Numerical solutions for the one-dimensional heat-conduction equation using a spreadsheet

Zohar Gvirtzman*, Zvi Garfunkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We show how to use a spreadsheet to calculate numerical solutions of the one-dimensional time-dependent heat-conduction equation. We find the spreadsheet to be a practical tool for numerical calculations, because the algorithms can be implemented simply and quickly without complicated programming, and the spreadsheet utilities can be used not only for graphics, printing, and file management, but also for advanced mathematical operations. We implement the explicit and the Crank-Nicholson forms of the finite-difference approximations and discuss the geological applications of both methods. We also show how to adjust these two algorithms to a nonhomogeneous lithosphere in which the thermal properties (thermal conductivity, density, and radioactive heat generation) change from the upper crust to the lower crust and to the mantle. The solution is presented in a way that can fit any spreadsheet (Lotus-123, Quattro-Pro, Excel). In addition, a Quattro-Pro program with macros that calculate and display the thermal evolution of the lithosphere after a thermal perturbation is enclosed in an appendix.

Original languageEnglish
Pages (from-to)1147-1158
Number of pages12
JournalComputers and Geosciences
Volume22
Issue number10
DOIs
StatePublished - Dec 1996

Keywords

  • Basin analysis
  • Crank-Nicholson
  • Explicit
  • Finite-difference methods
  • Heat conduction
  • Spreadsheet
  • Thermal modeling

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