A model of heat transfer in sapwood and implications for sap flux density measurements using thermal dissipation probes

A variety of thermal approaches are used to estimate sap flux density in stems of woody plants. Models have proved valuable tools for interpreting the behavior of heat pulse, heat balance and heat field deformation techniques, but have seldom been used to describe heat transfer dynamics for the heat dissipation method. Therefore, to better understand the behavior of heat dissipation probes, a model was developed that takes into account the thermal properties of wood, the physical dimensions and thermal characteristics of the probes, and the conductive and convective heat transfer that occurs due to water flow in the sapwood. Probes were simulated as aluminum tubes 20 mm in length and 2 mm in diameter, whereas sapwood, heartwood and bark each had a density and water fraction that determined their thermal properties. Base simulations assumed a constant sap flux density with sapwood depth and no wounding or physical disruption of xylem beyond the 2 mm diameter hole drilled for probe installation. Simulations across a range of sap flux densities showed that the dimensionless quantity k [defined as (Delta Tm - Delta T)/Delta T, where Delta T-m is the temperature differential (Delta T) between the heated and unheated probe under zero-flow conditions] was dependent on the thermal conductivity of the sapwood. The relationship between sap flux density and k was also sensitive to radial gradients in sap flux density and to xylem disruption near the probe. Monte Carlo analysis in which 1000 simulations were conducted while simultaneously varying thermal conductivity and wound diameter revealed that sap flux density and k showed considerable departure from the original calibration equation used with this technique. The departure was greatest for variation in sap flux density typical of ring-porous species. Depending on the specific combination of thermal conductivity and wound diameter, use of the original calibration equation resulted in an 81% under- to 48% overestimation of sap flux density at modest flux rates. Future studies should verify these simulations and assess their utility in estimating sap flux density for this widely used technique.