A new heat balance equation for sap flow calculation during continuous linear heating in tree sapwood

This article introduces a new “linear heat balance (LHB) method” that is based on exact (physically correct) equation analytically derived from fundamental conduction-convection heat transfer equation. Therefore, the aim of this paper is to derive and analyze a new heat balance equation for sap flow calculation from measured temperature differences around continuously heated needle. The formula is derived from the steady-state conduction and convection heat transfer equation with linear source of heat power. This paper deals with the theoretical (analytical and numerical) and experimental analysis of heat and water transfer in the conductive xylem (sapwood) of trees. The analysis and verification of the new formula is based on numerical simulation (using finite element method) and the new LHB method is demonstrated on experimentally measured data. This new approach is important not only because of more exact sap flow calculation but also for information about thermal conductivity that can be used for water content estimation.