  A major goal in solar physics has during the last five decades been to find
how energy flux generated in the solar convection zone is transported and
dissipated in the outer solar layers. Progress in this field has been slow and
painstaking. However, advances in computer hardware and numerical methods,
vastly increased observational capabilities and growing physical insight seem
finally to be leading towards understanding. Here we present exploratory
numerical MHD models that span the entire solar atmosphere from the upper
convection zone to the lower corona. These models include non-grey, non-LTE
radiative transport in the photosphere and chromosphere, optically thin
radiative losses as well as magnetic field-aligned heat conduction in the
transition region and corona.
