Obtaining the Sensed Temperatures From a Detailed Model of a Welded Thermocouple

When imbedded in dissimilar materials subject to large temperature gradients, thermocouples are known to yield erroneous (bias) temperature measurements. It has been established that the bias error may be accounted for with an appropriate computational model and the measured temperatures may be corrected with an appropriate kernel function. In this work, a thermocouple with a welded bead is considered. Early two-dimensional models considered the thermocouple to be a single wire with effective thermal properties. The model in the current investigation is three-dimensional and represents the sensor as two wires, each with unique thermal properties. The welded bead is represented as a separate entity with properties distinct from those of the wires. The problem of determining what location in the three-dimensional model corresponds to the measured temperature is considered. Earlier models have considered the sensed temperature to be the temperature at the tip of the two-dimensional thermocouple or, in three-dimensional models, the temperature at the center of the volume of the welded bead. In the current work, a theory is set forth for identifying the location at which the temperature is sensed by a thermocouple. This theory is in line with traditional thermoelectric theory and is supported with experimental evaluation with thermal imaging as well as examination of thermocouples by scanning electron microscopy and energy dispersive X-ray analysis. The significance of accurate modeling of the sensed temperatures is demonstrated with a numerical experiment.