Temperature prediction for multi-dimensional domains in standard fire

Zhi Hua Wang, Kang Hai Tan

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The existing ID analytical solution for heat conduction inside structural members plays an important role in the estimation of temperature field and prediction of member strength in fire. In this paper, the novelty lies in a set of proposed analytical formulations for the conduction heat transfer within multi-dimensional (2D and 3D) domains subjected to a particular time-varying boundary condition, i.e. the standard fire conditions. Solutions of multi-dimensional conduction are based on the eigenfunction approach using the technique of separation of variables. The multi-dimensional effect is incorporated by the product of respective solutions of ID transient heat conduction (1D step functions) of the plate and the infinite cylinder that serve as a set of basis for derivation of analytical solutions. Fire boundary conditions are incorporated using the Duhamel's principle, where the time-varying fire temperature curve is imposed on the step functions. In this paper, the boundary conditions of the first and the third kind are considered, respectively. The analytical solutions are compared with results obtained from finite element analysis for verification.

Original languageEnglish (US)
Pages (from-to)1035-1055
Number of pages21
JournalCommunications in Numerical Methods in Engineering
Issue number11
StatePublished - Nov 2007
Externally publishedYes


  • Analytical formulation
  • Heat transfer
  • Multi-dimension
  • Standard fire

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • General Engineering
  • Computational Theory and Mathematics
  • Applied Mathematics


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