Part I
The one-dimensional, time-dependent equations describing laminar deflagration are solved by an integral method, under the assumption of a physical model for the flame structure and behavior, with restrictions on the type of deviation from steady-state behavior. By virtue of application of a hot-boundary approximation of the vonKármán type, certain sensitive integrals are expressed in a form independent of the temperature profile assumed. Two cases are considered: the "thermal theory" neglecting diffusion, and the case of unity Lewis number (temperature/concentration similarity). Only first order reactions are considered. Arguments supporting the generality of the results are included, along with a discussion of accuracy, and some comparison with experimental work. Graphical display of the results anticipates the utility of the theory for correlating and cross-checking experimental data.
It is concluded that the relaxation time is closely related to the time required for the gas undergoing rapid chemical reaction to pass through the flame.
Part II
The interaction of an electromagnetic wave with a mildly ionized gas is described by an ensemble average treatment of electron motion, and under this description, electromagnetic wave propagation parameters derived. Motivated by the fact that mildly ionized gases in general exhibit inhomogeneous boundary regions, exemplary transition zones are described in terms of varying electron density but constant collision frequency, in order to simplify the solution of wave problems. The half-space reflection problem with a linear transition zone is solved exactly and under two approximations. It is discovered that the reflection and transmission coefficients are strong functions of zone thickness for thin zones. A piecewise-linear transition zone solution exemplifies the procedure for constructing an approximate solution to an arbitrary profile and illustrates the relative insensitivity of reflection and transmission coefficients to detailed zone structure. The "slab" reflection problem with symmetrical, linear transition zones is solved exactly, and it is discovered that the basic periodicity of reflection and transmission coefficients with slab thickness is unchanged, although shifted to higher values of slab thickness/wavelength. The text is supported by fairly extensive graphical presentation of results.
