scholarly journals Steady-state flows in a visco-resistive magnetohydrodynamic model of tokamak plasmas with inhomogeneous heating

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
E. Roverc'h ◽  
H. Oueslati ◽  
M.-C. Firpo
Keyword(s):  
Steady State ◽  
Temperature Gradient ◽  
Velocity Fields ◽  
Tokamak Plasmas ◽  
Uniform Temperature ◽  
Toroidal Plasma ◽  
Spatially Inhomogeneous ◽  
Symmetry Argument ◽  
Magnetohydrodynamic Model ◽  
Moderate Magnitude

The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanishing velocity fields) are computed for a toroidal JET-like geometry. It is shown that a spatially inhomogeneous heating of moderate magnitude leads to an increase of typical toroidal speeds with respect to the situation with uniform temperature with identical mean Hartmann numbers. A symmetry argument is introduced to capture the symmetry breaking, induced by the temperature gradient, that produces a net toroidal plasma flow.

Temperature profiles in endothermic and exothermic reactions and the interpretation of experimental rate data

1970 ◽  
Vol 320 (1540) ◽  
pp. 71-100 ◽  
Keyword(s):  
Steady State ◽  
Correction Factor ◽  
Exothermic Reaction ◽  
Kinetic Studies ◽  
Activation Energies ◽  
Uniform Temperature ◽  
Exothermic Reactions ◽  
Arrhenius Function ◽  
Point To Point ◽  
Reacting Systems

Any endothermic or exothermic reaction is accompanied by self-cooling or self-heating. In reacting systems in which heat transfer is controlled by conduction, non-uniform temperature-position profiles are established. Examples of this situation are the exothermic decomposition of gaseous diethyl peroxide and the endothermic decomposition of nitrosyl chloride at low pressures (when convection is unimportant). In kinetic studies, allowance must be made for the non-uniform temperature to derive accurate isothermal velocity constants and Arrhenius parameters. In the present paper, the necessary corrections have been derived for a reactant in the steady state whose reaction rate varies exponentially with temperature and in which the temperature excess varies from point to point, being zero at the boundary (Frank-Kamenetskii’s conditions). The geometries considered are the slab, cylinder and sphere. The temperature gradient at the surface in the steady state ( Г ) occupies a key position, and this is exploited to find the correction factor required to convert 'observed’ rate constants to isothermal conditions, and thence to correct ‘observed’ activation energies and pre-exponential factors. The correction factor is found to be simply related to Frank- Kamenetskii’s δ (a dimensionless measure of heat-release rate). A similar analysis is given for systems hotter or cooler than their surroundings but uniform in temperature—such as well stirred fluid systems or small solid crystals (Semenov’s conditions). In these circumstances, systems of arbitrary geometry may be studied, and no approximation need be made to the Arrhenius function. For either type of boundary condition, uncorrected activation energies are overestimates in exothermic reactions and underestimates in endothermic reactions. Explicit relations are derived for making corrections. Boundary conditions intermediate between the two extremes investigated can also be treated though the resulting expressions are more cumbersome. In an appendix, an alternative ‘experimental’ approach is made to the elimination of errors from measured reaction velocities. This approach identifies the measured velocities with a temperature intermediate between those at centre and surface. The optimum choice, which weights the central and surface temperatures in the ratios 2:1 (slab), 1:1 (cylinder) and 2:3 (sphere), gives exactly correct results for the cylinder and acceptable precision for the slab and sphere even to within 5 K of the explosion limit. Other correction methods are also discussed.

Solutions for Non-Newtonian Flow Into Elliptical Openings

1991 ◽  
Vol 58 (3) ◽  
pp. 820-824 ◽  
Author(s):  
A. Bogobowicz ◽  
L. Rothenburg ◽  
M. B. Dusseault
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Steady State ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Velocity Fields ◽  
Newtonian Flow ◽  
Element Analysis ◽  
Elliptical Opening ◽  
Elliptical Coordinates

A semi-analytical solution for plane velocity fields describing steady-state incompressible flow of nonlinearly viscous fluid into an elliptical opening is presented. The flow is driven by hydrostatic pressure applied at infinity. The solution is obtained by minimizing the rate of energy dissipation on a sufficiently flexible incompressible velocity field in elliptical coordinates. The medium is described by a power creep law and solutions are obtained for a range of exponents and ellipse eccentricites. The obtained solutions compare favorably with results of finite element analysis.

scholarly journals DRIVEN DROPLETS BY THERMOCAPILLARY EFFECT: QUADRATIC DEPENDENCE OF THE SURFACE TENSION ON THE TEMPERATURE

Anales AFA ◽  
2020 ◽  
Vol 31 (3) ◽  
pp. 107-111
Author(s):  
J.R. Mac Intyre ◽  
◽  
J.M. Gomba ◽  
C. A. Perazzo ◽  
◽  
...  
Keyword(s):  
Surface Tension ◽  
Temperature Gradient ◽  
Present Article ◽  
Solid Surface ◽  
Linear Dependence ◽  
Complex Dynamics ◽  
Uniform Temperature ◽  
Thermocapillary Effect ◽  
Partial Wetting ◽  
Wetting Fluids

We study the migration of droplets on a solid surface which is under a uniform temperature gradient. The present article focus on partial wetting fluids which surface tension depends on the squared temperature. These type of liquids, called self-rewetting, show a complex dynamics and here we will compare with those liquids of linear dependence in the temperature. Unlike to the latter ones, the droplet width increases with the time.

Study on Radial Temperature Distribution of Aluminum Dispersed Nuclear Fuels: U3O8-Al, U3Si2-Al, and UN-Al

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Jayangani I. Ranasinghe ◽  
Ericmoore Jossou ◽  
Linu Malakkal ◽  
Barbara Szpunar ◽  
Jerzy A. Szpunar
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Gradient ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Temperature Profiles ◽  
Nuclear Fuels ◽  
State Heat ◽  
Steady State Heat

The understanding of the radial distribution of temperature in a fuel pellet, under normal operation and accident conditions, is important for a safe operation of a nuclear reactor. Therefore, in this study, we have solved the steady-state heat conduction equation, to analyze the temperature profiles of a 12 mm diameter cylindrical dispersed nuclear fuels of U3O8-Al, U3Si2-Al, and UN-Al operating at 597 °C. Moreover, we have also derived the thermal conductivity correlations as a function of temperature for U3Si2, uranium mononitride (UN), and Al. To evaluate the thermal conductivity correlations of U3Si2, UN, and Al, we have used density functional theory (DFT) as incorporated in the Quantum ESPRESSO (QE) along with other codes such as Phonopy, ShengBTE, EPW (electron-phonon coupling adopting Wannier functions), and BoltzTraP (Boltzmann transport properties). However, for U3O8, we utilized the thermal conductivity correlation proposed by Pillai et al. Furthermore, the effective thermal conductivity of dispersed fuels with 5, 10, 15, 30, and 50 vol %, respectively of dispersed fuel particle densities over the temperature range of 27–627 °C was evaluated by Bruggman model. Additionally, the temperature profiles and temperature gradient profiles of the dispersed fuels were evaluated by solving the steady-state heat conduction equation by using Maple code. This study not only predicts a reduction in the centerline temperature and temperature gradient in dispersed fuels but also reveals the maximum concentration of fissile material (U3O8, U3Si2, and UN) that can be incorporated in the Al matrix without the centerline melting. Furthermore, these predictions enable the experimental scientists in selecting an appropriate dispersion fuel with a lower risk of fuel melting and fuel cracking.

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