Superposition with Non-linear Boundary Conditions in Fire Sciences
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Linear response theory is widely used in science and engineering but its use in fire sciences is rare. This communication reviews shortly the Duhamel superposition technique for solving problems in fire sciences where the response of a material maybe assumed linear but the boundary conditions (BC) are non-linear. The method can be used as an alternative to e.g. finite element methods for problems where analytical solutions are not available. Examples include temperature distribution in solids with time-varying and non-linear heat flux boundaries using a simple spreadsheet solution technique. Supplementary material contains an Excel spreadsheet solving problems with non-linear BC.
KeywordsLinear response Heat transfer Duhamel superposition principle
Financially supported by the Swedish Fire Research Board—Brandforsk.
- 3.Zubair SM, Chaudhry MA (1993) Heat conduction in a semi-infinite solid subject to time-dependent surface heat fluxes: an analytical study. Heat Mass Transf 28:357–364Google Scholar
- 6.Rocket JA, Milke JA (2008) Conduction of heat in solids. In: SFPE handbook on fire protection engineering, 4th edn, NFPA, QuincyGoogle Scholar
- 8.Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford Press, LondonGoogle Scholar
- 9.VanSant JH (1980) Conduction heat transfer solutions. Lawrence Livermore National Laboratory, LivermoreGoogle Scholar