  The technique of periodic homogenization with two-scale convergence is
applied to the analysis of a two-phase Stefan-type problem that arises in the
study of a periodic array of melting ice bars. For this "reduced model" we
prove results on existence, uniqueness and convergence of the two-scale limit
solution in the weak form, which requires solving a macroscale problem for the
global temperature field and a reference cell problem at each point in space
which captures the underlying phase change process occurring on the microscale.
We state a corresponding strong formulation of the limit problem and use it to
design an efficient numerical solution algorithm. The same homogenized
temperature equations are then applied to solve a much more complicated problem
involving multi-phase flow and heat transport in trees, where the sap is
present in both frozen and liquid forms and a third gas phase is also present.
Our homogenization approach has the advantage that the global temperature field
is a solution of the same reduced model equations, while all the remaining
physics are relegated to the reference cell problem. Numerical simulations are
performed to validate our results and draw conclusions regarding the phenomenon
known as sap exudation, which is of great importance in sugar maple trees and
few other related species.
