  This paper uses linear magnetohydrodynamics to model resonant absorption in
coronal plasma with a Cartesian coordinate system. We impose line-tied boundary
conditions and tilt the background magnetic field to be oblique to the
transition region. Halberstadt & Goedbloed (1993, 1995); Goedbloed& Halberstadt
(1994); Arregui et al. (2003) show that line-tied boundary conditions cause
their resonant absorption models to produce steep boundary layers/evanescent
fast waves. We aim to study the importance of the boundary layers and assess
their significance in a solar context. We calculate the solutions in a model
where we impose line-tied boundary conditions and compare this with a model
where we include the chromosphere instead. Results are calculated analytically
and then verified numerically. We show that line-tied boundary conditions can
cause the model to overestimate the boundary layers' amplitude significantly.
If the fast waves can propagate in the chromosphere, then the line-tied model
accurately predicts the boundary layers' amplitude. However, if the fast waves
are evanescent, then the boundary layers' size is reduced significantly, and
the line-tied model overestimates their amplitude. This leads to the
counter-intuitive result that the length scales tangential to the transition
region can play an essential role in determining line-tied boundary conditions'
validity. The results suggest that line-tied boundary conditions can cause the
model to generate unphysically large boundary layers. However, researchers may
wish to continue to use them in their models for their simplicity and ability
to significantly reduce computation time if they understand and are aware of
their flaws.
