Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6301, USA.
Tree Physiol. 2011 Jun;31(6):669-79. doi: 10.1093/treephys/tpr051. Epub 2011 Jul 8.
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 (ΔT(m) -ΔT)/ΔT, where ΔT(m) is the temperature differential (ΔT) 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.
多种热方法被用于估计木本植物茎干的液流密度。模型已被证明是解释热脉冲、热平衡和热场变形技术行为的有价值的工具，但很少用于描述散热技术的热传递动力学。因此，为了更好地理解散热探针的行为，开发了一个模型，该模型考虑了木材的热特性、探针的物理尺寸和热特性，以及由于木质部中的水流而发生的传导和对流热传递。探针被模拟为长 20 毫米、直径 2 毫米的铝管，而边材、心材和树皮各自具有密度和水分分数，决定了它们的热特性。基础模拟假设边材深度的液流密度恒定，并且在用于探针安装的 2 毫米直径孔之外，木质部没有受伤或物理破坏。在一系列液流密度下的模拟表明，无量纲量 k[定义为(ΔT(m)-ΔT)/ΔT，其中 ΔT(m)是零流量条件下加热和未加热探针之间的温度差(ΔT)]取决于边材的热导率。液流密度与 k 之间的关系也对液流密度的径向梯度和探针附近的木质部破坏敏感。在同时改变热导率和伤口直径的情况下进行了 1000 次模拟的蒙特卡罗分析表明，液流密度和 k 与该技术最初使用的校准方程有很大的偏离。对于典型的环孔物种的液流密度变化，偏离最大。取决于热导率和伤口直径的具体组合，使用原始校准方程会导致在适度通量率下液流密度的低估 81%至高估 48%。未来的研究应该验证这些模拟，并评估它们在估计这种广泛使用的技术的液流密度方面的实用性。
