What is the relation between the temperature and the radius for an expanding cylindrical thermal shock wave?

I’m reading a paper written by De Rujula and Glashow called "Nuclearites: a novel form of cosmic radiation". In this paper the authors propose the existence of nuggets of strange quark matter called nuclearites whose behavior when entering the atmosphere resemble that of a meteoroid.

It is stated that while travelling through the atmosphere they would produce an expanding cylindrical thermal shockwave and that the effective temperature of this shock depends on the radius according to:

Also, the rate of expansion of the shock is given as:

Where $m$ is the molecular mass of the medium and $n$ is the effective number of submolecular species which are excited (e.g. in water it is 3).

I don’t really now how to retrieve these equations, as it is the first time that I have to deal with shock waves. Anyone could give me a hint on how to work out this problem or give me some bibliographical references?

Thank you in advance.