One-Dimensional Systemic Modeling of Thermal Sensors Based on Miniature Bead-Type Thermistors

Accurate measurements of thermal properties is a major concern, for both scientists and the industry. The complexity and diversity of current and future demands (biomedical applications, HVAC, smart buildings, climate change adapted cities, etc.) require making the thermal characterization methods used in laboratory more accessible and portable, by miniaturizing, automating, and connecting them. Designing new materials with innovative thermal properties or studying the thermal properties of biological tissues often require the use of miniaturized and non-invasive sensors, capable of accurately measuring the thermal properties of small quantities of materials. In this context, miniature electro-thermal resistive sensors are particularly well suited, in both material science and biomedical instrumentation, both in vitro and in vivo. This paper presents a one-dimensional (1D) electro-thermal systemic modeling of miniature thermistor bead-type sensors. A Godunov-SPICE discretization scheme is introduced, which allows for very efficient modeling of the entire system (control and signal processing circuits, sensors, and materials to be characterized) in a single workspace. The present modeling is applied to the thermal characterization of different biocompatible liquids (glycerol, water, and glycerol-water mixtures) using a miniature bead-type thermistor. The numerical results are in very good agreement with the experimental ones, demonstrating the relevance of the present modeling. A new quasi-absolute thermal characterization method is then reported and discussed. The multi-physics modeling described in this paper could in the future greatly contribute to the development of new portable instrumental approaches.