Thermocouple Effective Length under Sinusoidal Gas Temperature Condition

When a thermocouple is used to measure gas temperature, the measured temperature is the thermocouple bead temperature, which is not equal to the gas temperature. The bead temperature results from its energy balance. Through the wire convection and conduction, the temperature of the bead is related to the gas temperature within a certain geometric range around it, and this range is quantified by the effective length. Under the sinusoidal incoming gas temperature condition, the analytical expression for the effective length is deduced, and its accuracy is validated by the one-dimensional numerical solution. The differences between the analytical and numerical effective lengths are less than 10.5% for the test cases. Similar to that under the uniform incoming gas temperature condition, the effective length under the sinusoidal gas temperature condition increases with the thermal conductivity and the diameter of the wire and decreases with the heat transfer coefficient of the wire. The influence of the amplitude, wavelength and phase of the gas temperature on the effective length are very weak, meaning that the theoretical expression under the uniform gas temperature can calculate the effective length under the non-uniform gas temperature with good accuracy.