Comparison of the new plane source method to the step wise transient method for thermal conductivity and diffusivity measurement

Abstract

This paper describes a new method for measuring both the thermal conductivity and thermal diffusivity for solid materials, referred to as the new plane source (NPS) method. This method is quite similar to the Extended dynamic plane source (EDPS) method; however, the essential difference is the location of the temperature measurement. The NPS measures the temperature of the specimen at both the heat source and also at the heat sink using a thermocouple. The accuracy of the NPS method was verified by comparing the measurement results with the step-wise transient (SWT) method for two solid materials: silica glass and polymethylmethacrylate (PMMA). The difference in results between the NPS method and the SWT method was found to be 0.6%. The results of conductivity measurements by the NPS method of glass and PMMA were 1.019 and 0.1904 W·K⁻¹ m⁻¹, respectively. As for the measured thermal diffusivities, they were 0.504 and 0.1136 mm² s⁻¹, respectively. The standard uncertainties of the estimates were less than 0.9%.

Introduction

Knowledge of thermal properties and specifically the thermal conductivity and diffusivity is vital for a broad range of applications, including but not limited to injection molding, power electronics thermal management systems, insulation materials for buildings, and design of heat transfer devices. At present, numerous experimental techniques are available for measuring the transport properties, which fall under two categories: transient and steady-state. Guarded hot plate and radial heat flow meter are the most popular devices of the steady-state group. Several transient methods are commercially available, such as transient plane source (TPS) [1,2] transient hot wire (THW) [3], transient hot strip [4], laser flash [5], and the step-wise transient method (SWT) [6]. Each of the mentioned methods above operates for a specific range of materials and temperatures with certain accuracy. For instance, the THW technique introduced by Assael [7] was developed for the absolute, accurate measurements of the thermal conductivity of solids. The uncertainty of the measurement results was assessed to be less than 1%. The dynamic plane source (DPS) method and other transient techniques can be found in Refs. [[8], [9], [10]]. The reader can refer to a literature review paper for more details about each technique [11].

Among these techniques, transient methods, such as TPS, DPS, and the SWT, have recently gained much attention due to their capability to measure both thermal properties simultaneously from a single experiment. The theory of the SWT method depends on subjecting the sample surface to a known input heat flux, having a step-wise form, and measuring the temperature response at a different plane away from the surface by a specific distance. Fitting the SWT theoretical model to the temperature response permits the determination of all the thermal properties, including the heat capacity.

The dynamic plane source (DPS) method is developed for the simultaneous determination of thermal conductivity and diffusivity of metals. The heat source, in the form of a thin disc, is placed between two identical specimens, which rear sides are pressed against two heat-insulating materials [8]. The heat source also serves as the thermometer. The heat is produced by an electrical current having a form of step-wise function. The specimen's thermal properties are determined by fitting the temperature function to the measured temperature response. The theoretical temperature function is the solution of the 1D-heat conduction equation exposed to the imposed boundary conditions of the experiment.

The extended dynamic plane source (EDPS) method is a modification of the DPS method for characterizing the thermal properties of low conductive materials. The modification depends on replacing the isolating material with a well heat-conducting material (heat sink). Hence the temperature approaches the steady-state conditions after some time. This method has an accuracy of 5%, according to Ref. [12].

The EDPS method suffers from several sources of errors, namely: the surface effect, the source effect, and the heat sink effect. The surface effect is caused by the heat losses from the lateral sides of the specimen. The remedy for this issue is to increase the specimen diameter and measure the temperature of the heat source at its center by a thermocouple. The source effect is caused by neglecting the thermal capacity of the heat source in the EDPS model. The error introduced by this effect can be mitigated by estimating thermal capacity from the heater's dimensions and material properties and incorporating it into the theoretical model. The last problem is the heat sink effect, which should be, according to the theoretical model, infinitely long. As it can hardly be fulfilled, this effect can result in an unpredictable error.

Jannot et al. [13] developed a transient method employing the conventional hot plate device to simultaneously measure the thermal conductivity and thermal diffusivity from a single experiment. This was achieved by introducing two thermocouples: one located at the front face, which is in contact with the heater, and the other at the rear face, which is in contact with Polystyrene insulation material. The 1D-quadrupolar model was used to predict both surfaces’ temperatures. This method was validated for high conductive metals [13] via comparison with the DSC and the hot disk. The results showed a large deviation compared to the hot disk, which reached up to 10% for the thermal conductivity and 6% for the thermal diffusivity. The same technique was also investigated for low conductive building materials using only one thermocouple at the hot front surface compared to simultaneous measurements at both surfaces using two thermocouples [14]. The viability of the method was examined by comparing the thermal capacity results with the DSC. It was observed that the two temperatures approach improved the accuracy of the thermal capacity measurement by decreasing the deviation with the DSC from 10% to 2%. No validation was carried out for the thermal conductivity and the thermal diffusivity.

The aim of this work is to design a new method for measuring the thermal conductivity and diffusivity of low conductive solid materials, denominated as the “new plane source (NPS) method” and compare it with the SWT method for silicate glass and polymethylmethacrylate (PMMA). The structure of the current paper starts with a summary of the theoretical model of the SWT method, along with a review of its previous model modification suggested in the literature, to provide a context for the current work. This is followed by a description of the proposed technique and its theoretical background. Finally, the method is validated experimentally by comparing its results with the SWT method.