THE SOLUTION OF A CLASS OF TWO-DIMENSIONAL MELTING AND SOLIDIFICATION PROBLEMS.

Abstract

Two-dimensional melting and solidification problems are divided into three convenient classes and a general method of solution for one of these is presented. The concept is used of a fictitious body of constant geometry, in which is embedded the real body (whose dimensions are changing due to the change in phase); the fictitious body is acted upon by a fictitious heat flux or (in some problems) a fictitious initial temperature distribution. A set of integro-differential equations is presented to be solved simultaneously, numerically or in series form. The melting of a finite, insulated slab with the melt immediately removed is formulated and an example for a semi-infinite, insulated strip is given. The solidification of a finite insulated slab with zero superheat is formulated and an example for a specific cooling history is given. Two-dimensional effects are introduced by spatial variations of heating or cooling conditions, and short-time series solutions are developed. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1964
Accession Number
AD0617330

Entities

People

  • Bruno A. Boley
  • David L. Sikarskie

Organizations

  • Columbia University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Geometry
  • Heat Energy
  • Heat Flux
  • Mathematics
  • Solidification
  • Transition Temperature
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Combustion and Flow Dynamics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Microelectronics