  We have studied the space-time evolution of minimally viscous
($\frac{\eta}{s}$=0.08) QGP fluid, undergoing boost-invariant longitudinal
motion and arbitrary transverse expansion. Relaxation equations for the shear
stress tensor components, derived from the phenomenological Israel-Stewart's
theory of dissipative relativistic fluid, are solved simultaneously with the
energy-momentum conservation equations. Comparison of evolution of ideal and
viscous fluid, both initialized under the similar conditions, e.g. same
equilibration time, energy density and velocity profile, indicate that in
viscous fluid, energy density or temperature of the fluid evolve slowly than in
an ideal fluid. Transverse expansion is also more in viscous evolution. We have
also studied particle production in viscous dynamics. Compared to ideal
dynamics, in viscous dynamics, particle yield at high $p_T$ is increased.
Elliptic flow on the other hand decreases. Minimally viscous QGP fluid,
initialized at entropy density $s_{ini}$=110 $fm^{-3}$ at the initial time
$\tau_i$=0.6 fm, if freeze-out at temperature $T_F$=130 MeV, explains the
centrality dependence of $p_T$ spectra of identified particles. Experimental
$p_T$ spectra of $\pi^-$, $K^+$ and protons in 0-5%, 5-10%, 10-20%, 20-30%,
30-40% and 40-50% Au+Au collisions are well reproduced through out the
experimental $p_T$ range. This is in contrast to ideal dynamics, where, the
spectra are reproduced only up to $p_T\approx$1.5 GeV. Minimally viscous QGP
fluid, also explain the elliptic flow in mid-central (10-20%, 16-23%, 20-30%)
collisions. The minimum bias elliptic flow is also explained. However, the
model under-predict/over-predict the elliptic flow in very central/peripheral
collisions.
