  We explore the performance of three- and two-stroke heat engines with a
qutrit working substance in charging two-level quantum batteries. We first
classify the heat engines into two groups depending on their working methods.
The first type of heat engine, the sequential engine, evolves through three
distinct strokes, viz., heat, work, and cold strokes. In the second kind of
engine, a simultaneous engine, all the three events are made to occur
simultaneously in one stroke, followed by an additional stroke to thermalize
the working substance, i.e., the qutrit with a cold bath. We further categorize
these two types of engines into two classes depending on the type of
interaction between the working substance and the baths or the battery, viz.,
out-and-out engines, where the system bath interactions can invoke population
transitions between any two energy levels of the qutrit, and fragmented
engines, where only selective transition is materialized. Considering these
four types of heat engines, we analyze the work done by the working substance,
the percentage of charge accumulated by the quantum battery, and the efficiency
of the engine. By drawing a comparison between the charging schemes, we find
that the sequential out-and-out heat engines are most advantageous, providing
unit efficiency and transferring the most energy to the quantum battery, in the
optimal case. The ranking of the benefits obtained from the other three engines
depends on the quantity of interest.
