Calibration of non-ideal thermal conductivity sensors

Abstract

A popular method for measuring the thermal conductivity of solid materials is the transient hot needle method. It allows the thermal conductivity of a solid or granular material to be evaluated simply by combining a temperature measurement with a well-defined electrical current flowing through a resistance wire enclosed in a long and thin needle. Standard laboratory sensors that are typically used in laboratory work consist of very thin steel needles with a large length-to-diameter ratio. This type of needle is convenient since it is mathematically easy to derive the thermal conductivity of a soft granular material from a simple temperature measurement. However, such a geometry often results in a mechanically weak sensor, which can bend or fail when inserted into a material that is harder than expected. For deploying such a sensor on a planetary surface, with often unknown soil properties, it is necessary to construct more rugged sensors. These requirements can lead to a design which differs substantially from the ideal geometry, and additional care must be taken in the calibration and data analysis. In this paper we present the performance of a prototype thermal conductivity sensor designed for planetary missions. The thermal conductivity of a suite of solid and granular materials was measured both by a standard needle sensor and by several customized sensors with non-ideal geometry. We thus obtained a calibration curve for the non-ideal sensors. The theory describing the temperature response of a sensor with such unfavorable length-to-diameter ratio is complicated and highly nonlinear. However, our measurements reveal that over a wide range of thermal conductivities there is an almost linear relationship between the result obtained by the standard sensor and the result derived from the customized, non-ideal sensors. This allows for the measurement of thermal conductivity values for harder soils, which are not easily accessible when using standard needle sensors.