We develop a 3D porous medium model for sap flow within a tree stem, whichconsists of a nonlinear parabolic partial differential equation with a suitabletranspiration source term. Using an asymptotic analysis, we derive approximateseries solutions for the liquid saturation and sap velocity for a general classof coefficient functions. Several important non-dimensional parameters areidentified that can be used to characterize various flow regimes. Weinvestigate the relative importance of stem aspect ratio versus anisotropy inthe sapwood hydraulic conductivity, and how these two effects impact the radialand vertical components of sap velocity. The analytical results are validatedby means of a second-order finite volume discretization of the governingequations, and comparisons are drawn to experimental results on Norway sprucetrees.
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