Abstract
Speed of sap flow in plants and trees is of interest to botanists and environmentalists because of its connection with the rate of utilisation of nutrients in the soil. An established method uses the transport of heat where an impulsive heat source is introduced along a radial line by a probe in the trunk sapwood. The temperature is monitored, upstream and downstream, and, by solving the heat flow equation in the moving fluid, the sap velocity may be deduced indirectly under some simplifying assumptions which chiefly render the method most useful when applied to trees of relatively large diameter. Transform methods are used to obtain the appropriate threedimensional time-dependent solution in explicit form and values for the resulting sap velocity are compared with the existing two-dimensional theory.
Highlights
Botanists and others concerned with forest management are interested in knowing the speed at which sap rises in trees, since it is directly related to the rate at which nutrients in the soil can be utilised
Various methods of finding the sap speed are needed in practice including introduction of dyes, for example, but a common -applicable one in the field employs a probe which can introduce an impulsive heat source at time t = 0 into the sapwood of the trunk and monitor the temperature 1 cm or so above and below its location
It is of interest to determine whether results for the estimation of the sap velocity
Summary
Botanists and others concerned with forest management are interested in knowing the speed at which sap rises in trees, since it is directly related to the rate at which nutrients in the soil can be utilised. Information about the speed of flow, u, of sap in the tree trunk (see Edwards, et al (1996) for a proposed standard nomenclature) can be deduced. Various assumptions have been made in the modelling process in order to simplify the mathematical solution of the problem and thereby render the determination of u as straightforward as possible. In that work a solution for the temperature is used in which it is assumed that the heat source is an instantaneous line source along the whole z-axis directed normally to the trunk surface, which is itself assumed to be the xy plane in this approximation. _In order to take some account of variations, including heat flow, in the z direction, we here assume the thickness L of the xylem is finite with an instantaneous line source placed along the z-axis in 0 < z
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