The Stefan problem for a slightly wavy wall (Q804334)

In the paper a fully two-dimensional Stefan problem is solved by a regular perturbation method for the case of a general slight deviation of wall geometry. An approximate solution is obtained in terms of linearized two-dimensional perturbations of a one-dimensional case. Three particular examples are given, namely, a sinusoidal corrugation on the wall (as is seen in refrigerator freezer compartments), a slight hump, and a plane wall rotated very slightly.