Transient thermal mixed boundary value problems in the half-space

The Wiener-Hopf and Cagniard-de Hoop techniques are employed in order to solve a range of transient thermal mixed boundary value problems on the half-space. The thermal field is determined via a rapidly convergent integral, which can be evaluated straightforwardly and quickly on a desktop PC

The quasistatics thermal stress analysis in coated half-space with mixed boundary heating conditions

Побудовано розв’язок плоскої квазістатичної задачі термопружності для півпростору з покриттям, на границі якого в смузі певної ширини задана температура, а зовні відбувається теплообмін за законом Ньютона. Розв’язок отримано із використанням інтегральних перетворень Лагерра й Фур’є та методу рядів Фур’є при розв’язуванні послідовностей парних інтегральних рівнянь. Наведено результати числового аналізу термонапруженого стану в півпросторі та покритті залежно від відносної товщини покриття та інтенсивності охолодження.Analysis of thermal stresses in bodies with coatings is important for many engineering researches. Taking into account the actual operating conditions of these structures frequently leads to mixed heating condition. The steady problem of thermoelasticity with mixed boundary conditions currently is sufficiently investigated. However, the corresponding transient problem, despite its relevance, is poorly understood. This is due to mathematical difficulties that arise in applying the integral Laplace transform. The authors of this paper developed a new effective method of constructing solutions of mixed boundary-value non-stationary problems. The half-space with a coating, on the surface of which on the band of 2d width the temperature distribution is given and outside of this area the heat transfer according to the Newton's law is performed, is analysed in the work. On the surface of separation of materials of half-space and coating the conditions of ideal thermomechanical contact are satisfied. The initial temperature of the coating and half-space is equal to zero. To the heat conductivity problem the Laguerre integral transformation in time variables and integral Fourier transformation in spatial variable are applied. As a result the triangular sequence of ordinary differential equations is obtained. The general solution of these sequences is obtained in the form of algebraic convolution. Taking into account the mixed boundary conditions results in dual integral equations. For solution of this problem the method of Newton's series is proposed. Taking advantage of this method the problem is reduced to the infinite system of algebraic equations, for which the convergence of reduction procedure is proved. The solution of thermoelasticity problem is built using resulting temperature field in the assumption, that the border of coating is free of load. The solution is obtained in the form of series in Laguerre polynomials. Calculations were carried for the half-space made of titanium alloy and ceramic coating

3-D inelastic analysis methods for hot section components (base program)

A 3-D inelastic analysis methods program consists of a series of computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of combustor liners, turbine blades, and turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. These models are used to solve 3-D inelastic problems using linear approximations in the sense that stresses/strains and temperatures in generic modeling regions are linear functions of the spatial coordinates, and solution increments for load, temperature and/or time are extrapolated linearly from previous information. Three linear formulation computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), were developed and are described

Development of an Analytic Nodal Diffusion Solver in Multigroups for 3D Reactor Cores with Rectangular or Hexagonal Assemblies.

More accurate modelling of physical phenomena involved in present and future nuclear reactors requires a multi-scale and multi-physics approach. This challenge can be accomplished by the coupling of best-estimate core-physics, thermal-hydraulics and multi-physics solvers. In order to make viable that coupling, the current trends in reactor simulations are along the development of a new generation of tools based on user-friendly, modular, easily linkable, faster and more accurate codes to be integrated in common platforms. These premises are in the origin of the NURESIM Integrated Project within the 6th European Framework Program, which is envisaged to provide the initial step towards a Common European Standard Software Platform for nuclear reactors simulations. In the frame of this project and to reach the above-mentioned goals, a 3-D multigroup nodal solver for neutron diffusion calculations called ANDES (Analytic Nodal Diffusion Equation Solver) has been developed and tested in-depth in this Thesis. ANDES solves the steady-state and time-dependent neutron diffusion equation in threedimensions and any number of energy groups, utilizing the Analytic Coarse-Mesh Finite-Difference (ACMFD) scheme to yield the nodal coupling equations. It can be applied to both Cartesian and triangular-Z geometries, so that simulations of LWR as well as VVER, HTR and fast reactors can be performed. The solver has been implemented in a fully encapsulated way, enabling it as a module to be readily integrated in other codes and platforms. In fact, it can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. Verification of performance has shown that ANDES is a code with high order definition for whole core realistic nodal simulations. In this paper, the methodology developed and involved in ANDES is presented

An integrated approach to indoor contaminant modelling

Air pollutants are those chemicals that are not generally present in the atmosphere because of natural causes but are disseminated into the air by human activity. In most parts of Europe, outdoor pollutants are principally the products of combustion from space heating, power generation, chemical industry waste, or from motor vehicle traffic (McGinlay 1997). Indoor air environments contain a myriad of inorganic and organic gases and vapors typically in trace (parts-per-billion) quantities. The chemical composition of air varies widely between particular locations as well as between measurements taken at different times for the same location. The nature of these variations is such that it is difficult to definitively characterize a typical indoor air environment with respect to specific contaminants present and concentration levels. A large number of air pollutants have known or suspected harmful effects that can be manifested on plant or animal life and/or the environment. Pollutants may not only prove a problem in the immediate vicinity of their emission, but they can travel long distances and react with other species present in the atmosphere to produce secondary pollutants (Weschler 2004)

Algorithmic aspects of transient heat transfer problems in structures

It is noted that the application of finite element or finite difference techniques to the solution of transient heat transfer problems in structures often results in a stiff system of ordinary differential equations. Such systems are usually handled most efficiently by implicit integration techniques which require the solution of large and sparse systems of algebraic equations. The assembly and solution of these systems using the incomplete Cholesky conjugate gradient algorithm is examined. Several examples are used to demonstrate the advantage of the algorithm over other techniques

Oscillatory convection in binary mixtures: thermodiffusion, solutal buoyancy, and advection

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numerically obtained solutions of the field equations in the form of spatially extended relaxed traveling waves, of standing waves, and of the transient growth of standing waves and their transition to traveling waves are discussed as well as spatially localized convective states of traveling waves that are surrounded by the quiescent fluid.Comment: 30 pages, 10 figure

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated

Temperature surges in current-limiting circuit devices.

This paper studies the problem of heat transfer in a thermistor, which is used as a switching device in electronic circuits. The temperature field is coupled to the current flow by ohmic heating in the device, and the problem is rendered highly nonlinear by a very rapid variation of electrical conductivity with temperature. Approximate methods based on high activation energy asymptotics are developed to describe the transient heat flow, which occurs when the circuit is switched on. In particular, it is found that a transient 'surge' phenomenon (akin to thermal runaway, but self-saturating) occurs, and we conjecture that this phenomenon may be associated with cracking of thermistors, which sometimes occurs during operation