A MONTE CARLO SOLUTION FOR HEAT TRANSFER IN RAREFIED GASES

Abstract

The nonlinear heat transfer problem in the transition regime between free molecule and continuum flow is solved by an iterative Monte Carlo method, and the results are compared with both linear and nonlinear analytical solutions. The statistical procedure consists of constructingAN IMPROVED DISTRIBUTION FUNCTION BY RECORDING THE HISTORY OF A SINGLE TEST MOLECULE WHICH WANDERS THROUGH A PHASE SPACE POPULATED BY MOLECULES OF THE PREVIOUS ITERATE. Molecular wanderings are determined by selecting events at random from the probability distributions that govern the interaction process. For a nominal Knudsen number of 2.0 and a temperature ratio of 4:1, the Monte Carlo results differ from both the linear and nonlinear analytical solutions by no more than 10-15%. Moreover, these statistical results seem to substantiate Mott-Smith's prediction of a Knudsen layer adjacent to the boundary. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1961
Accession Number
AD0259049

Entities

People

  • Milton L. Lavin

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Distribution Functions
  • Flow
  • Gases
  • Heat Transfer
  • Knudsen Number
  • Mathematics
  • Molecules
  • Monte Carlo Method
  • Probability
  • Probability Distributions
  • Rarefied Gases
  • Transitions

Readers

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

Technology Areas

  • Space