  We obtain solutions of the time-dependent Einstein Field Equations which
satisfy the Karmarkar condition via the method of Lie symmetries. Spherically
symmetric spacetime metrics are used with metric functions set to impose
conformal flatness, Weyl-free collapse and shear-free collapse. In particular,
a solution was found which satisfies the heat-flux boundary condition of
Santos, and a radiating stellar model was then obtained and investigated.
Solutions obtained which do not allow for the application of the junction
conditions at a boundary surface may lend themselves to cosmological models.
This is a first attempt in generating solutions satisfying the Karmarkar
condition via the method of Lie symmetries and our example of a radiating model
highlights the viability of this method.
