  In Brans Dicke theory of gravity, from the nature of the scalar
field-potential considered, the dark energy, dark matter, radiation densities
predicted by different observations and the closedness of the universe
considered, we can fix our $\omega_{BD}$, the Brans Dicke parameter, keeping
only the thing in mind that from different solar system constrains it must be
greater than $5\times 10^{5}$. Once we have a value, satisfying the required
lower boundary, in our hand we proceed for setting unknown parameters of the
different dark energy models' EoS parameter. In this paper we work with three
well known red shift parametrizations of dark energy EoS. To constrain their
free parameters for Brans Dicke theory of gravity we take twelve point red
shift vs Hubble's parameter data and perform $\chi^{2}$ test. We present the
observational data analysis mechanism for Stern, Stern+BAO and Stern+BAO+CMB
observations. Minimising $\chi^2$, we obtain the best fit values and draw
different confidence contours. We analyze the contours physically. Also we
examine the best fit of distance modulus for our theoretical models and the
Supernovae Type Ia Union2 sample. For Brans Dicke theory of gravity the
difference from the mainstream confidence contouring method of data analysis id
that the confidence contours evolved are not at all closed contours like a
circle or a ellipse. Rather they are found to be open contours allowing the
free parameters to float inside a infinite region of parameter space. However,
negative EoSs are likely to evolve from the best fit values.
