Estimating Surface Temperature of a Calibration Apparatus for Contact Surface Thermometers from Its Internal Temperature Profile

Abstract

A calibration apparatus for contact surface thermometers was developed. Temperature of the upper surface of a copper cube of the calibration apparatus was used as reference surface temperature, which was estimated at around $$50\,{^{\circ }}\hbox {C}$$ , $$100\,{^{\circ }}\hbox {C}$$ , and $$150\,{^{\circ }}\hbox {C}$$ by not only two conventional industrial platinum resistance thermometers (IPRTs) but also five small-sized platinum resistance thermometers (SSPRTs) calibrated based on the International Temperature Scale of 1990 (ITS-90). These thermometers were inserted horizontally into the copper cube and aligned along the center axis of the copper cube. In the case of a no-load state without anything on the upper surface, the temperature profile inside the copper cube linearly decreased from the lower part to the upper surface, which suggests that the heat conduction inside the copper cube can be regarded as a one-dimensional steady state. On the other hand, in the case of a transient state just after the contact surface thermometer was applied to the upper surface, the temperature profile became a round shape. We obtained good agreement between the curvature of the temperature profiles and the results estimated by using an error function used for a one-dimensional transient heat conduction problem. The temperature difference between the estimated temperature by linear extrapolation using two IPRTs and that by extrapolation using the error function was within $$0.2\,{^{\circ }}\hbox {C}$$ in the transient state at around $$150\,{^{\circ }}\hbox {C}$$ . Over 10 min after the contact surface thermometer was applied, the temperature profile showed a linear shape again, which indicated that linear extrapolation using two IPRTs was well for the estimation of the reference surface temperature because the heat conduction state inside the copper cube came back to the one-dimensional steady state. Difference between the surface temperature and temperature detected by the contact surface thermometer was also observed after the contact surface thermometer touched on the upper surface. The difference was over $$0.1\,{^{\circ }}\hbox {C}$$ at several minutes after the contact surface thermometer touching on the reference surface and was suppressed with passing time in the transient state and became negligible over 10 min.