ON THE CONDUCTION OF HEAT IN A MELTING SLAB

Abstract

A new method for the solution of the problem of heat conduction in a melting slab, where the molten material is immediately removed upon formation, is presented. No restrictions are placed on the boundary conditions which may be imposed on the slab and the material properties are allowed to be temperature dependent. The problem of determining the temperature distribution in the slab and the amount of material melted is reduced to finding the solution of an ordinary differential equation on the amount of material melted. This reduction from a partial differential equation problem is accomplished by determining a Taylor's series expansion in space for the temperature distribution. The equation so obtained for the determination of the amount of material melted is of a form readily solved numerically. Comparisons with known results for a slab insulated on one face and subjected to a constant heat input on the other face are given.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1961
Accession Number
AD0256456

Entities

People

  • Stephen J. Citron

Organizations

  • Columbia University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Civil Engineering
  • Coefficients
  • Differential Equations
  • Engineering
  • Equations
  • Government Procurement
  • Governments
  • Heat Energy
  • Heat Flux
  • Latent Heat
  • Materials
  • Numerical Integration
  • Partial Differential Equations
  • Thermal Properties
  • United States
  • United States Government

Readers

  • Linear Algebra
  • Thermal Physics or Thermal Science.

Technology Areas

  • Microelectronics
  • Space
  • Space - Hall-Effect Thruster