  The heating of coronal loops is investigated to understand the observational
consequences in terms of the thermodynamics and radiative losses from the Sun
as well as the magnetized coronae of stars with an outer convective envelope.
The dynamics of the Parker coronal heating model are studied for different
ratios of the photospheric forcing velocity timescale $t_p$ to the Alfv\'en
crossing time along a loop $t_A$. It is shown that for $t_p/t_A \gtrsim$ 10--24
the heating rate and maximum temperature are largest and approximately
independent of $t_p/t_A$, leading to a strong emission in X-rays and EUV. On
the opposite decreasing $t_p/t_A$ to smaller values leads to lower heating
rates and plasma temperatures, and consequently fading high-energy radiative
emission once $t_p/t_A \lesssim$ 1--3. The average volumetric loop heating rate
is shown to scale as $\ell_p u_p B_0^2/4\pi L^2$, where $\ell_p$ and $u_p$ are
respectively the convective granule length-scale and velocity, $B_0$ is the
intensity of the strong magnetic field threading the loop, and $L$ the loop
length. These findings support a recent hypothesis explaining ultracool dwarf
observations of stars with similar magnetic field strength but radically
different topologies displaying different radiative emission.
