  The fluid models mentioned in the title are studied in a modified approach,
based on two formulas for the mass function. All characteristics of the fluid
are expressed through a master potential, satisfying an ordinary second order
differential equation. Different constraints are imposed on this core of
relations, finding new solutions and deriving the classical results for perfect
fluids as particular cases. All charged anisotropic solutions, all conformally
flat and all uniform density solutions are found. A large class of solutions
with linear equation among the two pressures is derived, including the case of
vanishing tangential pressure. The mechanism responsible for the appearance of
equation of state is elucidated.
