Nonlinear finite element analysis of thermal inertia in heat-balance sap flow measurement

• We model transient nonlinear heat transfer in the sapwood of trees during sap flow measurement.
• The difference between the nonstationary and the stationary results is significant, especially for lower flows.
• We compare two variants of temperature sensors arrangement.
• We confirm the hypothesis that the influence of sapwood moisture on the recorded sap flow is negligible.

This paper deals with the numerical solution of a three-dimensional model of nonstationary nonlinear heat transfer in the sapwood of trees during sap flow measurement by a thermodynamic method based on volumetric heating of a stem segment (Trunk Heat Balance – THB – method). The model respects the dependence of physical properties on temperature and moisture and also the anisotropic nature of wood. The corresponding partial differential equation is then solved by finite element method.The main aim of this study was to analyze the thermal inertia of the THB method with horizontal references thermocouples. We compared the results of the simpler stationary and the more complex nonstationary model and we can conclude that the thermal inertia of the THB method is not negligible (mainly for smaller flows around 0.01 kg m−2 s−1). In addition, the authors have shown that the influence of moisture on the recorded sap flow data Qrec is negligible but there is small influence on Qfic and hence on the resulting sap flow measurement as was shown in their previous work. We also tested two new variants of temperature sensors arrangement and proved that the difference between them is very small and can be ignored.