  In the framework of Brans-Dicke (BD) theory, the first part of the present
study determines the time dependence of BD parameter, energy density and
equation of state (EoS) parameter of the cosmic fluid in a universe expanding
with acceleration, preceded by a phase of deceleration. For this purpose, a
scale factor has been chosen such that the deceleration parameter, obtained
from it, shows a signature flip with time. Considering the dark energy to be
responsible for the entire pressure, the time evolution of energy parameters
for matter and dark energy and the EoS parameter for dark energy have been
determined. An effective interaction term, between matter and dark energy, has
been proposed and calculated. Its negative value at the present time indicates
conversion of matter into dark energy. Using this term, the time dependence of
the rates of change of matter and dark energy has been determined. It is found
that the nature of dependence of the scalar field upon the scale factor plays a
very important role in governing the time evolution of the cosmological
quantities studied here. The present study provides us with a simple way to
determine the time evolution of dark energy for a homogeneous and isotropic
universe of zero spatial curvature, without involving any self-interaction
potential or cosmological constant in the formulation.
