Generalized Stefan Problem Research Articles

A generalized Stefan problem in several space variables

A multidimensional, multiphase problem of Stefan type, involving quasilinear parabolic equations and nonlinear boundary conditions is considered. Regularization techniques and monotonicity methods are exploited. Existence and uniqueness of a weak solution to the problem, as well as continuous and monotone dependence of the solution upon data are shown.

A Mathematical Description of Open and Closed Flame Tips

Abstract The tips of two-dimensional premixed flames are analyzed for both plane and axisymmetric geometries. Using activation energy asymptotics and slender flame theory the problem of solving the model aerothermochemical equations is reduced to a generalized Stefan problem which is solved numerically. The qualitative nature of the solutions depends critically on the Lewis Number, L. For most values of L they correspond to closed tips, the most commonly observed laboratory situation. But for values of L significantly less than 1 solutions corresponding to open tips are formed, of the kind sometimes seen in the combustion of lean mixtures of hydrogen.

The quenching of a deflagration wave held in front of a bluff body

This paper describes the analysis of two-dimensional premixed flames located in a nonuniform straining flow with particular attention to the case of flame held in front of a circular cylinder in a potential flow. Using activation energy asymptotics and a slow flame approximation, the problem of solving the aerothermomechanical equations is reduced to a generalized Stefan problem. In the neighborhood of the front stagnation point appropriate similarity equations are solved in closed form, and downstream of that point a numerical description is obtained. The behavior at the stagnation point depends in a complicated fashion on the straining rate β and the Lewis Number L, and for some values of these parameters the speed of the stretched flame is greater than the adiabatic flame speed, for others it is less. Quenching occurs if β is large enough, at a nonvanishing flame speed for some values of L, at zero flame speed for others. The full nature of the quenching phenomenon is revealed by a stability analysis. Numerical integration downstream of the stagnation point is carried out for a variety of cases. For a flame attached to a cylinder both the flame speed and the standoff distance increase significantly. For other flows it is possible to quench the flame downstream of the stagnation point.

Nonlinear equations of evolution and a generalized Stefan problem

Nonlinear equations of evolution and a generalized Stefan problem