Simultaneous Estimation of Principal Thermal Conductivities of an Anisotropic Composite Medium: An Inverse Analysis

Abstract

This paper reports the results of an experimental study to determine the principal thermal conductivities (kx,ky, and kz) of an anisotropic composite medium using an inverse heat transfer analysis. The direct problem consists of solving the three dimensional heat conduction equation in an orthotropic composite medium with the finite difference method to generate the required temperature distribution for known thermal conductivities. The measurement technique involves dissipating a known heat flux at the central region of a square sample and allowing it to conductively transfer the heat to an aluminium cold plate sink via a square copper ring. At steady state, temperatures at 28 (19 are used for retrievals due to symmetry) discrete locations are logged and used for parameter estimation. The entire measurement process is conducted in a vacuum environment. The inverse heat conduction problem (IHCP) for retrieving the orthotropic thermal conductivity tensor(parameter estimation) is then solved using a two layer feed forward back propagation artificial neural network (ANN) trained using the Levenberg–Marquardt algorithm (LMA), with temperatures as input and thermal conductivity values kx,ky, and kz as the output. The method is first validated against a stainless steel(SS-304) sample of known thermal properties followed by the determination of the orthotropic conductivities of the honeycomb composite material.

An inverse approach to characterize anisotropic thermal conductivities of a dry fibrous preform composite

“…Improvements in the model may be made to capture the fiber contact between adjacent layers through-the-thickness of the preform and the bridging effect due to the stitching threads for predicting preform thermal conductivity under different compaction conditions. In principle, anisotropic preform thermal conductivities may be estimated from the preheating test by solving an inverse heat transfer problem using approaches similar to those of Tian and Cole 21 and Chanda et al 6 However, obtaining in-plane thermal conductivities can be challenging in the VARTM setup due to the insignificant heat flow in the in-plane directions. Furthermore, compared with the integrated heater/sensor in the hot disk apparatus, the utilization of TCs and heaters in the VARTM setup creates twice as many contact issues, which makes it unrealistic to characterize the anisotropic preform thermal conductivities using the VARTM setup.…”

“…Most recently, simultaneous estimation of three-dimensional principal thermal conductivities of an orthotropic honeycomb composite material was performed by solving an inverse heat transfer problem using experimentally determined temperature fields as input. 6 However, poor contact between test samples and measuring sensors still remains a challenge using any of the above techniques for the determination of thermal conductivities of fibrous preforms. To combat the abovementioned issues, an inverse approach is introduced in this article to estimate the anisotropic thermal conductivities of porous glass-fiber mats based on the thermal conductivity measurements of cured glass-fiber/ epoxy composites.…”

A novel inverse method for identification of 3D thermal conductivity coefficients of anisotropic media by the boundary element analysis

“…They considered two cylindrical samples and a thin heater sandwiched between the samples in their measurement technique. For determining the orthotropic conductivities of a honeycomb composite material, Chanda et al [8] presented a method based on the finite difference method in conjunction with a two layer feed forward back propagation artificial neural network.…”

Simultaneous and direct identification of thermophysical properties for orthotropic materials

“…The consideration of new boundary conditions, with the aim of a best the environmental conditions control of the experiments, combined with the increase in the calculation capacity, brings new estimation methods based on numerical simulations. Several methods that solve the 3D heat conduction problem using the finite difference or finite volume techniques [11], [12] the finite element method [13]- [15] the boundary element method [16], [17] and the singular boundary method [18], have proven to be highly time consuming.…”

“…One should notice that some works are purely theoretical, others are based on experiments that rely on intrusive measurements (e.g. thermocouples) [8], and/or intrusive heating source [11]- [13], [27]. Also, the experimental protocol may be sophisticated, where some authors have developed methods based on two experiments (e.g.…”