Temporal Evolution Of Temperature Research Articles

APPLICATIONS OF INTEGRATED BATCH ANNEALING FURNACE SIMULATOR

An integrated process simulator with a capability to predict spatial and temporal evolution of temperature, microstructure, and mechanical properties in cold rolled coils during the batch annealing process has been developed. The model predictions have been validated using results obtained with large-scale industrial batch annealing operations. Potential applications of such a simulator include product development, efficient process optimization, and online control resulting in benefits in terms of overall cost reduction, energy reduction, productivity enhancement, and quality improvement. In this article, the salient features as well as the potential applications of this integrated Batch Annealing Furnace simulator have been presented. Furthermore, the utility of this simulator in designing the thermal cycle and optimizing the coil dimensions for improving furnace productivity has been demonstrated.

Successive Deposition of Metals in Solid Freeform Fabrication Processes, Part 1: Thermomechanical Models of Layers and Droplet Columns

Solid Freeform Fabrication (SFF) processes allow the automated building of three-dimensional shapes by successively depositing material in layers. Residual stress-induced tolerance losses are principal concerns in using these processes to create functional parts. Thermomechanical models of temperatures and stresses are presented, which are relevant to controlling residual stress effects in SFF processes. Models are applied to a particular SFF process; however, insights and conclusions are applicable to a large number of related processes. The temporal evolution of temperatures and stresses is investigated at two levels of detail. The successive deposition of layers of material is investigated first using one-dimensional simulations, approximating the build-up of residual stress in a multi-layered part. The successive deposition of a column of molten metal droplets (a technique used to create thick layers) is then modeled using two-dimensional axisymmetric simulations. Insights are given into process changes that can minimize residual stress-related effects in manufactured parts, including part constraint and localized preheating near the point of deposition. Results for thermomechanical interactions between droplets deposited in a column provide the foundation for studying interactions between adjacently deposited droplets, which is addressed in Part 2.

A comparison of the temperatures and electron densities of laser-produced plasmas obtained in air, argon, and helium at atmospheric pressure

Time-resolved measurements of temperatures and electron densities of laser-produced plasmas generated in air, argon, and helium at atmospheric pressure are presented. The plasmas are obtained by the focusing of a Nd:YAG laser on a low-alloyed steel sample. The relative experimental error for temperatures is in the range 0.6–3% and for electron densities, it is 4.5%. The higher temperatures and electron densities are obtained in argon, and the lower ones are found in helium. The temporal evolution of temperature and electron density in the three gases is compared, showing that a faster decay of both magnitudes takes place in helium.

The role of thermal and transport properties on the binder burnout of injection-molded ceramic components

A mathematical model is developed for describing the decomposition and removal of binder from ceramic components formed by injection molding. The model takes into account heat transfer by conduction within the ceramic body, mass transfer by convective flow of gas products, and an Arrhenius dependence of the decomposition rate. The model is solved numerically to determine the spatial and temporal evolution of temperature, reaction rate, concentration, porosity, and pressure. The influences of the thermal and transport properties on the distribution of binder and on the buildup of pressure within the body are examined. When small temperature gradients exist across the body, the binder is removed homogenously, whereas when large temperature gradients are present, the binder is removed as a receding planar front.

Density equilibration near the liquid-vapor critical point of a pure fluid. II. Coexisting phases for T

Measurements were carried out on the density change \ensuremath{\delta}\ensuremath{\rho}(t) in a pure fluid ${(}^{3}$He) after a small step change in the temperature of its container. The sample fluid was kept at constant average densities \ensuremath{\Delta}\ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} and in the coexisting liquid and vapor phases below the critical temperature ${\mathit{T}}_{\mathit{c}}$. The measurements were performed via two superposed capacitive sensors. At temperatures far below ${\mathit{T}}_{\mathit{c}}$, the equilibration in the liquid and vapor phases, measured, respectively, by the top and bottom sensors, are found to proceed very differently. As ${\mathit{T}}_{\mathit{c}}$ is approached, this difference diminishes; both the measured effective relaxation times level off and join smoothly the data obtained above ${\mathit{T}}_{\mathit{c}}$. This coexisting liquid-vapor system of $^{3}\mathrm{He}$ is simulated in one dimension. The results are presented for the spatial and temporal evolution of temperature and density in the fluid following a temperature step of the enclosure. The profiles \ensuremath{\delta}\ensuremath{\rho}(t) and their effective relaxation times are compared with the experimental observations in both phases. There is a qualitative agreement between the simulation and experiment for (${\mathit{T}}_{\mathit{c}}$-T)/${\mathit{T}}_{\mathit{c}}$\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}3}$, and the quantitative differences further away from ${\mathit{T}}_{\mathit{c}}$ are discussed. The results of experimental measurements and of computer simulations along isotherms are discussed and lead to complementary information on the equilibration dynamics as a function of average density. The asymptotic relaxation times obtained from simulation and from a formula based on the average thermal diffusivity of the entire fluid sample are compared and discussed, both for normal gravity, and also under microgravity conditions where both diverge as ${\mathit{T}}_{\mathit{c}}$ is approached. \textcopyright{} 1996 The American Physical Society.

Plasma temperature and density dynamics including particle and heat pinch effects

The spatial and temporal evolutions of temperature and density of plasmas, governed by coupled nonlinear diffusion equations with source terms and finite boundary effects, are studied by means of a central expansion technique for "bell-shaped" plasma profiles. Four coupled first order nonlinear equations in time are obtained for the amplitudes (central values) and widths of the temperature and density distributions. The roles played by the various processes, considering also particle and heat pinch effects, are discussed and the conditions for possible equilibria are formulated.

Interaction of imploding shock waves with expanding central plasma in spherical pinch experiments: Simulation analysis

In the spherical pinch scheme, the hot D-T plasma produced in the center of the high pressure spherical vessel is confined by means of imploding shock waves launched from the periphery of the vessel for a time sufficiently long to achieve break-even conditions for plasma fusion. Theoretical studies on spherical pinch made so far have been limited up to the conditions of substantial expansion of the central plasma and the well-defined time delay between the creation of central plasma and the launching of the peripheral shock which led to the conclusion that, in realistic situations of SP experiments, negative time delays should be adopted, i.e., the launching of the imploding shock wave should precede the formation of the central plasma. However, the interaction of converging shock wave with the central plasma causing an additional heating and compression of the central plasma favoring plasma fusion conditions was not taken into account. Starting from the hydrodynamic equations of the system, the proposed simulation code deals with the propagation of converging shock waves and its interaction with the expanding central plasma. Considering the above-mentioned interaction in a self-consistent manner, the temporal evolution of temperature of central plasma is studied. Some results of the numerical simulation on the dynamics of shock wave propagation are also compared with the predictions of “point strong explosing theory.”

A parametrized model of seasonal temperature changes in lakes

A one-dimensional model of the heat regime in a reservoir is described, based on a parametric representation of the vertical temperature structure in the form of an homogeneous mixed layer and an underlying thermocline. The self-similar expressions of the type suggested by Kitaigorodski and Miropolski (1970) and refined by Mälkki and Tamsaly (1985) are used for the latter. The thickness of the mixed layer is determined in the following way: at a very small heat flux into water — in accordance with the classical Rossby-Montgomery formula; at large values of stabilizing heating — in accordance with the formula derived by Zilitinkevich (1972); in the case of convection — with the help of the Driedonks and Tennekes equation (1984). The model is intended for calculation of the temporal evolution of temperature and the bulk characteristics of turbulent mixing (thickness of the upper homogeneous layer, friction velocity, convective velocity scale) in any natural lake or man-made reservoir under the following conditions: 1. (a) the horizontal extent of a reservoir is not so great as to generate significant climatic differences between various parts of the water area and at the same time it is not so small as to negate the assumption of horizontally homogeneous wind-induced mixing; 2. (b) the lake depth does not exceed a hundred metres (in which case Eqaations (5) and (17) for the temperature profile at z > h are not applicable); 3. (c) currents due to inflowing and outflowing rivers and streams are not large enough to affect significantly the turbulence regime; 4. (d) the major part of the basin has a more or less horizontal bottom. The results of the model verification and the example of its prognostic applications are presented.

On the influence of the initial data in a combustion problem

AbstractThe combustion of a material can be modelled by two coupled parabolic partial differential equations for the temperature and concentration of the material. This paper deals with properties of the solution of these equations inside a cylinder or a sphere and under given initial conditions. Bounds for the variation of the temperature with the initial conditions are first established by considering a decoupled form of the equations. Then the coupled system is used to obtain approximate expressions for the temporal evolution of temperature and concentration.