  We propose a novel approach to parameterize the equation of state for Scalar
Field Dark Energy (SFDE) and use it to derive analytical solutions for various
cosmological parameters. Using statistical MCMC with Bayesian techniques, we
obtain constraint values for the model parameters and analyze three
observational datasets. We find a quintessence-like behavior for Dark Energy
(DE) with positive values for both model parameters $\alpha$ and $\beta$. Our
analysis of the $CC$+$BAO$+$SNe$ datasets reveals that the transition redshift
and the current value of the deceleration parameter are
$z_{tr}=0.73_{-0.01}^{+0.03}$ and $q_{0}=-0.44_{-0.02}^{+0.03}$, respectively.
We also investigate the fluid flow of accretion SFDE around a Black Hole (BH)
and analyze the nature of the BH's dynamical mass during accretion, taking into
account Hawking radiation and BH evaporation. Our proposed model offers insight
into the nature of DE in the Universe and the behavior of BHs during accretion.
