= Solution
The unperturbed <temperature> is linear in each material. Continuity of the conductive <heat flux> at $x=h$ gives
$$
k_w\frac{T_m-T_h}{h}
=k_a\frac{T_h-T_a}{\delta}.
$$
On defining
$$
\epsilon=\frac{k_a}{k_w}\frac h\delta,
$$
this becomes $T_m-T_h=\epsilon(T_h-T_a)$. Therefore
$$
\boxed{
T_m-T_h=
\frac{\epsilon}{1+\epsilon}(T_m-T_a)}.
$$
Let $\rho_i$ be the ice <mass density> and $L_f$ its <latent heat> of fusion per unit mass. The ice is isothermal in this model, so the <Stefan condition> equates latent-heat production to the <heat flux> conducted through the water:
$$
\rho_iL_fV
=k_w\frac{T_m-T_h}{h}.
$$
Consequently the unperturbed lateral solidification speed is
$$
\boxed{
V=\frac{k_w}{\rho_iL_fh}
\frac{\epsilon}{1+\epsilon}(T_m-T_a)
=\frac{k_a}{\rho_iL_f\delta}
\frac{T_m-T_a}{1+\epsilon}}.
$$
The material parameters are the <thermal conductivities> $k_w,k_a$, ice density $\rho_i$, and specific latent heat $L_f$; the geometric thermal length is $\delta$.
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