  Chondrules are considered to have much information on dust particles and
processes in the solar nebula. It is naturally expected that protoplanetary
disks observed in present star forming regions have similar dust particles and
processes, so study of chondrule formation may provide us great information on
the formation of the planetary systems.
  Evaporation during chondrule melting may have resulted in depletion of
volatile elements in chondrules. However, no evidence for a large degree of
heavy-isotope enrichment has been reported in chondrules. In order to meet this
observed constraint, the rapid heating rate at temperatures below the silicate
solidus is required to suppress the isotopic fractionation.
  We have developed a new shock-wave heating model taking into account the
radiative transfer of the dust thermal continuum emission and the line emission
of gas molecules and calculated the thermal history of chondrules. We have
found that optically-thin shock waves for the thermal continuum emission from
dust particles can meet the rapid heating constraint, because the dust thermal
emission does not keep the dust particles high temperature for a long time in
the pre-shock region and dust particles are abruptly heated by the gas drag
heating in the post-shock region. We have also derived the upper limit of
optical depth of the pre-shock region using the radiative diffusion
approximation, above which the rapid heating constraint is not satisfied. It is
about 1 - 10.
