Flow line

Abstract: Introduction.- Issues, Goals, and Methods of Flow Line Analysis.- Variability and the Performance of Flow Lines.- Non-Linearities in the Flow of Material.- Economic Design Problems in Flow Line Analysis.- Methods of Performance Analysis.- Two-Machine Decomposition of Flow Lines.- Review of the Literature.- Assembly/Disassembly Systems with Random Processing Times.- Discrete and Continuous Time Models.- Exact Solution of a Two-Machine Subsystem.- Decomposition Equations for Assembly/Disassembly Systems.- Two Algorithms to Determine Performance Measures.- Numerical Results.- Optimal Design of Assembly/Disassembly Systems.- Flow Lines with Rework Loops and Identical Processing Times.- Discrete-Material Flow Line Model with Identical Deterministic Processing Times.- Decomposition Equations for Loops and Identical Processing Times.- The Algorithm to Determine Performance Measures.- Numerical Results: Algorithms and Flow Line Behavior.- Optimal Design of Systems with Loops and Identical Processing Times.- Flow Lines with Rework Loops and Machine-Specific Processing Times.- Continuous-Material Flow Line Model with Machine-Specific Processing Times.- Decomposition Equations for Loops and Different Processing Times.- The Algorithm to Determine Performance Measures.- Numerical Results: Algorithms and Flow Line Behavior.- Optimal Design of Systems with Loops and Different Processing Times.- Conclusions and Suggestions for Further Research.- Derivation for the Discrete Material Flow Line.- Derivation for the Continuous Material Flow Line..

Abstract: A flow-line model is presented for calculating the surface profile and the velocity, strain-rate, and stress fields in an ice sheet with given base-elevation profile, ice thickness at the dome (divide), flow-law parameters, mass-balance distribution, and convergence/divergence conditions along the flow line. The model, which is based on a “quasi-similarity” hypothesis as regards the horizontal velocity-depth profiles, accounts for changes along the flow line in the depth distributions of temperature, normal stress deviators, and possible enhanced flow of deep ice of Wisconsin origin. A curvilinear coordinate system is applied with horizontal axes along flow lines and surface-elevation contours, respectively. The flow equations are reduced to two differential equations, one for the surface-elevation profile, and the other for a profile function that determines the depth distributions of velocities and strain-rates. The two equations are coupled through a profile parameter that communicates the influence of velocity-profile changes to the surface-profile equation. It is shown that the variation along the flow line of this parameter should also be considered when deriving flow-law parameters from ice-sheet flow-line data. For a symmetric dome, explicit expressions are derived for the depth distributions of the vertical velocity, strain-rates, and stresses. The strain-rate profiles display an inflection about half-way down the ice sheet, and, in the case of isothermal ice, have surface values 2.2 times their depth-averaged values. The depth distribution of the vertical velocity indicates that a relatively thick layer of almost stagnant ice is present at the ice-sheet base below a dome.