Lie symmetry approach to the time-dependent Karmarkar condition

We obtain solutions of the time-dependent Einstein Field Equations which satisfy Karmarkar condition via method 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 satisfies heat-flux boundary Santos, radiating stellar model then obtained investigated. Solutions do not allow for application junction conditions at surface may lend themselves cosmological models. This is first attempt in generating satisfying symmetries our example highlights viability this method.