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RESEARCH PAPERS

Spontaneous Ignition: Finite Element Solutions for Steady and Transient Conditions

[+] Author and Article Information
C. A. Anderson

University of Wales at Swansea; Los Alamos Scientific Laboratory, Los Alamos, N. M.

O. C. Zienkiewicz

Department of Civil Engineering, University of Wales at Swansea, Wales, U. K.

J. Heat Transfer 96(3), 398-404 (Aug 01, 1974) (7 pages) doi:10.1115/1.3450212 History: Received July 16, 1973; Online August 11, 2010

Abstract

Steady-state and transient ignition problems are solved by the finite element method. Discretized equations for the reactive heat equation are set down using Galerkin’s method. The steady-state discretized equations are solved by an incremental Newton-Raphson procedure using the Frank-Kamenetskii parameter as the incremented or “loading” variable. Critical values of the Frank-Kamenetskii parameter are given for both common and unusual shapes using isoparametric finite elements to describe the geometrical features of the bodies. The transient ignition problem is solved by using the finite element spatial description together with a midinterval time differencing scheme.

Copyright © 1974 by ASME
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