Heat transfer analysis using a Green’s function approach for uniformly insulated steel members subjected to fire

An efficient numerical approach is developed in this paper for heat transfer analysis of insulated steel members exposed to fire, characterized by one-dimensional conduction through an insulation layer. The numerical schemes make use of Green’s function solutions of diffusion equations, and consequently no spatial discretization is involved. Two types of time-varying boundary conditions, namely, the essential (Dirichlet) and the natural (Neumann), are treated individually. Computational models are developed for boundary conditions of each type, in which the choice of sampling time does not have the numerical stability requirement imposed. The numerical algorithm can be implemented in an Excel spreadsheet for engineering use.