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Development of a mathematical model and its numerical solution to estimate sap flow applying a transient heating system

Fernandes de Sousa, E., Santolin, M.A., Vandegehuchte, M.W., Compostrini, E., de Jesus Soares, K.
Acta horticulturae 2013 no.991 pp. 37-44
cooling, heat, mathematical models, sap flow, sapwood, sawdust, temperature, thermal properties
In this work, a general mathematical model to describe the temperature variation in sapwood during application of a linear and cyclic heating system is proposed. The input parameters of the model are the geometry of the sensor (length and diameter), the thermal properties of the sapwood surrounding the heater, and the period of heating and cooling of the heat source. The model was solved using the Gauss quadrature method and the Newton-Raphson method. This model was then validated in a hydraulic column filled with sawdust, testing three different sensor compositions. In static conditions of flow, the mathematical model was used to determine the thermal properties of the medium in the hydraulic column. The results indicate a satisfactory agreement between the measured flux density values and those estimated by the model. There was no marked difference in performance between the three sensor compositions.