Abstract
It is radiant heat (the solar radiation and thermal radiation), the heat transferred from the air and the latent heat of vapor that participate mainly in snow melting.
Now, there is the analogy between heat transfer and condensation to pans. (Reynolds' analogy.) On this theory, I find the following formulas, for the small pans.
(1) When windless,
m = 2.1 l-1/4 θ'5/4× 10-3 gr/cm2. hr.
where (m) is the rate of snow melting by the heat transferred, (l) is the length of the pan in cm and (θ') is temperature of the air current. And
m= 4.9 l-1/4|co-c'|θ1/4 ×104 gr/cm2. hr.
where (m') is the rate of snow melting by the latent heat of the vapor, (co) anc (c') are respectively vapor concentration on the snow surface and in the air current in gr/cm2.
(2) Under the laminar boundary condition,
m= 4.0 l-1/2U1/2θ' × 10-3 gr/cm2. hr.
where (U) is the wind valocity in cm/sec. And
m'=9.0l1/2U1/2|co-c'|× 10-3
=7.2 l-1/2U1/2|p'-6.1|× 10-3gr/cm2
where (p') is vapor pressure in the air current in mb.
(3) Under the turbulent boundary condition,
m=3.4 l-1/5U4/5 θ'10-4 gr/cm2. hr.
and
m'=6.4l-1/5U4/5|co-c'|× 102
=5.1l-1/5U4/5|p'-6.1|× 10-4gr/cm2.hr
But the above-mentioned are the case of smooth surface. In the cases of rough surface, perhaps, the rate of snow melting may be much more rapid.
