  In this manuscript, the field equations of a chameleon field in which the
matter Lagrangian term is a general function of the scalar field as well as
matter field, are derived. The equations are then expressed in
Friedmann--Lema\^itre--Robertson--Walker~(FLRW) framework and the associated
phase portraits and a power law solution are discussed in details. It is shown
that why non-minimal coupling between the chameleon and matter fields leads to
an energy transfer between the fields which consequently, affects the expansion
rate of the universe. The transfer direction is determined by the second law of
thermodynamics. The solution indicates that an accelerating expansion of the
universe can be described as a result of the energy flow from the chameleon
field to matter field.
