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Theory of Ignition Considered as a Thermal Reaction
1.F. L. Alt, Ballistic Research Laboratories Report No. 682 (1948).
2.D. A. Frank‐Kamenetzky, J. Phys. Chem. (U.S.S.R.) 13, 738 (1939);
2.P. V. Melentjev and O. M. Todes, Acta Physicochim. U.R.S.S. 14, 27 (1941);
2.O. K. Rice, J. Chem. Phys. 8, 727 (1940);
2.E. K. Rideal and A. J. B. Robertson, Third Symposium on Combustion (Williams and Wilkins, Baltimore, Maryland, 1949), p. 536;
2.M. W. Evans, Technical Report No. 27, Project SQUID (Princeton, New Jersey, 1951)—a review of theories of steady‐state flame propagation.
3.C. Lowener, NDRC Appl. Math. Panel Memos 131.1M and 131.2M, (1945);
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3.C. H. Bamford, J. Crank, and D. H. Malan, Proc. Camb. Phil. Soc. 42, 166 (1946);
3.J. Crank and P. Nicolson, Proc. Camb. Phil. Soc., 43, 50 (1947);
3.D. Altman and A. F. Grant, Jr., Abstracts of Papers for Fourth Symposium on Combustion (Massachusetts Institute of Technology, 1952), p. 19.
4.J. H. Frazer and B. L. Hicks, J. Phys. and Colloid Chem., 54, 872 (1950).
5.We have made extensive calculations, to be described elsewhere, of reaction models that allow for diffusion of a single reactant as well as of heat. The stability aspects of these calculations were discussed at the Pittsburgh meeting of the American Physical Society in 1951.
6.J. H. Frazer, New York City Meeting of Am. Chem. Soc., September 15, 1947;
6.B. L. Hicks and H. G. Landau, Math. Tables and Aids to Computation 3, 207 (1948);
6.B. L. Hicks, Phys. Rev. 76, 166(A (1949).
7.The medium can be taken to be solid. We shall not consider here the ignition process after the surface begins to regress. [H. G. Landau, Quar. Appl. Math., 7, 81 (1950).)] The medium could be liquid or gas if the density and position of all of its parts remain fixed.
8.Any later temperature distribution developed by the internal and external heating in the propellant could likewise be considered to be an initial condition.
9.We note that a steady state for a thermal, infinite model is possible when burning (with surface regression) rather than ignition of the propellant is considered. See reference 1.
10.Except where there is a possibility of confusing the reduced (dimensionless) and the dimensional variables or parameters we shall generally omit the word “reduced” in the remainder of the paper.
11.To be read “seven values of which the smallest was 0.010 and the largest, 0.034.”
12.The less accurate linear method described by Altman and Grant (reference 3) appears to be satisfactory for correlating ignition data for a composite solid propellant. Our linear method may be required, however, when correlation of data for propellants whose parameters are considerably different is attempted.
13.Bernard Lewis and Guenther von Elbe, J. Chem. Phys. 11, 803 (1947). We note that their q must be taken to include both a chemical heat production term and a lateral heat loss if (see reference 1), the equation is to describe a stable combustion wave of constant velocity for an initial propellant temperature above absolute zero.
14.It should be noted that accurate coverage in this way of the whole range of each of the original dimensional parameters requires that numerical integrations be performed for sets of the reduced (i.e., independent) parameters which cover the whole multidimensional space of variation of these parameters. This requirement is only partially satisfied by the data reported in the present paper.
15.The parameters could also have been chosen to be and (see Section 3) and would have somewhat different physical significance. These parameters have not been discussed separately here, however, because and vary over a small range compared to (qf) and K.
16.H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (The Clarendon Press, Oxford, 1947), p. 55.
17.If or if were not constant for could be obtained from Eq. (A‐8) by integration. (See reference 16, Sec. 10 and p. 55.) If, in particular, is constant for each of a number of intervals of τ separated by discontinuous jumps, then can be found by addition of functions such as that in Eq. (A‐8).
18.In part of the calculations, an had been defined as was taken equal to and 5.0 in finding The calculation of α from numerical integration data however is easier if it is denned as in Eq. (4‐3). Since is a good approximation to in the linear period of heating and we see that leading, for the above values of to and 0.833, respectively.
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