Solutions for the correction of temperature measurements based on beaded thermocouples

Thermocouples are a practical and potentially accurate means for determining surface temperatures in many applications. Yet, significant errors can often arise during the usage of beaded thermocouples because of the effects of junction displacement, contact resistance, and stray heat transfer to the surrounding environment. To help offset these potentially significant sources of errors, Duhamelʹs integral in Laplace form was first used to relate the response of a surface thermocouple to the true substrate temperature. Once formulated, both exact and approximate Laplace inversion methods were used to derive closed-form corrective solutions. The resulting thermocouple correction curves show good agreement between themselves and existing analytical expressions and indicate the potentially deleterious effects of junction displacement, contact resistance, and the stray heat transfer to the surrounding environment.