  This paper deals with the spherically symmetric self-gravitating star which
is considered to be expansion free dissipative perfect fluids distribution.
Some recent research reveals that expansion free dynamical star must be
accelerating and dissipating. We adopted some conjectures to obtain the
analytical solution for the dynamical model of such stars. Firstly, it has
shown that density of dynamical star is homogeneous and \Lamada-dominated under
quasi-static diffusion approximation. Secondly, the self-similar solution is
also discussed to describe the dynamical model.
