Simultaneous estimation of in- and out-of-plane thermal conductivities of composite materials using a contact-heating technique: an optimum experimental set-up design

The optimum set-up of a two-dimensional (2D), transient, three-layer, heat conduction experiment aimed at simultaneously estimating the thermal properties of composite materials is designed. The experimental apparatus is based on the plane-source method consisting of a thin electrical heater in contact with two larger samples of the same material and thickness. Due to the thermal symmetry of the apparatus and neglecting the thermal heater inertia and related contact resistance with the sample, the three-layer composite conduction problem is modeled through only one orthotropic rectangular plate (sample) whose thermal properties are assumed temperature-independent. This plate is partially heated for a finite period at the front boundary through a surface heat flux (due to the thin heater), whereas its opposite boundary is subject to heat losses with the environment simulated by a heat transfer coefficient (the remaining boundaries are kept insulated). This coefficient accounts only for free convection when the unheated back side of the sample is exposed to the surrounding air and, hence, its temperature is measured using an infrared camera or a pyrometer. However, if thermocouples are used on the back side of the sample, it is a common practice to thermally insulate it to reduce the air disturbance on the thermal measurements. In this case, the above coefficient accounts for both the insulating material and free convection with the air. The exact analytical temperature solution of the addressed heat conduction problem is obtained using a generalized solution available in the specialized literature. The superposition principle is also applied to account for a finite heating period. Then, the scaled sensitivity coefficients of temperature with respect to the parameters of interest (in- and out-of-plane thermal conductivities, volumetric heat capacity, and the heat transfer coefficient with the surrounding ambient) are computed on the back side of the specimen, and a sensitivity analysis is performed to establish whether correlation between them exists at different locations. Finally, the optimum experiment is designed by applying one of the D-optimum criteria, known as Δ+ criterion. Its application leads to the optimum heating and experiment times, the optimum sample aspect ratio, and the optimum width of the heated region.