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Implementation of an Experimental Setup Based on the Three-Omega Method for Thermal Conductivity Measurements of Molten Salts

Molten salt reactors (MSRs) are one of the most promising next-generation nuclear reactor designs which use molten salts as the fuel and coolant. To design, model, predict, license, and operate MSRs, the behavior of the fuel and coolant must be understood as a function of temperature and irradiation, i.e., burnup. Of particular importance and complexity is the reliable and reproducible measurement of thermal conductivity of molten salts at high temperatures (> 500 °C). Thermal conductivity provides information on the rate at which heat passes through a specified material and is dependent on chemical composition. Currently, in the national laboratory complex, several methods for measuring thermal conductivity on molten salt systems are under development, however, to date, consistent data have not been produced. Typically, thermal conductivity measurements of high-temperature melts have been conducted by using the Transient Hot Wire (THW) method where thermal conductivity is determined by the change in temperature over time at a certain distance from a heating wire. Another time-dependent technique is the laser flash method, commonly used for solid samples. Laser flash requires prior measurements of density and heat capacity to calculate the thermal conductivity of the sample, introducing additional measurement errors. Steady state and time-dependent measurements such as THW and laser flash have errors from convection and ambient temperature fluctuations (heat radiation). In order to produce high fidelity thermal conductivity data, a measurement technique needs to be developed that will reduce the effect of convection at high temperatures by measuring in a very fast time window. In addition, to measure on actinide and irradiated salts the sample size should be small. Therefore, this project aims to develop a frequency-domain technique based on the three-omega (3?) method, previously proven to work on solids, nanofluids and low temperature solar salts (25 to 250 °C). If the 3?-device can be designed with materials that can withstand high temperatures (>500 °C) and can be configured to reduce errors due to convection, then it would prove to be a valuable technique for ensuring thermal conductivity on molten salt systems needed for MSR development. For this proposal, the 3? instrument will be designed, assembled, and tested on non-radioactive salts before being used on actinide bearing salts. In addition, a thermal model will be developed to determine the thermal conductivity of the sample from the measured thermal oscillation of the sensor. Because 3? is a direct method that requires a small volume of sample and works in a very fast time window, it will aid in suppressing the interference due to convection which is ideal when working with high temperature liquid samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Three-omega thermal-conductivity measurements with curved heater geometries

The three-omega method, a powerful technique to measure the thermal conductivity of nanometer-thick films and the interfaces between them, has historically employed straight conductive wires to act as both heaters and thermometers. When investigating stochastically prepared samples such as two-dimensional materials and nanomembranes, residue and excess material can make it difficult to fit the required millimeter-long straight wire on the sample surface. There are currently no available criteria for how diverting three-omega heater wires around obstacles affects the validity of the thermal measurement. In this Letter, we quantify the effect of the wire curvature by performing three-omega experiments with a wide range of frequencies using both curved and straight heater geometries on SiO 2 /Si samples. When the heating wire is curved, we find that the measured Si substrate thermal conductivity changes by only 0.2%. Similarly, we find that wire curvature has no significant effect on the determination of the thermal resistance of an ~65 nm SiO 2 layer, even for the sharpest corners considered here, for which the largest measured ratio of the thermal penetration depth of the applied thermal wave to radius of curvature of the heating wire is 4.3. This result provides useful design criteria for three-omega experiments by setting a lower bound for the maximum ratio of the thermal penetration depth to wire radius of curvature.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

A simple numerical method for evaluating heat dissipation from curved wires with periodic applied heating

In many situations, the dual-purpose heater/thermometer wires used in the three-omega method – one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces – must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that in some cases curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calculate the temperature of three-omega heating wires with arbitrary wire geometries. Furthermore, this method provides experimentalists with a simple quantitative procedure for calculating how large the systematic error caused by a particular wire asymmetry will be. We show calculations of two useful cases: a straight wire with a single bend of arbitrary angle and a wire that forms a circle. We find that the amplitude of the in-phase temperature oscillations near a wire that forms a circle differs from the prediction using the analytic straight-line source solution by <12%, provided that the thermal penetration depth is less than ten times the radius of curvature of the wire path. The in-phase temperature amplitude 1.5 wire widths away from a 90° bend in a wire is within 11% of the straight-line source prediction for all penetration depths greater than the wire width. Our calculations indicate that the straight-line source solution breaks down significantly when the wire bend angle is less than 45°.

77 NANOSCIENCE AND NANOTECHNOLOGY↗