  Viscous accretion flow around a rotating supermassive black hole sitting in a
quintessence tub is studied in this article. To introduce such a dark energy
contaminated black hole's gravitational force, a new pseudo-Newtonian potential
is used. This pseudo-Newtonian force can be calculated if we know the distance
from the black hole's center, spin of the black hole and equation of state of
the quintessence inside which the black hole is considered to lie. This force
helps us to avoid complicated nonlinearity of general relativistic field
equations. Transonic, viscous, continuous and Keplerian flow is assumed to take
place. Fluid speed, sonic speed profile and specific angular momentum to
Keplerian angular momentum ratio are found out for different values of spin
parameter and quintessence parameter. Density variation is built and tallied
with observations. Shear viscosity to entropy density ratio is constructed for
our model and a comparison with theoretical lower limit is done.
