An Asymptotic, Thermo-Diffusive Ignition Theory of Porous Solid Fuels

[+] Author and Article Information
Choong Se Kim

Chemical Engineering Division, Argonne National Laboratory, Argonne, Ill.

Paul M. Chung

Department of Energy Engineering, University of Illinois at Chicago Circle, Chicago, Ill.

J. Heat Transfer 98(2), 269-275 (May 01, 1976) (7 pages) doi:10.1115/1.3450530 History: Received March 08, 1976; Online August 11, 2010


The governing equations of thermal ignition are analyzed for porous solid fuel, such as coal, of various two-dimensional and axisymmetric geometries by the Laplace asymptotic method. Mass diffusion of the gaseous oxidant through the porous fuel is included. The nonlinear partial differential equations of energy and mass balances in time-space coordinates containing the Arrhenius volumic chemical reaction terms are analyzed. By employing the Laplace asymptotic technique and by invoking a certain limit theorem, the governing equations are reduced to a first order ordinary differential equation governing the fuel surface temperature, which is readily solved numerically. Detailed discussion of the effects of the various governing parameters on ignition is presented. Because of the basically closed-form nature of the solutions obtained, many general and fundamental aspects of the ignition criteria hitherto unknown are found.

Copyright © 1976 by ASME
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