Test use of Biot number to set solid resolution

[rmcdermo]

Not for this release, but we have floated the idea of using a Biot number criterion to set the solid phase resolution near the surface. To me, this is more justifiable than assuming the time scale of 1 s applied to the thermal diffusivity. Jason has roughed out that they are reasonably similar in many cases. But I routinely find that I have to increase solid resolution to get grid converged results.

[drjfloyd]

To illustrate, the table below generates dx using a Biot number of 0.1 and dx using Sqrt(diffusivity). This is for an AST of 1000 C with h=50 W/m/K to a 20 C wall (~190 kW/m2). The effective h (radiation and convection) is ~200 W/m/K. The rows can roughly be thought of as an insulating material, something like wood, something like a plastic, a liquid pool with an effective k for convection, and a metal. At this high flux for wood like materials and insulating materials the diffusivity result is a bit large. For metals it smaller than we need. If we were at 10 % of the incident flux, the Biot dx would be 10 x bigger. We'd still be on the small side for insulating materials.

rho	k	cp	dx Biot	dx Diff^0.5	B / D
100	0.01	1000	5.0E-06	3.2E-04	1.6E-02
1000	0.1	1000	5.0E-05	3.2E-04	1.6E-01
1000	1	1000	5.0E-04	1.0E-03	5.0E-01
1000	10	1000	5.0E-03	3.2E-03	1.6E+00
10000	100	1000	5.0E-02	3.2E-03	1.6E+01