Power output from an irreversible heat engine with a nonuniform working fluid

The upper bound is calculated for the average power output of an irreversible heat engine whose working fluid is viscous and not necessarily uniform in temperature. The calculation is done via the generalized formalism of finite-time thermodynamics. The working fluid of the heat engine is described by partial-differential equations containing parameters in the boundary conditions. With some restrictions on parameters, the estimated power coincides with the optimal power output for the classical lumped-parameter (uniform-T) irreversible Carnot engine.