical reaction is considered. The Dufour effect is
taken into account. The free stream velocity is supposed to follow the exponentially
increasing small perturbation law. The non-dimensional governing equations are
solved analytically by two-term harmonic and non-harmonic functions. The velocity,
temperature and concentration distributions are analyzed for different values of
parameters.

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We have developed a two-dimensional semiempirical MHD model of the solar corona and solar wind. The model uses empirically derived electron density proÐles from white-light coronagraph data measured during the Skylab period and an empirically derived model of the magnetic Ðeld which is Ðtted to observed streamer topologies, which also come from the white-light coronagraph data. The electron density model comes from that developed by Guhathakurta and coworkers. The electron density model is extended into interplanetary space by using electron densities derived from the Ulysses plasma instrument. The model also requires an estimate of the solar wind velocity as a function of heliographic latitude and radial component of the magnetic Ðeld at 1 AU, both of which can be provided by the Ulysses spacecraft. The model makes estimates as a function of radial distance and latitude of various Ñuid parameters of the plasma such as Ñow velocity V, e †ective temperature and e †ective heat Ñux T eff , q eff , which are derived from the equations of conservation of mass, momentum, and energy, respectively. The term "" e †ective ÏÏ indicates that wave contributions could be present. The model naturally provides the spiral pattern of the magnetic Ðeld far from the Sun and an estimate of the large-scale surface magnetic Ðeld at the Sun, which we estimate to be D12È15 G. The magnetic Ðeld model shows that the large-scale surface magnetic Ðeld is dominated by an octupole term. The model is a steady state calculation which makes the assumption of azimuthal symmetry and solves the various conservation equations in the rotating frame of the Sun. The conservation equations are integrated along the magnetic Ðeld direction in the rotating frame of the Sun, thus providing a nearly self-consistent calculation of the Ñuid parameters. The model makes a minimum number of assumptions about the physics of the solar corona and solar wind and should provide a very accurate empirical description of the solar corona and solar wind. Once estimates of mass density o, Ñow velocity V, e †ective temperature e †ective heat Ñux and T eff , q eff , magnetic Ðeld B are computed from the model and waves are assumed unimportant, all other plasma parameters such as Mach number, speed, gyrofrequency, etc. can be derived as a function of Alfve n radial distance and latitude from the Sun. The model can be used as a planning tool for such missions as Solar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind. The model will be used to construct a semiempirical MHD description of the steady state solar corona and solar wind using the SOHO Large Angle Spectrometric Coronagraph (LASCO) polarized brightness white-light coronagraph data, SOHO Extreme Ultraviolet Imaging Telescope data, and Ulysses plasma data.

In the present article, we have studied the two dimensional tangent hyperbolic fluid flow towards a stretching sheet with a magnetic field. Governing equations for the proposed model are modelled and then simplified using boundary layer approach and similarity transformations. Simplified governing equations are then solved numerically with the help of fourth and fifth order Runge-Kutta-Fehlberg method. Physical features of the involved parameters are presented and discussed.

An analysis of unsteady MHD flow of an electrically conducting visco-elastic fluid confined between two horizontal parallel non conducting plates in presence of a transverse magnetic field and Hall current is presented. The lower plate is a stretching sheet while the upper one is an oscillating porous plate, which is oscillating in its own plane. The motion of the fluid is produced by the stretching of the lower plate. A constant suction is applied at the upper plate and the stretching velocity is taken to be a linear function of distance along the channel. The equations governing the flow field are solved by perturbation technique. Expressions for velocity distribution of the flow field and non-dimensional skin-friction coefficient are obtained and presented graphically to observe the visco-elastic effect in combination of other flow parameters involved in the solution. The flow field is observed to be considerably affected by the visco-elastic parameter.

We present a detailed numerical study of the Gough & McIntyre model for the solar tachocline. This model explains the uniformity of the rotation profile observed in the bulk of the radiative zone by the presence of a large-scale primordial magnetic field confined below the tachocline by flows originating from within the convection zone. We attribute the failure of previous numerical attempts at reproducing even qualitatively Gough & McIntyre's idea to the use of boundary conditions which inappropriately model the radiative-convective interface. We emphasize the key role of flows downwelling from the convection zone in confining the assumed internal field. We carefully select the range of parameters used in the simulations to guarantee a faithful representation of the hierarchy of expected lengthscales. We then present, for the first time, a fully nonlinear and self-consistent numerical solution of the Gough & McIntyre model which qualitatively satisfies the following set of observational constraints: (i) the quenching of the large-scale differential rotation below the tachocline-including in the polar regions-as seen by helioseismology (ii) the confinement of the large-scale meridional flows to the uppermost layers of the radiative zone as required by observed light element abundances and suggested by helioseismic sound-speed data.

Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.

We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and 2D magnetic Bénard problem and also some shell models of turbulence. We first prove the existence and uniqueness theorem for the class considered. Our main result is a Wentzell-Freidlin type large deviation principle for small multiplicative noise which we prove by weak convergence method.

The aim of this work was to characterize lipid nanoparticles from a rheological point of view, intended for drug delivery after parenteral administration. The conditions to obtain a re-dispersible powder using freeze-drying and spray-drying have also been investigated. Lipid nanoparticles (179.9 ± 6.2 nm) were prepared with the high pressure homogenization technique, using previously established optimal conditions (lipid volume fraction of 0.121), though particle size increased (285.9 ± 4.3 nm) in suspensions produced with higher lipid volume fractions (0.255). Rheology evidenced an expected increase of viscosity with the volume fraction and Newtonian behaviour was observed for volume fractions up to 0.161, while higher volume fractions showed shear thinning and shear thickening. In the suspension with a volume fraction of 0.255, a change of the complex modulus was observed at low shear stress. Freeze-drying and nano spray-drying were suitable only when trehalose was employed as an additive. In the former case, particle size was increased by 18% (198.7 ± 1.1 nm) using 20 fold water dilution. With spray-drying, the use of 20 fold dilution in water:ethanol (8:2) led to particle dimensions of 207.7 ±10.0 ( size 20%). In conclusion, cetylpalmitate nanoparticles seem to be suitable for parenteral application, up to volume fractions of 0.16, and pharmaceutical operations, which submit suspensions to shear stress, should not be a critical issue.

We show that the generally neglected Hall term in the equations for two-fluid magnetohydrodynamics may have a profound effect on a-dynamo action. The new calculation, in addition to subsuming the standard results from the mean field approach, contains a contribution to the a-coefficient entirely due to the Hall current in the microscale.

In this paper, the unsteady magneto hydrodynamic flow past an oscillating vertical plate under the influence of Soret and Dufour effects has been investigated. The nonlinear partial differential equations governing the flow are solved by an iterative technique based on finite difference scheme. The flow phenomenon is characterized with the help of velocity, temperature and concentration profiles for different parameters.

Aim of the paper is to investigate the hydromagnetic effects on the unsteady free convection flow, heat and mass transfer characteristics in a viscous, incompressible and electrically conducting fluid past an exponentially accelerated vertical plate by taking into account the heat due to viscous dissipation. The problem is governed by coupled non-linear partial differential equations. The dimensionless equations of the problem have been solved numerically by the unconditionally stable finite difference method of Dufort -Frankel's type. The effects of governing parameters on the flow variables are discussed quantitatively with the aid of graphs for the flow field, temperature field, concentration field, skin-friction, Nusselt number and Sherwood number.

ABSTRACT In this paper we analyzed the effect of magnetic field on stagnation point flow and heat transfer due to nanofluid towards a stretching sheet. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters viz. velocity ratio parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations to coupled higher order nonlinear ordinary differential equation. These equations were numerically solved using Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for velocity, temperature and concentration distribution, as well as the skin friction coefficient, local Nusselt number and Sherwood number. The results indicate that the skin friction coefficient Cf and local Nusselt number increases with an increase in velocity ratio parameter A. Likewise, the local Sherwood number increases with an increase in both velocity ratio A and Lewis number Le. Besides, it is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. A &amp;gt; 1, and it decreases when A &amp;lt; 1. A comparison with a previous study available in the literature has been done and we found an excellent agreement with them.

The effects of heat and mass transfer on MHD mixed convection flow of a vertical surface with radiation, heat source/absorption and chemical reaction has been is discussed. The resulting set of coupled non-linear ordinary differential equations is solved by perturbation technique and for graphs we used MATLAB software. Approximate solutions have been derived for the velocity, temperature, concentration profiles, skin friction and Nusselt number. The obtained results are discussed with the help of the graphs to observe the effect of various parameters like Grashof number, modified Grashof number, Schmidt number, Prandtl number, Magnetic parameter, Radiation parameter, Chemical reaction, Heat source parameter, Radiation absorption parameter.

The paper describes fluidic networks consisting of individually controlled branches. The networks' basic building blocks are conduits equipped with two electrodes positioned on opposing walls. The entire device is either subjected to an external uniform magnetic field or fabricated within a magnetic material. When a prescribed potential difference is applied across each electrode pair, it induces current in the liquid (assumed to be at least a weak electrolyte solution). Analogously with electric circuits, by judicious application of the potential differences at various branches, one can direct liquid flow in any desired way without a need for mechanical pumps or valves. Equipped with additional, internally located electrodes, the network branches double as stirrers capable of generating chaotic advection. The paper describes the basic building blocks for such a network, the operation of these branches as stirrers, a general linear graph-based theory for the analysis and optimal control of fluidic magneto-hydrodynamic networks, an example of a network fabricated with low temperature, co-fired ceramic tapes, and preliminary experimental observations that illustrate that the ideas described in this paper can, indeed, be implemented in practice.

A model for GRMHD disk outflows with neutrino-driven mass ejection is developed, and employed to calculate the structure of the outflow in the sub-slow magnetosonic region and the mass loading of the outflow, under conditions anticipated in the central engines of gamma-ray bursts. The dependence of the mass flux on the conditions in the disk, on magnetic field geometry, and on other factors is carefully examined for a range of neutrino luminosities expected in hyperaccreting black holes. It is found that a fraction of up to a few percent of the neutrino luminosity produced inside the disk is deposited in the upper disk layers, resulting in a steep rise of the specific entropy and the consequent ejection of baryons along magnetic field lines. For the range of conditions explored the final value of the dimensionless entropy per baryon in the wind is typically below 100. The fraction of neutrino luminosity that is ultimately being converted to kinetic energy flux is shown to be a sensitive function of the effective neutrino temperature at the flow injection point, and the shape of magnetic field lines in the sub-slow region, but is practically independent of the strength of poloidal and toroidal magnetic fields. We conclude that magnetic launching of ultra-relativistic polar outflows from the innermost parts of the disk is in principle possible provided the neutrino luminosity is sufficiently low, L ν < ∼ 10 52 erg s −1 or so. The conditions found to be optimal for the launching of an ultra-relativistic jet are also the conditions favorable for large neutron-to-proton ratio in the disk, suggesting that a large neutron excess in GRB jets, as often conjectured, may be possible. However, the outflow time appears to be comparable to the neutronization timescale, implying that the electron fraction should evolve during the initial acceleration phase. Further analysis is required to determine the composition profile in the wind.

Helicity and \alpha effect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak)

We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.

Effect of radiation and mass transfer on the transient free convection flow of a dissipative past semi-infinite vertical plate with uniform heat and mass flux is analyzed, by taking into account the effect of viscous dissipation. This type of problems finds application in many technological and engineering fields such as plasma studies, petroleum industries, MHD energy generators, cooling of nuclear reactors, the boundary layer control in aerodynamics, crystal growth and furnace engineering. The Rosseland approximation is used to describe the radiative heat transfer in the limit of the optically thick fluid. The non-linear, coupled equations are solved using an implicit finite difference scheme of Crank-Nicolson type. Transient temperature, concentration and velocity profiles, local and average skinfriction coefficient, Nusselt number and Sherwood number are presented graphically and discussed. It is observed that, when the radiation parameter increases the velocity and temperature decrease accompanied by simultaneous reduction in both momentum and thermal boundary layers.

We report preliminary results of a three-dimensional simulation of the buoyant rise of a strongly twisted, kinkunstable magnetic flux tube through a gravitationally stratified layer representing the solar convection zone. The numerical calculations employ the well-known anelastic approximation, which is suitable for studying slow, subsonic dynamical processes in the pressure-dominated, high-b plasma of the solar interior. This Letter investigates the case in which the initial twist of the buoyant flux tube is sufficiently high that the e-folding growth times of the unstable kink modes are short in comparison to the rise time of the flux tube. Our simulation shows that the flux tube becomes kinked and that the top portion of the flux tube evolves into a buckled shape with the tube axis being deflected by more than 90Њ from its original orientation. We suggest that the emergence of this buckled flux tube can give rise to a compact magnetic bipole with polarity order inverted from Hale's polarity law, similar to the configuration often seen in d spots.