Pseudo-updated constrained solution algorithm for nonlinear heat conduction

Parameters in the heat conduction equation are frequently modeled as temperature dependent. Thermal conductivity, volumetric heat capacity, convection coefficients, emissivity, and volumetric source terms are parameters that may depend on temperature. Many applications, such as parameter estimation, optimal experimental design, optimization, and uncertainty analysis, require sensitivity to the parameters describing temperature-dependent properties. A general procedure to compute the sensitivity of the temperature field to model parameters for nonlinear heat conduction is studied. Parameters are modeled as arbitrary functions of temperature. Sensitivity equations are implemented in an unstructured grid, element-based numerical solver. The objectives of this study are to describe the methodology to derive sensitivity equations for the temperature-dependent parameters and present demonstration calculations. In addition to a verification problem, the design of an experiment to estimate temperature variable thermal properties is discussed.

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Heat-Flux Estimation in a Nonlinear Heat Conduction Problem with a Dual-Phase-Lag Model

Journal of Thermophysics and Heat Transfer ◽

10.2514/1.t5013 ◽

2018 ◽

Vol 32 (1) ◽

pp. 196-204 ◽

Cited By ~ 3

Author(s):

M. Baghban ◽

M. B. Ayani

Keyword(s):

Heat Flux ◽

Heat Conduction ◽

Heat Conduction Problem ◽

Phase Lag ◽

Dual Phase ◽

Nonlinear Heat Conduction ◽

Heat Flux Estimation ◽

Lag Model ◽

Flux Estimation

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

Journal of Fluid Mechanics ◽

10.1017/s0022112008001043 ◽

2008 ◽

Vol 603 ◽

pp. 151-178 ◽

Cited By ~ 12

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.

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