  The formation of chondrules in the protoplanetary nebulae causes many
questions concerning the formation process, the source of energy for melting
the rims, and the composition of the origin material. The aim of this work is
to explore the heating of the chondrule in a single precursor as is typical for
radiation hydrodynamical shock waves. We take into account the gas-particle
friction for the duration of the shock transition and calculate the heat
conduction into the chondrules. These processes are located in the
protoplanetary nebulae at a region around 2.5 AU, which is considered to be the
most likely place of chondrule formation. The present models are a first step
towards computing radiative shock waves occurring in a particle-rich
environment. We calculated the shock waves using one-dimensional,
time-independent equations of radiation hydrodynamics involving realistic gas
and dust opacities and gas-particle friction. The evolution of spherical
chondrules was followed by solving the heat conduction equation on an adaptive
grid. The results for the shock-heating event are consistent with the
cosmochemical constraints of chondrule properties. The calculations yield a
relative narrow range for density or temperature to meet the requested heating
rates of $R > 10^4\,K\, h^{-1}$ as extracted from cosmochemical constraints.
Molecular gas, opacities with dust, and a protoplanetary nebula with accretion
are necessary requirements for a fast heating process. The thermal structure in
the far post-shock region is not fully consistent with experimental constraints
on chondrule formation since the models do not include additional molecular
cooling processes.
