Monte Carlo method of solving heat conduction problems
Abstract
A new approach in the use of Monte Carlo to solve heat conduction problems was developed using a transport equation approximation to the heat conduction equation. The method was shown to be applicable to the solution of multimedia problems in complex geometries with no inherent limitations as to the geometric complexity of problems which can be solved. Nuclear radiation transport and heat conduction problems can be calculated with the same computer code; and, in the case where the nuclear reactions are the heat source, the problem can be performed in a coupled mode with a single computer run. The method was demonstrated for problems involving multimedia, internal sources, fixed temperature boundary conditions, convective boundary conditions, time-dependent sources, and for a coupled nuclear radiation-heat conduction problem. Comparisons were made to analytical solutions when they were available or could be generated. The adjoint formulation was found to be the most suitable mode of solution for the class of problems which was considered and therefore the method appears to be more useful for calculating temperatures at specific points rather than temperature distributions.
- Authors:
- Publication Date:
- Research Org.:
- Oak Ridge National Lab., Tenn. (USA)
- OSTI Identifier:
- 5161662
- Report Number(s):
- ORNL/NUREG/CSD-3
TRN: 78-006110
- DOE Contract Number:
- W-7405-ENG-26
- Resource Type:
- Technical Report
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; THERMAL CONDUCTION; MONTE CARLO METHOD; COMPUTER CODES; MATHEMATICAL MODELS; NUMERICAL SOLUTION; TEMPERATURE DISTRIBUTION; TIME DEPENDENCE; ENERGY TRANSFER; HEAT TRANSFER; 420400* - Engineering- Heat Transfer & Fluid Flow
Citation Formats
Fraley, S.K., Hoffman, T.J., and Stevens, P.N.. Monte Carlo method of solving heat conduction problems. United States: N. p., 1977.
Web. doi:10.2172/5161662.
Fraley, S.K., Hoffman, T.J., & Stevens, P.N.. Monte Carlo method of solving heat conduction problems. United States. doi:10.2172/5161662.
Fraley, S.K., Hoffman, T.J., and Stevens, P.N.. Thu .
"Monte Carlo method of solving heat conduction problems". United States.
doi:10.2172/5161662. https://www.osti.gov/servlets/purl/5161662.
@article{osti_5161662,
title = {Monte Carlo method of solving heat conduction problems},
author = {Fraley, S.K. and Hoffman, T.J. and Stevens, P.N.},
abstractNote = {A new approach in the use of Monte Carlo to solve heat conduction problems was developed using a transport equation approximation to the heat conduction equation. The method was shown to be applicable to the solution of multimedia problems in complex geometries with no inherent limitations as to the geometric complexity of problems which can be solved. Nuclear radiation transport and heat conduction problems can be calculated with the same computer code; and, in the case where the nuclear reactions are the heat source, the problem can be performed in a coupled mode with a single computer run. The method was demonstrated for problems involving multimedia, internal sources, fixed temperature boundary conditions, convective boundary conditions, time-dependent sources, and for a coupled nuclear radiation-heat conduction problem. Comparisons were made to analytical solutions when they were available or could be generated. The adjoint formulation was found to be the most suitable mode of solution for the class of problems which was considered and therefore the method appears to be more useful for calculating temperatures at specific points rather than temperature distributions.},
doi = {10.2172/5161662},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 1977},
month = {Thu Dec 01 00:00:00 EST 1977}
}
-
Monte Carlo method of solving heat conduction problems
A new approach in the use of Monte Carlo to solve heat conduction problems is developed using a transport equation approximation to the heat conduction equation. A variety of problems is analyzed with this method and their solutions are compared to those obtained with analytical technique. This Monte Carlo approach appears to be limited to the calculation of temperatures at specific points rather than temperature distributions. The method is applicable to the solution of multimedia problems with no inherent limitations as to the goemetric complexity of the problem.