  Since the late 1990's observations of type Ia Supernova, our universe is
predicted to experience a late time cosmic acceleration. Theoretical support to
this observation were intended to be built via proposition of a hypothetical
fluid which staying inside the universe exerts negative pressure. Cosmologists
have prescribed many candidates for this exotic fluid so far. In this alley, a
popular method is to choose time dependent equation of state parameter $\omega
= \frac{p}{\rho}$ and to parametrize it as a function of redshift. Again some
common families of such parametrizations are constructed among which different
members justify different properties of observed universe. Mainly, these were
model dependent studies which comprise free parameters to be constrained by
different observations. In this present article, a new expression for redshift
parametrization is considered and we have constrain its free parameters for two
Hubble parameter vs redshift data sets. These data sets are obtained depending
on two basic methodologies known as different ages method and baryonic acoustic
oscillation method. Different confidence contours for our model are located
under the constraints of said data sets. Besides, different thermodynamic
parameters related to the evolution of our universe are analysed. It is
notified that our model indicates towards a delayed dark matter model which
mimics EoS = $-1(\Lambda)$ phenomena at the present epoch. Deceleration
parameters behaviour's are studied. It is noticed that a possibility of future
deceleration may occur for this new model. Outcomes for both the data sets are
compared with each other.
