  We consider Taylor dispersion for tracer particles in micro-fluidic planar
channels with strong confinement. In this context, the channel walls modify the
local diffusivity tensor and also interactions between the tracer particles and
the walls become important. We provide a simple and general formula for the
effective diffusion constant along the channel as well as the first non-trivial
finite time correction for arbitrary flows along the channel, arbitrary
interaction potentials with the walls and arbitrary expressions for the
diffusion tensor. The formula are in particular amenable to a straightforward
numerical implementation, rendering them extremely useful for comparison with
experiments. We present a number of applications, notably for systems which
have parabolically varying diffusivity profiles, to systems with attractive
interactions with the walls as well as electroosmotic flows between plates with
differing surface charges within the Debye-H\"uckel approximation.
