Determining thermal properties via parameter estimation of a one-dimensional, analytical model

“In thermal applications, thermal conductivity is used to predict how well a material conducts heat. The accuracy of the magnitude of the thermal conductivity becomes increasingly essential to optimize part geometry. Thermal conductivity can vary significantly from the nominal value due to post-processing. The ASTM standards available to measure thermal conductivity are challenging to reproduce because of the insulated and prescribed temperature boundary conditions that are needed. The research introduces two new methods for estimating thermal conductivity that deliver the same accuracy as the existing ASTM standards and are easier to implement. The methods account for losses in the heating to enable a better estimation of thermal conductivity. This research is directly applicable to estimating the thermal conductivity of additively manufactured materials. Additive manufacturing (AM) is being increasingly used for thermal applications; However, additive manufacturing can significantly affect thermal conductivity”--Abstract, page iv

Data on the Validation to Determine the Material Thermal Properties Estimation Via a One-Dimensional Transient Convection Model

These data were acquired to estimate the parameters of a closed form solution of a one-dimensional transient convection heat diffusion PDE. The purpose was to demonstrate that the model could be used to determine the thermal conductivity. The system was tested for a wide range of thermal conductivity, 15-400 W/mK, in order to verify that the method was applicable for various materials. The data reported here refer to the study in the research articles, Material Thermal Properties Estimation Via a One-Dimensional Transient Convection Model [1] and Influence of porosity on the thermal, electrical, and mechanical performance of selective laser melted stainless steel [2]. The dataset contains the raw data obtained from the temperature acquisition system as well as the processed results from a Python program to determine the thermal conductivity from a forced convection, transient one-dimensional heat diffusion equation

Data on the Validation to Determine the Material Thermal Properties Estimation via a One-Dimensional Transient Convection Model

These data were acquired to estimate the parameters of a closed form solution of a one-dimensional transient convection heat diffusion PDE. The purpose was to demonstrate that the model could be used to determine the thermal conductivity. The system was tested for a wide range of thermal conductivity, 15-400 W/mK, in order to verify that the method was applicable for various materials. The data reported here refer to the study in the research articles, “Material Thermal Properties Estimation Via a One-Dimensional Transient Convection Model” and “Influence of porosity on the thermal, electrical, and mechanical performance of selective laser melted stainless steel”. The dataset contains the raw data obtained from the temperature acquisition system as well as the processed results from a Python program to determine the thermal conductivity from a forced convection, transient one-dimensional heat diffusion equation

Material Thermal Properties Estimation Via a One-Dimensional Transient Convection Model

This study investigates an approach to determine the thermal conductivity of a material from transient temperature data. For this study, a one-dimensional transient convection heat diffusion PDE with a closed-form solution is used to model slender test coupons. The inhomogeneous boundary condition is handled using eigenfunction expansion and Green\u27s second identity. A modified Levenberg-Marquardt (LM) nonlinear least squares (NLS) algorithm is used to determine the thermal conductivity from the experimental data using a flux boundary condition. The boundary conditions require an open-loop heater control and forced convection along the rod, which is simpler to implement than current methods. The estimated thermal conductivity from the experimental data was within ten percent of the nominal published values of the materials tested. The method described here promises to be easier to implement than current standards with similar accuracy and is applicable over a wide range of thermal conductivities -ranging from 15 to 400 W/mK. The method utilizes a small amount of material and a simple geometry, and is therefore suitable for the thermal characterization of additively-manufactured materials on a batch-by-batch basis

Thermal Conductivity Estimation Via a Multi-Point Harmonic One-Dimensional Convection Model

The estimation of thermal conductivity (k) by Ångström\u27s method is well known and a popular alternative to the existing ASTM standards because it allows for an easier setup due to the model\u27s simpler boundary conditions. The shortcomings of this approach are that only two temperature locations are used, making it highly sensitive to temperature sensor placement. Moreover, the approach uses only the first term in the Fourier series of the solution causing inaccuracies in the model. An alternative multi-point model presented in this study corrects both of these problems. The study uses the new multi-point method to estimate k and compares the accuracy to the Ångström\u27s method. The benefit of Ångström\u27s method and other existing steady state harmonic methods is that they manipulate the solution so that k decouples from the unknown heat transfer coefficient (h). The multi-point model uses parameter estimation to estimate both h and k simultaneously. In this study, the accuracy of the k estimation was examined for three materials with a k range of 15-400 W/mK at three different oscillation periods: 50, 100, and 200 s. The results show that the proposed new method is more robust than the previous methods, with the same order of accuracy as existing ASTM standards

Thermal Conductivity Estimation Via a Multi-Point Harmonic One-Dimensional Convection Model

The estimation of thermal conductivity (k) by Ångström\u27s method is well known and a popular alternative to the existing ASTM standards because it allows for an easier setup due to the model\u27s simpler boundary conditions. The shortcomings of this approach are that only two temperature locations are used, making it highly sensitive to temperature sensor placement. Moreover, the approach uses only the first term in the Fourier series of the solution causing inaccuracies in the model. An alternative multi-point model presented in this study corrects both of these problems. The study uses the new multi-point method to estimate k and compares the accuracy to the Ångström\u27s method. The benefit of Ångström\u27s method and other existing steady state harmonic methods is that they manipulate the solution so that k decouples from the unknown heat transfer coefficient (h). The multi-point model uses parameter estimation to estimate both h and k simultaneously. In this study, the accuracy of the k estimation was examined for three materials with a k range of 15–400 W/mK at three different oscillation periods: 50, 100, and 200 s. The results show that the proposed new method is more robust than the previous methods, with the same order of accuracy as existing ASTM standards

Influence of Porosity on the Thermal, Electrical, and Mechanical Performance of Selective Laser Melted Stainless Steel

This study verifies a novel approach to determine the thermal conductivity developed by the first two authors (Tomanek and Stutts) [1] as applied to additively manufactured selective laser melted stainless steel 304L specimens having a range of 1.4 to seven percent porosity. The selective laser melting technique is highly dependent on the process parameters used, unlike traditionally manufactured materials, and can cause the thermal, electrical, and mechanical properties to vary considerably from the bulk alloy. For this study, the thermal conductivity and several auxiliary parameters were estimated using a Levenberg-Marquardt nonlinear least squares algorithm. The parameter estimation used a model of a one-dimensional transient heat diffusion PDE with a closed-form solution of a slender rod under forced convection. In addition to the thermal conductivity\u27s dependency on porosity, the correlated porosity dependency on electrical conductivity was examined. The results were corroborated by mechanical tensile tests as well. The stainless steel 304L selective laser melted specimens saw a degradation of mechanical, thermal, and electrical performance with increasing porosity