Estimation of linearly temperature-dependent thermal conductivity using an inverse analysis

Farzad Mohebbi, Mathieu Sellier, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


A linearly temperature-dependent thermal conductivity is estimated in steady state heat conduction problems using an inverse analysis. A body fitted grid generation technique is employed to mesh the two-dimensional body and solve the direct heat conduction problem. An efficient, accurate, and easy to implement method is presented to compute the sensitivity coefficients through derived expressions. The main feature of the sensitivity analysis is that all sensitivities can be obtained in one solve, irrespective of the number of unknown parameters. The conjugate gradient method along with the discrepancy principle is used in the inverse analysis to minimize the objective function and achieve the desired solution. The ability to efficiently and accurately recover the non-constant thermal conductivity is demonstrated through a number of benchmark problems.

Original languageEnglish
Pages (from-to)68-76
Number of pages9
JournalInternational Journal of Thermal Sciences
Publication statusPublished - 2017 Jul 1
Externally publishedYes


  • Conjugate gradient method
  • Elliptic grid generation
  • Finite difference method
  • Inverse heat transfer
  • Sensitivity analysis
  • Variable thermal conductivity

ASJC Scopus subject areas

  • Condensed Matter Physics
  • General Engineering


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