We study the one-phase Stefan problem on a semi-infinite strip
x
≥
0
x \ge 0
, with the convective boundary condition
−
K
T
x
(
0
,
t
)
=
h
[
T
L
−
T
(
0
,
t
)
]
- K{T_x}\left ( {0, t} \right ) = h\left [ {{T_L} - T(0, t)} \right ]
. Points of interest include: a) behavior of the surface temperature
T
(
0
,
t
)
T\left ( {0, t} \right )
; b) asymptotic behavior as
h
→
∞
h \to \infty
; c) uniqueness, and d) bounds on the phase change front and total system energy.