Elasticity problems in a half-strip

This LDRD Senior's Council Project is focused on the development, implementation and evaluation of Reduced Order Models (ROM) for application in the thermal analysis of complex engineering problems. Two basic approaches to developing a ROM for combined thermal conduction and enclosure radiation problems are considered. As a prerequisite to a ROM a fully coupled solution method for conduction/radiation models is required; a parallel implementation is explored for this class of problems. High-fidelity models of large, complex systems are now used routinely to verify design and performance. However, there are applications where the high-fidelity model is too large to be used repetitively in a design mode. One such application is the design of a control system that oversees the functioning of the complex, high-fidelity model. Examples include control systems for manufacturing processes such as brazing and annealing furnaces as well as control systems for the thermal management of optical systems. A reduced order model (ROM) seeks to reduce the number of degrees of freedom needed to represent the overall behavior of the large system without a significant loss in accuracy. The reduction in the number of degrees of freedom of the ROM leads to immediate increases in computational efficiency and allows many design parameters and perturbations to be quickly and effectively evaluated. Reduced order models are routinely used in solid mechanics where techniques such as modal analysis have reached a high state of refinement. Similar techniques have recently been applied in standard thermal conduction problems e.g. though the general use of ROM for heat transfer is not yet widespread. One major difficulty with the development of ROM for general thermal analysis is the need to include the very nonlinear effects of enclosure radiation in many applications. Many ROM methods have considered only linear or mildly nonlinear problems. In the present study a reduced order model is considered for application to the combined problem of thermal conduction and enclosure radiation. The main objective is to develop a procedure that can be implemented in an existing thermal analysis code. The main analysis objective is to allow thermal controller software to be used in the design of a control system for a large optical system that resides with a complex radiation dominated enclosure. In the remainder of this section a brief outline of ROM methods is provided. The following chapter describes the fully coupled conduction/radiation method that is required prior to considering a ROM approach. Considerable effort was expended to implement and test the combined solution method; the ROM project ended shortly after the completion of this milestone and thus the ROM results are incomplete. The report concludes with some observations and recommendations.

CHAPTER V - THERMAL CONDUCTION IN FLUIDS

NiCo@EG-based composite PCMs with boosted thermal conductivity and photothermal conversion efficiency for solar energy harvesting

A face based basis function solutions to thermal conduction problems for 3-D irregular shaped bodies using BEM

A previous difference method has a geometrical restriction in analyzing numerically thermal conduction problems about materials with any shape. Therefore it has been impossible to generalize the numerical solution of three-dimensional thermal conduction problems by the previous method. In this paper we propose a dual difference method which is free from the geometrical restriction of the previous method. Thereby the application of difference calculus can be extended to two-dimensional and three-dimentional problems about materials with any shape. The accuracy and the relative error depending on the shape of elements were compared and fount out to be smaller than in the previous method. Then, we made an experiment about the induction heating of a steel ball, and compare the experimental results with calculated results by dual difference method. A close agreement between measured and calculated values was obtained.

The electric potential drop (EPD) method is a laboratory technique to monitor the initiation and the propagation of a crack, mainly in the field of fatigue research. It can also be used in fracture experiments, involving plasticity and large deformations. The size of a crack in a metallic member is predicted by applying a constant d.c. (direct current) or a.c. (alternating current) to the member and by measuring an increase in electric resistance due to the crack. Practically, several pairs of probes are attached to the specimen crossing over the crack and the voltage drop is measured periodically along the test. The main difficulty is to correlate the EPD changes to the crack extension. Thanks to the analogy between the thermal conduction problem and the electrical conduction problem, a classical thermo-mechanical finite element solver can be used to predict the EPD along a crack, given the electrical resistivity of the material, the current intensity and the geometry of the structure and of the crack. This technique works well for fatigue studies, where the structure remains elastic and whose shape is unchanged. However, in fracture experiments, the change in geometry and the possible effect of the plastic strain on electrical resistivity make the problem much more complex. The paper presents the principle of the EPD method, a work on the effect of the plastic strain on the electrical resistivity, FE computations for the elastic case (for fatigue pre-cracking) and for the plastic case (for ductile tearing experiments). Several practical applications will be presented on various metallic materials.

Problems. Factorized operators can be applied to speed up the processes of solving boundary value problems of non-stationary thermal conductivity and dynamic load, which will lead to the appearance of additional approximation errors. The aim of the study: to obtain formulas that allow controlling the values of these errors. Methodology of implementation: mathematical analysis, programming, numerical experiment. Research results. It is proposed to reduce these additional errors by imposing restrictions on the time step: the corresponding formulas are obtained. Conclusions. Effective formulas and algorithms for their implementation are proposed, which allow you to control the accuracy of the solution of boundary value problems of non-stationary thermal conductivity and dynamic load in schemes with factorized operators due to the limitation of the time step. Practical implementation has shown their effectiveness and expediency.

A mathematical model for solving the problem of one-dimensional thermal conductivity has been developed and implemented programmatically. The purpose of the simulation is to compare the performance of algorithms on the central and graphics processors. The task of parallelization is relevant, since back in 2015 the number of stream processors in the most powerful video card was 2816, and in 2021 there were video cards with 10 496 stream processors. Applications running on NVIDIA GPUs demonstrate greater performance per dollar of invested funds and per watt of energy consumed compared to implementations built on the basis of central processors alone. This is confirmed by the high demand for video cards from miners, which has led to a 1.5-2.5 times increase in the price of video cards at the moment. The requirements for the hardware and software components necessary for the start of modeling are presented. Three methods of finite difference approximation are implemented: explicit, implicit and Crank-Nicolson on the central and graphics processors. The programming languages chosen are C (CPU) and CUDA C (GPU). For a well-parallelized task, when each thread is executed separately and it does not need data from other threads, the acceleration of calculations on the video card increased up to 60 times (an entry-level video card was used). The CUDA C language appeared relatively recently in 2006 and has a number of features when implementing a parallel algorithm. For the selected schemes: explicit, implicit, Crank-Nicolson, at each iteration, it is necessary to access neighboring threads and synchronize the threads. Synchronization of threads occurs in such a way that all threads wait for the slowest of them at each iteration, so solving problems using finite-difference approximation will be performed slower. A fragment of code on a GPU for implementing the Crank-Nicolson scheme is presented. The implementation of the Crank-Nicolson scheme requires the use of fast shared memory for data exchange between threads. The amount of shared memory is limited and affects the number of cells in the grid. The use of graphics cards gave a significant increase in execution speed even on an entry-level card with a number of 384 stream processors. The article presents a comparative analysis of the computing speed for different grid sizes from 1024 to 4000, as well as for different amounts of computing volumes in one thread.

本文はHeaviside演算法の一應用として、初に各層異種等質材の2,3及4層體-主として円柱及球の一元的傳熱問題を、次に中心層を均質體とし外層を漸變材質體として2及3層円柱體の問題をベッセル函數を以て解いて居る。勿論表面温度は時間の周期的及び非周期的函數であり、初温零の場合である。因みに本文は拙文「Bromwich算法に依る均質有限體の一元的熱傳導問題」(昭和8年1月号)の続編である。

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Microstructural design of connective base cells for functionally graded materials

Analytical layered solution of radiation and non–Fourier conduction problems in optically complex media

The theory of the lifetime of a quasi-particle at finite temperatures is developed by using a generalization of the Green's function formalism of Nambu. The explicit results for the lifetime, as a function of the excitation energy and the temperature, are applied to the problem of electronic thermal conductivity when interaction with the phonons is the limiting mechanism for the heat flux. The lifetime appears in a general expression for the thermal conductivity which is derived from the corresponding Boltzmann equation by making a relaxation-time approximation. The resulting curve for the ratio of the thermal conductivity in the superconducting state to that in the normal state versus the reduced temperature is found to decrease monotonically and to have a slope of about 2 at the transition temperature. (auth)

In this work, the thermal conductivity problem is solved for fourth layer plate at the heat flux action on one of surfaces. The interfaces between layers are assumed non ideal that leads to appearance of thermal resistances between layers. Additionally thermal resistances are inhomogeneous due to curved surfaces of materials. The existence of curved surfaces and porosity of layers are connected with the way of specimen manufacturing. Thermal conductivity coefficients of layers can by changed when their porosity changes. The problem is solved numerically. It was found that curved interfaces and thermal resistance affect process only at initial stage of the heating. Temperature gradients depend essentially on porosity and thickness of layers.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods