A simple shear-free non-singular spherical model with heat flux

We obtain an exact simple solution of the Einstein equation describing a spherically symmetric cosmological model without the big-bang or any other kind of singularity. The matter content of the model is shear free isotropic fluid with radial heat flux and it satisfies the weak and strong energy conditions. It is pressure gradient combined with heat flux that prevents occurrence of singularity. So far all known non-singular models have non-zero shear. This is the first shear free non-singular model, which is also spherically symmetric.