Self-Consistent Models for Small Photospheric Flux Tubes

We give a short summary of some results of a numerical study of magnetic field concentrations in the solar photosphere and upper convection zone. We have developed a 2D time dependent code for the full MHD equations (momentum equation, equation of continuity, induction equation for infinite conductivity and energy equation) in slab geometry for a compressible medium. A Finite-Element-technique is used. Convective energy transport is described by the mixing-length formalism while the diffusion approximation is employed for radiation. We parametrize the inhibition of convective heat flow by the magnetic field and calculate the material functions (opacity, adiabatic temperature gradient, specific heat) self-consistently. Here we present a nearly static flux tube model with a magnetic flux of ∼ 1018 mx, a depth of 1000 km and a photospheric diameter of ∼ 300 km as the result of a dynamical calculation. The influx of heat within the flux tube at the bottom of the layer is reduced to 0.2 of the normal value. The mass distribution is a linear function of the flux function A: dm(A)/dA = const. Fig. 1 shows the model: Isodensities (a), fieldlines (b), isotherms (c) and lines of constant continuum optical depth (d) are given. The “Wilson depression” (height difference between τ = 1 within and outside the tube) is ∼ 150 km and the maximum horizontal temperature deficit is ∼ 3000 K. Field strengths as function of x for three different depths and as function of depth along the symmetry axis are shown in (e) and (f), respectively. Note the sharp edge of the tube.

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29. The internal constitution of sunspots

Symposium - International Astronomical Union ◽

10.1017/s0074180900237856 ◽

1958 ◽

Vol 6 ◽

pp. 263-274 ◽

Cited By ~ 24

Author(s):

A. Schlüter ◽

S. Temesváry

Keyword(s):

Magnetic Field ◽

Physical Properties ◽

Flux Tube ◽

Energy Transport ◽

Convection Zone ◽

Vertical Component ◽

Relative Distribution ◽

Physical Processes ◽

Internal Constitution ◽

The Magnetic Field

The constitution of stationary single sunspots of circular shape is considered. Account is taken of the mechanical effects of the magnetic field, including those which arise from the curvature of the lines of force. To make the system of magneto-hydrostatic equations manageable, it is assumed that the relative distribution of the vertical component of the magnetic field is the same across the flux-tube of the spot in all depths. Preliminary results indicate that suppression of convective energy transport by the magnetic field in those depths in which ionization of hydrogen takes place, will give the essential observable properties of sunspots, relatively independent on the asumptions about the physical processes in greater depths. There the physical properties of matter can deviate but very little from those of the indisturbed hydrogen convection zone.

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Forced Convection in High Porosity Metal Foams

Journal of Heat Transfer ◽

10.1115/1.1287793 ◽

2000 ◽

Vol 122 (3) ◽

pp. 557-565 ◽

Cited By ~ 567

Author(s):

V. V. Calmidi ◽

R. L. Mahajan

Keyword(s):

Forced Convection ◽

Energy Transport ◽

Numerical Study ◽

Momentum Equation ◽

Metal Foams ◽

Local Thermal Equilibrium ◽

High Porosity ◽

Fluid Medium ◽

Practical Applications ◽

Semi Empirical

This paper reports an experimental and numerical study of forced convection in high porosity (ε∼0.89–0.97) metal foams. Experiments have been conducted with aluminum metal foams in a variety of porosities and pore densities using air as the fluid medium. Nusselt number data has been obtained as a function of the pore Reynolds number. In the numerical study, a semi-empirical volume-averaged form of the governing equations is used. The velocity profile is obtained by adapting an exact solution to the momentum equation. The energy transport is modeled without invoking the assumption of local thermal equilibrium. Models for the thermal dispersion conductivity, kd, and the interstitial heat transfer coefficient, hsf, are postulated based on physical arguments. The empirical constants in these models are determined by matching the numerical results with the experimental data obtained in this study as well as those in the open literature. Excellent agreement is achieved in the entire range of the parameters studied, indicating that the proposed treatment is sufficient to model forced convection in metal foams for most practical applications. [S0022-1481(00)01903-4]

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Computational Dynamics of Arterial Blood Flow in the Presence of Magnetic Field and Thermal Radiation Therapy

Advances in Mathematical Physics ◽

10.1155/2014/915640 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 10

Author(s):

T. Chinyoka ◽

O. D. Makinde

Keyword(s):

Magnetic Field ◽

Thermal Radiation ◽

Energy Transport ◽

Numerical Study ◽

Point Of View ◽

Arterial Blood Flow ◽

Hyperthermia Treatment ◽

Computational Dynamics ◽

Arterial Blood ◽

Tumor Tissues

We conduct a numerical study to determine the influence of magnetic field and thermal radiation on both velocity and temperature distributions in a single blood vessel. The model here assumes that blood is a Newtonian incompressible conducting fluid with radially varying viscosity due to hematocrit variation. The transient equations of momentum and energy transport governing the flow in an axisymmetric configuration are solved numerically using a semi-implicit finite difference method. Results are presented graphically and discussed both qualitatively and quantitatively from the physiological point of view. The results of this work may enhance current understanding of the factors that determine the effects of hyperthermia treatment on tumor tissues.

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Fluctuation dynamo in a weakly collisional plasma

Journal of Plasma Physics ◽

10.1017/s0022377820000860 ◽

2020 ◽

Vol 86 (5) ◽

Author(s):

D. A. St-Onge ◽

M. W. Kunz ◽

J. Squire ◽

A. A. Schekochihin

Keyword(s):

Magnetic Field ◽

Magnetic Energy ◽

Numerical Study ◽

Collisional Plasma ◽

Mhd Equations ◽

Saturated State ◽

Mhd Dynamo ◽

Pressure Anisotropy ◽

Field Lines ◽

The Magnetic Field

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

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2D numerical modeling of pulsed plasma acceleration by a magnetic field

Laser and Particle Beams ◽

10.1017/s0263034600182163 ◽

2000 ◽

Vol 18 (2) ◽

pp. 269-273

Author(s):

A.A. KONDRATYEV

Keyword(s):

Magnetic Field ◽

Numerical Study ◽

Initial Distribution ◽

Mhd Equations ◽

Pulsed Plasma ◽

Plasma Acceleration ◽

Plasma Parameters ◽

Current Channel ◽

Plasma Gun ◽

Neutral Gas

Pulsed plasma guns are used to obtain high-velocity (107–108 cm/s) plasma flows. Their performance is restricted by an instability of the plasma acceleration by a magnetic field. This paper presents results of a 2D numerical study of plasma dynamics in the plasma gun. The ZENIT-2D code solving the magnetohydrodynamic (MHD) equations on a fixed Eulerian mesh is used. The plasma parameters and geometry are chosen to be close to the parameters of the MK-200 installation (Sidnev et al., 1983). The influence of the initial distribution of a neutral gas on accelerator performance is investigated. A brief description of the code and details of the simulations are presented. It is shown that the instability of acceleration leads to turbulent mixing of the plasma and magnetic field and, correspondingly, to a broader current channel than that predicted by the classical diffusion with the Spitzer conductivity. Numerical results are compared with experimental data (Bakhtin & Zhitlukhin, 1998) displaying a good qualitative agreement.

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