Temperature T in the liquid:
k
Ñ
2
T + V
¶
T/
¶
z = 0
Conservation of energy:
Melting temperature:
-L
V
v
n
= k
¶
T/
¶
n
T = T
M
Far-field boundary condition (bath temperture):
T
®
T
¥
= T
M
-
D
T
Steady-State Isothermal Model of Dendritic Growth
k
=
thermal diffusivity
L
V
= latent heat per unit volume
V = dendrite growth velocity
k =
thermal conductivity
Characteristic scales: choose
D
T for (T – T
M
) and 2
k
/V for length.
Note:
¶
T/
¶
z is a solution if T is.