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Implicitly Coupling Heat Conduction Into a Zone Fire Model (NISTIR 4886)



W F. Moss, Glenn P. Forney


This report examines several methods for coupling the partial differential equations that arise in conductive heat transfer with the ordinary differential equations that arise in zone fire modeling. Two existing algorithms (method of lines and time splitting) are discussed and a new strategy is proposed for performing this coupling. This strategy couples the wall surface temperature rather than the entire wall temperature rpofile with the other zone fire modeling solution variables by requiring that the wall surface temperature gradient and the incident heat flux (sum of convective and net radiative flux) satisfy Fourier's law. Two prototype fire models were written to test the ideas discussed in this report. The first, CONRAD1, implements the method of lines strategy for solving heat conduction. The second, CONRAD2, implements the new strategy. Though inefficient, CONRAD1 uses will established numerical techniques and therefore serves as a benchmark to test the numerical ideas implemented in CONRAD2. Both programs use the stiff differential-algebraic equation solver DASSL. Supporting numerical results are presented.
NIST Interagency/Internal Report (NISTIR) - 4886
Report Number


conductive heat transfer, fire models, zone models, equations, computer models, algorithms


Moss, W. and Forney, G. (1992), Implicitly Coupling Heat Conduction Into a Zone Fire Model (NISTIR 4886), NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online],, (Accessed April 19, 2024)
Created June 30, 1992, Updated October 12, 2021