A Model for the Time Response of Solid-embedded Thermocouples

Unlike the transient response of a fluidimmersed thermocouple, and in contrast to common belief, the time response of a solid-embedded thermocouple is far from being similar to that of a first-order process. The current study arises from efforts to characterize the transient response of a solid-embedded thermocouple as a result of a steplike temperature change of the measured domain. Results of this study suggest that the response function of the thermocouple is nearly exponentially dependent on the square root of Fourier number (dimensionless time). It follows that, with respect to fluid temperature measurements, significantly faster time response is expected at the initiation of the process on one hand, and much longer time is required for reaching a steady-state temperature on the other hand. It is shown that the thermal diffusivity of the thermocouple is required to be at least one order of magnitude higher than that of the measured domain in order to obtain meaningful results in transient measurements. KEY WORDS—Thermocouple, time response, mathematical analysis, solid domain