Horvay-Cahn Solution [1961] (2-fold)

Paraboloids with elliptical cross-section:

Here w is the independent variable, and b ≠ 0 generates an elliptical cross section.

Solid-liquid interface is w = P, temperature field is T = T(w):

Conservation of energy:

For b = 0, the axisymmetric Ivantsov solution is recovered.