  A quantitative vortex-fluid model for flux-flow resistivity $\rho$ and Nernst
signal $e_N$ in high-temperature superconductors (HTSC) is proposed. Two kinds
of vortices, magnetic and thermal, are considered, and the damping viscosity
$\eta$ is modeled by extending the Bardeen-Stephen model to include the
contributions of flux pinning at low temperature and in weak magnetic fields,
and vortex-vortex collisions in strong magnetic fields. Remarkably accurate
descriptions for both Nernst signal of six samples and flux flow resistivity
are achieved over a wide range of temperature $T$ and magnetic field $B$. A
discrepancy of three orders of magnitude between data and Anderson's model of
Nernst signal is pointed out and revised using experimental values of $\eta$
from magnetoresistance. Furthermore, a two-step procedure is developed to
reliably extract, from the Nernst signal, a set of physical parameters
characterizing the vortex dynamics, which yields predictions of local
superfluid density $n_s$, the Kosterlitz coefficient $b$ of thermal vortices,
and upper critical field and temperature. Application of the model and
systematic measurement of relevant physical quantities from Nernst signal in
other HTSC samples are discussed.
