  We develop a 3D porous medium model for sap flow within a tree stem, which
consists of a nonlinear parabolic partial differential equation with a suitable
transpiration source term. Using an asymptotic analysis, we derive approximate
series solutions for the liquid saturation and sap velocity for a general class
of coefficient functions. Several important non-dimensional parameters are
identified that can be used to characterize various flow regimes. We
investigate the relative importance of stem aspect ratio versus anisotropy in
the sapwood hydraulic conductivity, and how these two effects impact the radial
and vertical components of sap velocity. The analytical results are validated
by means of a second-order finite volume discretization of the governing
equations, and comparisons are drawn to experimental results on Norway spruce
trees.
