  Using analytic and numerical approaches, we study the spatio-temporal
evolution of a conserved order parameter of a fluid in film geometry, following
an instantaneous quench to the critical temperature $T_c$ as well as to
supercritical temperatures. The order parameter dynamics is chosen to be
governed by model B within mean field theory and is subject to no-flux boundary
conditions as well as to symmetric surface fields at the confining walls. The
latter give rise to critical adsorption of the order parameter at both walls
and provide the driving force for the non-trivial time evolution of the order
parameter. During the dynamics, the order parameter is locally and globally
conserved; thus, at thermal equilibrium, the system represents the canonical
ensemble. We furthermore consider the dynamics of the nonequilibrium critical
Casimir force, which we obtain based on the generalized force exerted by the
order parameter field on the confining walls. We identify various asymptotic
regimes concerning the time evolution of the order parameter and the critical
Casimir force and we provide, within our approach, exact expressions of the
corresponding dynamic scaling functions.
