A METHOD FOR THE NUMERICAL SOLUTION OF A HEAT CONDUCTION PROBLEM

Abstract

A method is given for the numerical solution of the partial differential equation governing heat flow in an infinite plate. The solution, obtained with appropriate boundary conditions, permits an estimation of the temperature of the outer shell of a high-velocity projectile during of the variation in thermal properties of steel over the temperature range encountered. At the inner surface, the boundary condition was taken to be that of heat transfer across the surface, the boundary condition took into account heat transfer both by conduction to or from the boundary layer and by radiation into space. An implicit method for numerical integration was used in which the values of the dependent variable on the new time step are expressed in terms of each other and must be obtained by solving a simple system of linear algebraic equations. Round-off errors were damped out regardless of the size of the time step.

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Document Details

Document Type
Technical Report
Publication Date
Dec 31, 1952
Accession Number
AD0005563

Entities

People

  • R. P. Eddy

Organizations

  • Naval Ordnance Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Differential Equations
  • Equations
  • Heat Transfer
  • Heat Transmission
  • Linear Algebraic Equations
  • Numerical Integration
  • Partial Differential Equations
  • Thermal Properties

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Structural Dynamics.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster