I was thinking about the physics behind a hypothetical scenario where a planet the size and the mass of the Earth is orbiting so close to a very hot star and what the long-term fate of such a planet would be. There are of course so many variables to consider if I expect this question to be answered, so I will try to make the most important assumptions.
Assumptions are as following:
1- The planet is an Earth-like planet.
2- The star is an O-type star with effective surface temperature of 40,000 °K and a radius of 15 solar radii.
3- The Earth-like planet is orbiting at 20 solar radii from the center of the star, or 5 solar radii from its surface.
I have calculated that an Earth-sized planet at this distance from this star would intercept ~ $5\times10^{-8}$ of the total radiation emitted by this star, or about $10^{25}$ W.
Let's now assume that it would take an amount of energy equal to the graviational potential energy of the Earth which is $2.5\times10^{32}$ J to disassemble all the planet's mass. It would actually take a little more energy than that in order to raise the temperature to the boiling point of rocks, but this energy should be less than the gravitational energy and so we can ignore it for simplicity.
To accumlate this amount of energy at the rate our hypothetical planet would be intercepting, it would take $25\times10^{6}$ seconds, or almost a year. This rate is about 60 million times the current rate at which the Earth is intercepting radiation from the Sun. And since radiant flux is proportional to the fourth power of temperature, then the temperature on this planet should reach about 25,000 °K, which is way higher than the boiling point of any known compound on Earth.
This is actually the part where my question lies. The heating of the planet can't be 100% efficient, and the planet will be re-radiating energy at a very high rate plus the fact that the already vaporized material will be shielding the material beneath it. So, would this planet ever get completely vaporized after a long time? Or would it heat to a point where its radiation flux is equal to its absorbed flux and so nothing happens?
Also one other thing I thought of is the thermal conductivity of rock. Since rock has an average thermal conductivity of about 2 W/m.K which is not that high, it would take so long for layers beneath the surface to actually heat up. But at the same time, the surface should be vaporizing, so would this accelerate the process and save the time needed for thermal conduction?
So if any mass-loss rate can be estimated within an order of magnitude level of accuracy, that would definitely answer my question.