Error in Temperature Measurements Due to Conduction Along the Sensor Leads

Abstract

When a sensor is embedded in a solid body to measure its internal temperature, any conduction to, or from, its sensing element may cause the indicated temperature to be different from the true temperature. This paper describes an analysis of the error caused by conduction when there is an arbitrary temperature distribution in thebbody along the sensor. The sensor is modeled as a cylindrical fin and the appropriate conduction equation is solved. The solution gives a correction for the error which depends on such parameters as, depth of immersion, thermocouple wire and insulation properties, contact between the sensor and the body, and temperature distribution in the body. The latter may not be known, but the measured temperature distribution can be used as a first approximation. The corrected value can then be used to obtain a better estimate of the error. The results show good agreement with experimental observations.

Effects of thermocouple electrical insulation on the measurement of surface temperature

“…Generally, we can conclude from these results that the effect of the stripped insulation of any length on the temperature measurement is negligible or, more accurately the experimental error for a typical system is higher than the effect of the stripped insulation [6], see Figure 2(ab). Besides, the temperature difference between the environment and the working range of the peltier surface 4 o C-35 o C is not high enough to have a strong effect on the temperature measurement, see Figure 13.…”

“…Fin analysis considers heat transfer by conduction occurring along the thermocouple wire due to its high thermal conductivity in comparison with the surrounding insulation, as such it assumes that there is no radial temperature gradient across the metal wire [6], see Table 1.…”

“…Equivalent thermal conductivity for a single wire model is calculated from [6,23] k weq = k w1 +k w2 2 (3) k w1 and k w2 are given in Table 1.…”

“…Therefore, they recommended placing the wires at the same isothermal surface of the junction for several diameters to minimize the error. Singh and Dybbs [6] measured temperature variation inside the body by inserting thermocouples at different depths parallel as well as normal to temperature variation through the body. They advised that the thermocouple wires and the junction should be at the same isothermal plane in order to reduce error.…”

Recommendations and guidelines for the performance of accurate heat transfer measurements in rapid forming processes

“…Singh et al [46] have given a more detailed solution including the end-effects, which reduces to Eq. (10) when endeffects are insignificant.…”