  The Enthalpy Based Thermal Evolution of Loops (EBTEL) approximate model for
static and dynamic coronal loops is developed to include the effect of a loop
cross-sectional area which increases from the base of the transition region
(TR) to the corona. The TR is defined as the part of a loop between the top of
the chromosphere and the location where thermal conduction changes from an
energy loss to an energy gain. There are significant differences from constant
area loops due to the manner in which the reduced volume of the TR responds to
conductive and enthalpy fluxes from the corona. For static loops with modest
area variation the standard picture of loop energy balance is retained, with
the corona and TR being primarily a balance between heating and conductive
losses in the corona, and downward conduction and radiation to space in the TR.
As the area at the loop apex increases, the TR becomes thicker and the density
in TR and corona larger. For large apex areas, the coronal energy balance
changes to one primarily between heating and radiation, with conduction playing
an increasingly unimportant role, and the TR thickness becoming a significant
fraction of the loop length. Approximate scaling laws are derived that give
agreement with full numerical solutions for the density, but not the
temperature. For non-uniform areas, dynamic loops have a higher peak
temperature and are denser in the radiative cooling phase by of order 50% than
the constant area case for the examples considered. They also show a final
rapid cooling and draining once the temperature approaches 1 MK. Although the
magnitude of the emission measure will be enhanced in the radiative phase,
there is little change in the important observational diagnostic of its
temperature dependence.
