  We consider a relativistic radiating spherical star in conformally flat
spacetimes. In particular we study the junction condition relating the radial
pressure to the heat flux at the boundary of the star which is a nonlinear
partial differential equation. The Lie symmetry generators that leave the
equation invariant are identified and we generate an optimal system. Each
element of the optimal system is used to reduce the partial differential
equation to an ordinary differential equation which is further analysed. We
identify new categories of exact solutions to the boundary conditions. Two
classes of solutions are of interest. The first class depends on a self similar
variable. The second class is separable in the spacetime variables.
