Finite Volume Algorithms for Heat Conduction

Abstract

Many modern computational fluid dynamics computer programs are developed by using the finite volume discretization method. It has an excellent numerical capability for capturing changes in conserved quantities such as mass, momentum and energy. In many cases, thermal energy is transferred from fluids to some adjacent solid mass. Head accumulation in this solid matter is an important engineering issue. To capture this energy transfer, it is important to have heat conduction algorithms that function well with fluid dynamics codes. The present work tackles this problem by presenting an algorithm for solving the heat equation in finite volume form. Although this derivation is cast in two dimensions, it may be readily generalized to three dimensions. Example problems are solved involving heat conduction within a section of an annular ring. Along the boundaries we enforce both Dirichlet and Neumann boundary conditions. For code validation, our numerical solutions, based upon the Douglas-Rachford ADI time integration scheme, are compared with exact mathematical solutions.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2010
Accession Number
ADA519644

Entities

People

  • Douglas V. Nance

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Cartesian Coordinates
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programming
  • Computer Programs
  • Computers
  • Differential Equations
  • Energy
  • Energy Transfer
  • Engineering
  • Equations
  • Fluid Dynamics
  • Heat Transfer
  • Mechanics
  • Partial Differential Equations
  • Temperature Gradients

Readers

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