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  • The TPS sensor used in the setup had a radius

    2018-10-31

    The TPS sensor used in the setup had a radius of 6.4mm and was placed between two samples (70×70×20mm3) of the material. A constant electric power of 0.02W was conducted through the spiral and the electric resistance was registered and transformed into a temperature increase. The measurements are based on 8 subsequent measurements with 30min break between.
    The transient plane source method Before introducing the measurements and modeling of the TPS method it is good to have knowledge of the measurement technique. The TPS method uses a circular double nickel spiral, 10μm thick, sandwiched between two layers of Kapton (polyimide film), each 25μm thick, in contact with the material sample. The spiral serves both as the heat source and as a resistance thermometer. The sensor is clamped between two samples of the same material and a constant electric power is conducted through the spiral. Heat is developed which raises the temperature and thus the resistance of the spiral. The rate of this temperature increase depends on how quickly the heat developed in the spiral is conducted away through the surrounding material. Heating is continued for a notch signaling of time, with the voltage across the coil being registered. As the power is held constant, the voltage changes in proportion to changes in the resistance of the coil. With knowledge of the voltage variation with time i.e., variation of temperature with time and the heat flow, it is possible to calculate the thermal conductivity and volumetric heat capacity of the material. The mathematical solution used in the TPS method is described by Gustafsson (1991). A number of studies of comparisons between TPS method and steady-state measurement techniques have been described in the literature. Almanza et al. (2004) tested the TPS method on low-density polyethylene foams with different density. The results were compared to steady-state measurements using heat-flow meters. It was found that the results from the TPS method follow the same trends as the steady-state measurements. However, the values obtained with the transient measurements were always 20% higher than the steady-state results. Round robin tests of the steady-state method showed that it has a precision of ±2.5%, while the precision of the TPS method still has to be evaluated. Furthermore, Almanza et al. (2004) discussed the sources of the deviation between steady-state and transient measurements. One of the suggested sources was the initial temperature gap between the heat flow sensor and the surfaces of the sample. By removing the first measurement points from the results, the deviation decreased by 7%. Other possible contributions to the deviation were the stiffness of the sample, differences in the average temperature in the sample and the different size of samples used in the two methods. Almanza et al. (2004) concludes that the TPS method is a powerful tool for comparative studies of thermal properties, but that the interpretation of the absolute values given by the method should be done with care. Analytical solutions or numerical simulations can be used in the evaluation of thermal properties based on the temperature increase in a sensor during transient conditions. Model (2005) proposed a method for determination of the thermal properties of layered materials from the temperature increase from transient measurements based on an analytical solution using Green\'s function. The thermal properties for a given temperature increase and experimental setup was found using the Levenberg–Marquardt method. Model and Hammerschmidt (2000) used numerical models to simulate the influence of different boundary conditions when measuring with transient methods. The models showed good agreement with measurements and an open problem was solved using numerical models. Carbon-filled nylon 6,6 composites were tested with the TPS method and compared to numerical finite-element analysis (Miller et al., 2006). The TPS method was evaluated for 5s with a supplied power of 1W. The sensor was a 3.5mm radius Kapton encapsulated nickel sensor clamped between two samples of 63.5mm diameter composite disks. FEMLAB was used for the numerical evaluation where the heat flux at the interface between the sample and sensor were continuous and all other boundaries were considered adiabatic. Calculations were performed for the first 5s with 0.025s resolution. The first time step was subtracted from the following results which made the results agree very well with the numerical calculations.