Heat conduction in weakly collisional, magnetized plasma is challenging to model accurately due to multifaceted physics governing heat-carrying electrons, including microinstabilities that scatter electrons and modify heat transport. Capturing these effects requires multidimensional kinetic theory simulations, which are computationally expensive. Experimental constraints overcome this issue, resulting in improved understanding of thermal transport in systems such as the intra-cluster medium of galaxy clusters, and the hot-spot in inertial confinement fusion. In this paper, we present a new experimental platform that produces a weakly collisional high-$\beta$ plasma expected to be susceptible to the whistler heat-flux instability. This platform, to be fielded on the Orion laser, enables characterization of whistler-regulated thermal conductivity. The platform design is assessed using radiation-magnetohydrodynamics simulations with the code FLASH. Simulations using three thermal conduction models predict conductivity suppression by over an order of magnitude relative to the Spitzer value at whistler saturation, demonstrating the efficacy of the platform.

Graphite flakes (Gf)/Si/Al composites have been fabricated with different volume fraction of graphite by vacuum gas pressure infiltration. In the composites, the addition of Si played a role of spacing apart graphite layers, which can produce voids between layers for the infiltration of molten aluminum. Microstructural characterization indicated that the reinforcements were fairly distributed in the Al and a clean interface lacking of Al3C4 phase was formed between Al and Gf. With the increase of Gf from 39 to 81 vol%, the longitudinal thermal conductivity (TC) of composites increased from 294 to 390 W/m K, but the open porosity increased from 1.85 to 6.03%. Besides, a joint M1–M2 prediction model was established, which considered that the microstructure of composites lies in between two models: (M1) a layered structure in binary metal-particle composites and (M2) ternary composites that oriented flakes randomly distributed in metal-particle confirmed a better theoretical prediction of TC.

A heated triangular cylinder is suddenly cooled in a constant temperature bath. The transient heat conduction problem is transformed to the Helmholtz equation related to the vibration of membranes. Using the membrane analogy, exact analytic solutions for the transient heat conduction problem for three triangular cross sections are found.

In this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.

A diesel particulate filter (DPF) is a key technology to meet future emission standards of particulate matters (PM), mainly soot. It is generally consists of a wall-flow type filter positioned in the exhaust stream of a diesel vehicle. It is difficult to simulate the thermal flow in DPF, because we need to consider the soot deposition and combustion in the complex geometry of filter wall. In our previous study, we proposed an approach for the conjugate simulation of gas-solid flow. That is, the gas phase was simulated by the lattice Boltzmann method (LBM), coupled with the equation of heat conduction inside the solid filter substrate. However, its numerical procedure was slightly complex. In this study, to reduce numerical costs, we have tested a new boundary condition with chemical equilibrium in soot combustion at the surface of filter substrate. Based on the soot oxidation rate with catalysts evaluated in experiments, the lattice Boltzmann simulation of soot combustion in the catalyzed DPF is firstly presented to consider the process in the after-treatment of diesel exhaust gas. The heat and mass transfer is shown to discuss the effect of catalysts.

A data-driven model reduction strategy is presented for the representation of random polycrystal microstructures. Given a set of microstructure snapshots that satisfy certain statistical constraints such as given low-order moments of the grain size distribution, using a non-linear manifold learning approach, we identify the intrinsic low-dimensionality of the microstructure manifold. In addition to grain size, a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used to reduce the texture representation. The space of viable microstructures is mapped to a low-dimensional region thus facilitating the analysis and design of polycrystal microstructures. This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture). We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation variability.

An analytical solution to compute the 3D steady state temperature distribution in abearing ring is presented in this paper. The ring is formed by a hollow cylinder of finitelength. Its radial external surface is subjected to localized, identical heat sources,equally spaced in the azimuth direction. This surface is also subjected to convectivecooling while as the internal surface is maintained at a uniform temperature. Thedeveloped solution is explicit and does not impose any restriction on the geometrical orphysical parameters.

A state space approach to heat conduction in a cylindrically anisotropic circular tube of functionally graded materials (FGM) is presented. A power-law type of the radial inhomogeneity for the FGM is considered. By means of eigenfunction expansion and matrix algebra, analytic solutions for transient and steady-state heat conduction in the FGM tube under general thermal boundary conditions are derived.

We consider a domain decomposition method for some unsteadyheat conduction problem in composite structures.This linear model problem is obtained by homogenization of thin layersof fibres embedded into some standard material.For ease of presentation we consider the case of two space dimensions only.The set of finite element equations obtained by the backward Euler schemeis parallelized in a problem-oriented fashion by some noniterative overlappingdomain splitting method,eventually enhanced by inexpensive local iterationsto reduce the overlap.We present a detailed convergence analysis of this algorithmwhich is particularly well appropriate to handle fibre layersof nonlinear material.Special emphasis is to take into account the specific regularity propertiesof the present mathematical model.Numerical experiments show the reliability of the theoretical predictions.

The moments and probability distribution of the lifetime of a configuration state relative to m disjoint regions in ℝd for particles under stochastic motion are expressed in terms of the derivatives at the origin of the probability after-effects for the m regions and for the union of the regions, together with the single integrated and the m randomized first-passage-time distributions, relative to the union of the m regions and to the separate complements of the m regions, respectively. The lifetime, suitably normed in terms of the mean lifetime, is shown to have a limiting standard exponential distribution. Finally, the distributions of lifetime when the motion of the particles is either Brownian or such as to generate a persistent generalized Smoluchowski process are discussed; in the first case, the distribution of lifetime reduces to a standard problem in heat conduction, and in the second case the distribution is expressed in terms of an exponential function and the m probability after-effects for the m regions.