scholarly journals Self-Similar Hydrodynamics with Heat Conduction

10.5772/27687 ◽  
2011 ◽  
Author(s):  
Masakatsu Murakami
Keyword(s):  
Heat Conduction ◽  
Self Similar

Self-similar solutions of unsteady ablation flows in inertial confinement fusion

2008 ◽  
Vol 603 ◽  
pp. 151-178 ◽  
Author(s):  
C. BOUDESOCQUE-DUBOIS ◽  
S. GAUTHIER ◽  
J.-M. CLARISSE
Keyword(s):  
Heat Conduction ◽  
Inertial Confinement Fusion ◽  
Group Symmetry ◽  
Physical Analysis ◽  
Inertial Confinement ◽  
Nonlinear Heat Conduction ◽  
Starting Point ◽  
Confinement Fusion ◽  
Self Similar ◽  
Similar Solutions

We exhibit and detail the properties of self-similar solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction which are relevant to inertial confinement fusion (ICF). These solutions have been found after several contributions over the last four decades. We first derive the set of ODEs – a nonlinear eigenvalue problem – which governs the self-similar solutions by using the invariance of the Euler equations with nonlinear heat conduction under the two-parameter Lie group symmetry. A sub-family which leaves the density invariant is detailed since these solutions may be used to model the ‘early-time’ period of an ICF implosion where a shock wave travels from the front to the rear surface of a target. A chart allowing us to determine the starting point of a numerical solution, knowing the physical boundary conditions, has been built. A physical analysis of these unsteady ablation flows is then provided, the associated dimensionless numbers (Mach, Froude and Péclet numbers) being calculated. Finally, we show that self-similar ablation fronts generated within the framework of the above hypotheses (electron heat conduction, growing heat flux at the boundary, etc.) and for large heat fluxes and not too large pressures at the boundary do not satisfy the low-Mach-number criteria. Indeed both the compressibility and the stratification of the hot-flow region are too large. This is, in particular, the case for self-similar solutions obtained for energies in the range of the future Laser MegaJoule laser facility. Two particular solutions of this latter sub-family have been recently used for studying stability properties of ablation fronts.

On the correctness of a model for phase transitions in binary alloys

1990 ◽  
Vol 1 (4) ◽  
pp. 327-338 ◽  
Author(s):  
I. G. Götz
Keyword(s):  
Phase Transitions ◽  
Heat Conduction ◽  
Stability Criterion ◽  
Binary Alloys ◽  
The Self ◽  
Self Similar Solution ◽  
Self Similar ◽  
The Stability ◽  
Similar Solutions ◽  
And Diffusion

The main result of this paper is a non-uniqueness theorem for the self-similar solutions of a model for phase transitions in binary alloys. The reason for this non-uniqueness is the discontinuity in the coefficients of heat conduction and diffusion at the inter-phase. Also the existence of a self-similar solution and the stability criterion are discussed.

scholarly journals Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium

2016 ◽  
Vol s2 ◽  
Author(s):  
Barna IF ◽  
Kersner R
Keyword(s):  
Heat Conduction ◽  
Shock Waves ◽  
Solid Medium ◽  
Self Similar

Thermal conductivity in a laser-created plasma heated by inverse bremsstrahlung absorption

1982 ◽  
Vol 28 (1) ◽  
pp. 65-92 ◽  
Author(s):  
R. Balescu
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Heat Conductivity ◽  
Time Dependent ◽  
Reference State ◽  
Inverse Bremsstrahlung ◽  
Conduction Theory ◽  
Self Similar ◽  
Inverse Bremsstrahlung Absorption

The heat conductivity of a laser-created plasma heated by inverse bremsstrahlung absorption is investigated in the vicinity of a self-similar state (SSS), taken as reference state. Under certain conditions, the slowly varying macroscopic quantities obey true, local hydrodynamical equations and a well-defined, positive, heat conductivity exists. The latter is strongly time-dependent through the unperturbed temperature. Its value, compared to the classical heat conductivity at the same temperature, shows a reduction of about 20%. It is shown that, for high intensities and/or long wavelengths, the linear heat conduction theory necessarily breaks down, even if the temperature gradient is very small.

scholarly journals Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Jun Yu ◽  
Yi Yang ◽  
Antonio Campo
Keyword(s):  
Heat Conduction ◽  
Energy Density ◽  
Approximation Method ◽  
Heat Conduction Equation ◽  
Boundary Energy ◽  
Approximate Solutions ◽  
Nonlinear Heat Conduction ◽  
Infinite Domain ◽  
Nonlinear Heat Conduction Equation ◽  
Self Similar

We use an approximation method to study the solution to a nonlinear heat conduction equation in a semi-infinite domain. By expanding an energy density function (defined as the internal energy per unit volume) as a Taylor polynomial in a spatial domain, we reduce the partial differential equation to a set of first-order ordinary differential equations in time. We describe a systematic approach to derive approximate solutions using Taylor polynomials of a different degree. For a special case, we derive an analytical solution and compare it with the result of a self-similar analysis. A comparison with the numerically integrated results demonstrates good accuracy of our approximate solutions. We also show that our approximation method can be applied to cases where boundary energy density and the corresponding effective conductivity are more general than those that are suitable for the self-similar method. Propagation of nonlinear heat waves is studied for different boundary energy density and the conductivity functions.

scholarly journals Integral formulation of solutions of boundary-value problems of heat and mass transfer in domains with moving boundaries

2021 ◽  
Vol 29 (1) ◽  
pp. 73-91
Author(s):  
Valentin V. Shevelev
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problems ◽  
Moving Boundary ◽  
Boundary Value ◽  
Phase Region ◽  
Integral Representations ◽  
Two Phase ◽  
Self Similar ◽  
The Fourier Transform ◽  
And Diffusion

Using the Fourier transform, integral representations of solutions to boundary value problems of heat conduction and diffusion in a two-phase region with a moving interface are obtained. The proposed approach makes it possible to obtain the equation of motion of the interface without the need to first find the temperature and (or) concentration fields. This makes it possible to study the stability of the interface with respect to disturbances in its shape. The validity of the proposed approach is demonstrated by the example of self-similar growth of a spherical crystal in a supercooled melt and crystallization of the melt on a substrate of the same substance. On the basis of the obtained equation, which determines the rate of self-similar motion of the interface, the features of the kinetics of crystallization of the melt on the substrate are analyzed. The conditions of applicability of the developed approach to the solution of boundary value problems of heat conduction and diffusion in regions separated by a moving boundary are briefly discussed.

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