Rapid thermal conductivity measurement with a hot disk sensor: Part 1. Theoretical considerations

Abstract

The hot disk technique represents a transient plane source method for rapid thermal conductivity and thermal diffusivity measurement. The main advantages of the hot disk technique include: wide thermal conductivity range, from 0.005 W/(m K) to 500 W/(m K); wide range of materials types, from liquid, gel to solid; easy sample preparation; non-destructive; and more importantly, high accuracy. In this paper, the basic theory of thermal conductivity measurement with hot disk sensor will be discussed. Starting from the instantaneous point source solution, the mathematical expression of the average temperature change in the sensor surface during a hot disk measurement will be derived. This temperature change, which can be accurately determined by measuring the electrical resistance of the sensor, is highly dependent on the thermal transport properties of the surrounding material. By analyzing this temperature change as a function of time, it is possible to deduce the thermal conductivity and the thermal diffusivity of the surrounding material. Several practical considerations, from sample size requirement to the elimination of thermal contact resistance, will also be discussed.