Validation of FE model for transient hot wire thermal conductivity measurements

The paper focuses on an analysis of the FE solution of a 2D model for the transient hot wire method which is a technique for measuring the thermal conductivity of fluids over a wide range of temperatures. Knowledge of the thermal conductivity of fluids and molten materials, especially metals, is of particular interest in the electronics manufacturing industry for the accurate modelling of various processes, such as soldering, casting, welding, etc. (Bilek, et al., 2004). Using the transient hot wire technique, the thermal conductivity can be derived from analytical solutions of the relevant differential heat transfer equations for simple experimental arrangements, where a measured fluid is in direct contact with a sensing device (hot wire). However, for highly electrically conductive fluids, this simple arrangement is impractical. Thus, more complex experimental arrangements have to be employed for which analytical solutions of the heat transfer problem do not exist. In these circumstances it is possible to employ a FE method to describe the experiment which can, in turn, be used to evaluate the desired material property from experimental measurements. In previous projects (Assael, et al., 1997), a simple FE model was designed using a program written in FORTRAN, but this model was found to be inadequate because the geometry of the sensor had to be approximated and the software was rather inflexible to changes in configuration. Therefore a new model has been created using ANSYS software. In order to achieve high accuracy in the measured property it is essential to attain a very close match between experimental observations and the FE model. The difference between values derived from the model and experiment is required to be less than 0.01 K for a total temperature rise of about 7 K. A detailed investigation of the model output and its validation is evidently necessary. The methodology to secure such a closeness of fit is best investigated by comparisons between an analytical solution for a specific case and FE calculations for the same problem. The paper investigates important factors of the modelling stage, such as meshing and time stepping. The analytical solution is discussed in detail, working equations are given, necessary corrections applied, and the results are compared directly with an FE solution. In a subsequent section, experimental results are also compared with both analytical and FE solutions and a procedure for deriving thermal conductivity values is described.