Solving System of DEs: T, u, phi w/ Constants & r

[msenousy]

Hello dear all;
I have been trying to solve a system of DE for a long time; however, I find it difficult to solve it.
I am wondering if anyone can help me in solving them ir at least telling me whether they have a closed form solution or not.

the equations are attached to this mail in a jpg format

The dependant variables are, "T", "u", and "phi"
the independant variable is "r"
other than that everything is constant

Thanks;
MoMo

 

[Clausius2]

Separation of variables?