Analysis of heat flow in modified transient plane source (MTPS) measurements of the thermal effusivity and thermal conductivity of materials

Abstract

An iterative algorithm for the diffusion of heat in layered structures is solved in cylindrical coordinates for the geometry used in measurements of thermophysical properties of materials by the modified transient plane source (MTPS) method. This solution for the frequency-domain temperature response is then used to model the transient temperature excursion and evaluate the accuracy of the measurements. We evaluate when the MTPS method is capable of separately determining the thermal conductivity and heat capacity per unit volume of a material. For a typical sensor design, data acquisition, and data analysis, the MTPS measurement has a small sensitivity to the thermal diffusivity of the sample when the thermal diffusivity is <5 mm2 s−1. We analyze the propagation of errors from uncertainties in the thermal contact between the sensor and the sample and evaluate the limitations of the MTPS method in accurately measuring samples with extremely low thermal effusivity, e.g., low density foam insulation. We find that uncertainties in the thickness of the contact region limit the accuracy of MTPS measurements when the data are analyzed in a conventional manner based on a single parameter, m−1, the inverse of the slope of the temperature excursion as a function of the square root of time.