Modeling Flash Diffusivity Experiments in Two Dimensions for Thick Samples

2008 ◽  
Author(s):  
Robert L. McMasters
Keyword(s):  
Experimental Data ◽  
Laser Flash ◽  
Two Dimensions ◽  
Flash Method ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
Dimensional Analysis Method ◽  
Flash Diffusivity

The laser flash method for measuring thermal diffusivity is well established and has been in use for many years. Early analysis methods employed a simple model, in which one dimensional transient conduction was assumed, with insulated surfaces during the time subsequent to the flash. More recently, models of grater sophistication have been applied to flash diffusivity experiments. These models have been matched to experimental data using nonlinear regression and assume one-dimensional conduction. The advanced models have achieved highly accurate agreement with experimental data taken from thin samples, on the order of one millimeter in thickness. As samples become thicker, models which neglect edge losses can lose some conformity to the experimental data. The present research involves the application of a two dimensional model which allows for penetration of the laser flash into the sample. The accommodation of the flash penetration is important for porous materials, where the coarseness of the porosity is more than one percent of the sample thickness. Variability of the area of incidence of the flash is also investigated to determine the effect on the model and the results. Statistical methods are used in order to make a determination as to the validity of the two dimensional model, as compared with the one dimensional analysis method.

scholarly journals Detecting isolation by distance using phylogenies of genes.

Genetics ◽  
1990 ◽  
Vol 126 (1) ◽  
pp. 249-260 ◽  
Author(s):  
M Slatkin ◽  
W P Maddison
Keyword(s):  
Migration Rate ◽  
Regression Coefficient ◽  
Isolation By Distance ◽  
Alternative Methods ◽  
Simple Relationship ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Structured Population ◽  
Two Dimensional Model

Abstract We introduce a method for analyzing phylogenies of genes sampled from a geographically structured population. A parsimony method can be used to compute s, the minimum number of migration events between pairs of populations sampled, and the value of s can be used to estimate the effective migration rate M, the value of Nm in an island model with local populations of size N and a migration rate m that would yield the same value of s. Extensive simulations show that there is a simple relationship between M and the geographic distance between pairs of samples in one- and two-dimensional models of isolation by distance. Both stepping-stone and lattice models were simulated. If two demes k steps apart are sampled, then, s, the average value of s, is a function only of k/(Nm) in a one-dimensional model and is a function only of k/(Nm)2 in a two-dimensional model. Furthermore, log(M) is approximately a linear function of log(k). In a one-dimensional model, the regression coefficient is approximately -1 and in a two-dimensional model the regression coefficient is approximately -0.5. Using data from several locations, the regression of log(M) on log(distance) may indicate whether there is isolation by distance in a population at equilibrium and may allow an estimate of the effective migration rate between adjacent sampling locations. Alternative methods for analyzing DNA sequence data from a geographically structured population are discussed. An application of our method to the data of R. L. Cann, M. Stoneking and A. C. Wilson on human mitochondrial DNA is presented.

scholarly journals Biomass/Coal Derived Gas Utilization in a Gas Turbine Combustor

1998 ◽  
Author(s):  
P. D. J. Hoppesteyn ◽  
J. Andries ◽  
K. R. G. Hein
Keyword(s):  
Experimental Data ◽  
Gas Turbine ◽  
Calorific Value ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Gas Turbine Combustor ◽  
Cylindrical Chamber ◽  
Fuel Gas ◽  
Gas Utilization ◽  
Two Dimensional Model

Low calorific value fuel gas, obtained by pressurized fluidized bed gasification of coal/biomass mixtures, is combusted at 0.8 MPa with air or oxygen in a vertical cylindrical chamber (D = 0.28 m, L = 2.0 m). The fuel (T = 1060 K) and oxydizer (air at 350 K, oxygen at 460 K) are injected coaxially, resulting in an essentially axissymmetric flow pattern. Particles have been removed from the fuel gas stream by a cyclone, mounted between the gasifier and the combustor. A two-dimensional model, implemented in the CFD code FLUENT was developed for the calculation of temperatures, flow patterns and species concentrations throughout the combustor. The calculated results are compared with experimental data for two low calorific value fuel gas compositions and two oxidizer compositions at two axial combustor locations (X/L = 0.175 and X/L = 1). The results appear to justify further investigation of the applicability of the model to low calorific value fuel gas fired gas turbine combustors.

A Two-Dimensional Model of the Fluid Dynamics of an Air Reverser

1998 ◽  
Vol 65 (1) ◽  
pp. 171-177 ◽  
Author(s):  
S. Mu¨ftu¨ ◽  
T. S. Lewis ◽  
K. A. Cole ◽  
R. C. Benson
Keyword(s):  
Design Guidelines ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Web Handling ◽  
One Dimensional ◽  
Air Supply ◽  
Two Dimensional Model ◽  
The One ◽  
The Web

A theoretical analysis of the fluid mechanics of the air cushion of the air reversers used in web-handling systems is presented. A two-dimensional model of the air flow is derived by averaging the equations of conservation of mass and momentum over the clearance between the web and the reverser. The resulting equations are Euler’s equations with nonlinear source terms representing the air supply holes in the surface of the reverser. The equations are solved analytically for the one-dimensional case and numerically for the two-dimensional case. Results are compared with an empirical formula and the one-dimensional airjet theory developed for hovercraft. Conditions that maximize the air pressure supporting the web are analyzed and design guidelines are deduced.

Numerical Simulation of the Austenitizing Process in Hypoeutectoid Fe-C Steels

2014 ◽  
Author(s):  
Dehao Liu ◽  
Gang Wang ◽  
Zhenguo Nie ◽  
Yiming (Kevin) Rong
Keyword(s):  
Front Tracking ◽  
Two Dimensional ◽  
Austenite Matrix ◽  
Transformation Kinetics ◽  
Special Volume ◽  
Dimensional Model ◽  
Austenitization Temperature ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
2D Model

For predicting of diffusive phase transformations during the austenitizing process in hypoeutectoid Fe-C steels, a two-dimensional model has been developed. The diffusion equations are solved within each phase (α and γ) using an explicit finite volume technique formulated using a square grid. The discrete α/γ interface is represented by special volume elements α/γ. The result showing the dissolution of ferrite particles in the austenite matrix are presented at different stages of the phase transformation. Specifically, the influence of the microstructure scale and heating rate on the transformation kinetics has been investigated. Final austenitization temperature calculated with this 2D model is compared with predictions of a simpler one dimensional (1D) front-tracking calculation.

The Waltzian ordering principle and international change: A two-dimensional model

2017 ◽  
Vol 24 (1) ◽  
pp. 130-152 ◽  
Author(s):  
Ryan D. Griffiths
Keyword(s):  
Structural Realism ◽  
Functional Differentiation ◽  
International Order ◽  
Two Dimensions ◽  
The Other ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Ideal Types ◽  
Classical Path ◽  
Two Dimensional Model

In his work on structural realism, Kenneth Waltz developed a theory of international order that is admired for its parsimony but criticized for its simplicity. Using his ordering principle as a foundation, I critique and extend his theory by constructing a model of international order with two dimensions: one of political centralization and the other of segmentary/functional differentiation. The resulting map locates different configurations of order and highlights four ideal-types: mechanical anarchy, organic hierarchy, mechanical hierarchy and organic anarchy. I then use the two-dimensional map and related ideal-types to outline two different processes of international change — a classical path and a modern path — that were invisible in the Waltzian model. This article is thus a contribution to the developing literature on conceptualizing different forms of international order and the dynamics of international change.

scholarly journals 2D Model of Transfer Processes for Water Boiling Flow in Microchannel

2021 ◽  
Vol 5 (3) ◽  
pp. 42
Author(s):  
Valery A. Danilov ◽  
Christian Hofmann ◽  
Gunther Kolb
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Transfer Processes ◽  
Two Dimensional Model ◽  
Boiling Flow ◽  
Homogeneous Mixture Model ◽  
2D Model

The modeling of transfer processes is a step in the generalization and interpretation of experimental data on heat transfer. The developed two-dimensional model is based on a homogeneous mixture model for boiling water flow in a microchannel with a new evaporation submodel. The outcome of the simulation is the distribution of velocity, void fraction and temperature profiles in the microchannel. The predicted temperature profile is consistent with the experimental literature data.

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