  We consider a generalized Brans-Dicke model in which the scalar field has a
potential function and is also allowed to couple non-minimally with the matter
sector. We assume a power law form for the potential and the coupling functions
as the inputs of the model and show that acceleration of the universe can be
realized for a constrained range of exponent of the potential function. We also
argue that this accelerating phase is consistent with a large and positive
Brans-Dicke parameter. In our analysis, the potential plays a more important
role with respect to the coupling function in dynamics of the universe as the
latter does not contribute to any of the relations characterizing evolution of
scale factor of the universe and the scalar field. However, we will show that
the coupling function is closely related to magnitude and direction of the
energy transfer between matter and the scale field. We use this fact and some
thermodynamic aspects of the model to put some constraints on the coupling
function. In particular, we argue that the second law of thermodynamics
constrains direction of the overall energy transfer.
