heat conductivity
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Yuki Homma

Abstract In plasmas of relatively lower collisionality, such as scrape-off layer (SOL) of fusion tokamak device, parallel heat conductivity of plasma ion becomes smaller than expected by the classical Spitzer-Harm model due to nonlocal kinetic effect. We have assessed, by simulation, impact and role of such kinetic effect of ion heat conductivity (abbreviated by ion KE in this paper) on DEMO relevant tokamak SOL plasma, supposing Japanese demonstration tokamak reactor concept JA DEMO. A series of test simulation, where the ion KE is modeled by a widely used Free-streaming energy (FSE) limited model, has demonstrated the following significant impact of the ion KE on JA DEMO SOL plasma at the baseline operation scenario: (1) the ion KE decreases the ion parallel heat flux density around X-point and further upstream of low field side (LFS) area along the separatrix, where the parallel collisionality tends to decrease due to combination of higher temperature, lower density (i.e. longer mean free path of ion collisions) and higher temperature gradient (shorter characteristic length). Up to 40-60 % of decrease, compared to the case w/o ion KE, is observed among the tested cases where the ion KE level, specified by parameter αi in the FSE-limited model, is scanned over the possible range 0.2 < αi < 2.0. (2) The ion KE leads to significant increase in the ion temperature Ti (up to 600 % of increase among the tested cases) and significant decrease in the ion density ni (up to -80 % of decrease among the tested cases), widely over SOL upstream. By energy balance analysis, it has been suggested that the ion KE affects the upstream ni and Ti, respectively by power of 0.4 and -0.4 of the flux limiting factor, around the separatrix upstream as far as spatial change in plasma parameters are moderate. The results of this study serve as a fundamental assessment of the ion KE for DEMO relevant SOL plasma, clarifying the need of further sophistication of the modeling toward quantitaive prediction.

2021 ◽  
pp. 181-190
D. A Shlyakhin ◽  
M. A Kalmova

А new closed-loop solution for the coupled nonstationary problem of thermoelectric elasticity is designed for a long piezoceramic radially polarized cylinder. The case of the nonstationary load acting on its inner cylindrical surface is considered as a function of temperature change at a given law of the convection heat exchange on the outer face wall (boundary conditions of heat conductivity of the 1st and 3rd types). Electrodynamic cylinder surfaces are connected to a measuring device with a high input resistance (electric idling). We investigate the problem where the rate of the temperature load changes does not affect the inertial characteristics of the elastic system. It makes it possible to expand the initial linear computational relations with the equilibrium, electrostatics and heat conductivity equations with respect to the radial component of the displacement vector, electric potential as well as the function of temperature field changes. Hyperbolic LS-theory of the thermal conductivity is used in the computations. The problem is solved with a generalized method of biorthogonal finite integral transformation based on a multicomponent ratio of eigen functions of two homogeneous boundary value problems. The structural algorithm of this approach allows identifying a conjugated operator, without which it is impossible to solve non-self-conjugated linear problems in mathematical physics. The resulted computational relations make it possible to determine the stress-strain state, temperature and electric fields induced in the piezoceramic element under an arbitrary external temperature effect. By connecting the electroelastic system to the measuring tool, we can find voltage. Firstly, the analysis of the numerical results allows identifying the rate of the temperature load changes, at which it is necessary to use the hyperbolic theory of thermal conductivity. Secondly, it allows determining the physical characteristics of the piezoceramic material for the case when the rate of changing the body volume leads to a redistribution of the temperature field. The developed computational algorithm can be used to design non-resonant piezoelectric temperature sensors.

2021 ◽  
Vol 2021 (1) ◽  
Tariq Mahmood ◽  
Mei Sun

AbstractThis paper considers the initial-boundary value problem of the one-dimensional full compressible nematic liquid crystal flow problem. The initial density is allowed to touch vacuum, and the viscous and heat conductivity coefficients are kept to be positive constants. Global existence of strong solutions is established for any $H^{2}$ H 2 initial data in the Lagrangian flow map coordinate, which holds for both vacuum and non-vacuum case. The key difficulty is caused by the lack of the positive lower bound of the density. To overcome such difficulty, it is observed that the ratio of $\frac{\rho _{0(y)}}{\rho (t,y)}$ ρ 0 ( y ) ρ ( t , y ) is proportional to the time integral of the upper bound of temperature and vector director field, along the trajectory. Density weighted Sobolev type inequalities are constructed for both temperature and director field in terms of $\frac{\rho _{0(y)}}{\rho (t,y)}$ ρ 0 ( y ) ρ ( t , y ) and small dependence on their dissipation estimates. Besides this, to deal with cross terms arising due to liquid crystal flow, higher order priori estimates are established by using effective viscous flux.

Coatings ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1439
Guodong Li ◽  
Fei Ma ◽  
Zhijie Li ◽  
Yi Xu ◽  
Fangyuan Gao ◽  

In this study, plasma electrolytic oxidation (PEO) was performed on Al and AlSi substrates using a pulsed direct current (DC) power source. The coating process was carried out in a Na2SiO3 electrolyte with the systematic change of pulse frequency (50–1400 Hz). The surface characteristics of the coatings were examined using scanning electron microscopy (SEM). The phase structure was characterized using X-ray diffraction (XRD). A differential scanning calorimeter (DSC) and a laser flash apparatus (LFA) were employed to test heat capacity and heat conductivity, respectively. Results showed that as the discharge frequency increased, the thermal physical properties of Al-PEO and AlSi-PEO coatings changed in different ways. At a high frequency, Al-PEO coatings had low porosity and were closed-pore structured whereas AlSi-PEO coatings had high porosity and large-size open-pore structures could be observed on their surfaces due to concentrated discharges. Based on these findings, it was found that the thermal productivity of coatings is closely correlated with the open-/closed-pore structure instead of porosity. PEO coatings with low heat capacity or low heat conductivity could be obtained with a controlled frequency.

2021 ◽  
pp. 103595
V.V. Makarova ◽  
S.N. Gorbacheva ◽  
A.V. Kostyuk ◽  
S.V. Antonov ◽  
Yu.Yu. Borisova ◽  

2021 ◽  
Vol 23 (4) ◽  
Nilasis Chaudhuri

AbstractThe goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of the compressible complete Euler system in full space $$ \mathbb {R}^d,\; d=2,3 $$ R d , d = 2 , 3 is a weak solution of the system, then the approximate solutions eventually converge strongly in suitable norms locally under a minimal assumption on the initial data of the approximate solutions. The class of consistent approximate solutions is quite general and includes the vanishing viscosity and heat conductivity limit. In particular, they may not satisfy the minimal principle for entropy.

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