Thermal Option

The thermal option in 3DEC allows the simulation of transient heat conduction. There are two separate formulations of the thermal logic. The first is a numerical formulation using the explicit or implicit finite difference method. This method is more accurate for short times, and includes thermal-mechanical fluid coupling. The second is an analytical formulation that uses superposition of point heat sources in an infinite medium. This method is suitable for long thermal times and is very fast. The comparative features of the two methods are listed below.

Table 1: Comparison of Features Available with Numerical vs Analytical Formulations

feature	numerical	analytical
thermal mechanical coupling	yes	yes
thermal fluid coupling	yes	no
thermal convection in fluid	yes	no
temperature boundary	yes	no
thermal flux boundary	yes	no
thermal convection boundary	yes	no
adiabatic boundary	yes	yes
nonhomogeneous thermal block properties	yes	no
heat sources	yes	yes

• Numerical Thermal Formulation
  • Introduction
  • Heat Conduction
    • Introduction
    • Mathematical Model Description
    • Numerical Formulation
    • Solving Thermal-Only and Thermal-Mechanical Problems
  • Heat Convection
    • Introduction
    • Mathematical Model Description
    • Numerical Formulation
    • Stability and Accuracy
    • Solving Thermal Convection Problems
  • Input Instructions for Thermal Analysis
    • 3DEC Commands
  • Systems of Units for Thermal Analysis
  • Verification Examples
    • Conduction in a Plane Sheet
    • Heating of a Hollow Cylinder
    • Infinite Line Heat Source in an Infinite Medium
    • One-Dimensional Thermal Transport by Conduction and Convection
  • Application Examples
    • Thermal Convection in a Fracture at Depth
• Analytical Thermal Formulation
  • Introduction
  • Theory
    • The Temperature Due to a Distribution of Heat Sources
    • Boundary Conditions
    • Thermally Induced Stress Changes
  • Application in 3DEC
  • Input Commands
  • Verification
    • A Single Non-decaying Point Heat Source
    • Superposition of Several Non-decaying Sources
    • Lines and Grids of Sources
    • Decaying Sources
    • Thermomechanical Effects
  • An Example Problem – Waste Repository Drift Model
• References