Attainability of maximum work and the reversible efficiency from minimally nonlinear irreversible heat engines

We use the general formulation of irreversible thermodynamics and study the minimally nonlinear irreversible model of heat engines operating between a time-varying hot heat source of finite size and a cold heat reservoir of infinite size. We find the criterion in which the optimized efficiency obtained by this minimally nonlinear irreversible heat engine can reach the reversible efficiency under the tight coupling condition: a condition of no heat leakage between the system and the reservoirs. We assume the rate of heat transfer from hot to cold heat reservoir obeys Fourier law and discuss physical conditions under which one can obtain the reversible efficiency in a finite time with finite power. We also calculate the efficiency at maximum power from the minimally nonlinear irreversible heat engine under the non-tight coupling condition.