Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design

The efficiency and precision of parameter calibration in discrete element method （DEM） are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity （ETC） of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design （CCD） is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.

Discrete element method for high-temperature spread in compacted powder systems

The discrete element method is applied to investigate high-temperature spread in compacted metallic particle systems formed by high-velocity compaction. Assuming that heat transfer only occurs at contact zone between particles, a discrete equation based on continuum mechanics is proposed to investigate the heat flux. Heat generated internally by friction between moving particles is determined by kinetic equations. For the proposed model, numerical results are obtained by a particle-flow-code-based program. Temperature profiles are determined at different locations and times. At a fixed location, the increase in temperature shows a logarithmic relationship with time. Investigation of three different systems indicates that the geometric distribution of the particulate material is one of the main influencing factors for the heat conduction process. Higher temperature is generated for denser packing, and vice versa. For smaller uniform particles, heat transfers more rapidly.

Microstructure and Thermal Conductivity of As-Cast and As-Solutionized Mg–Rare Earth Binary Alloys

The microstructure and thermal conductivity of four groups of Mg–rare earth（RE） binary alloys（Mg–Ce,Mg–Nd, Mg–Y and Mg–Gd） in as-cast and as-solutionized states were systematically studied. Thermal conductivity was measured on a Netzsch LFA457 using laser flash method at room temperature. Results indicated that for as-cast alloys, the volume fraction of second phases increased with the increase of alloying elements. After solutionizing treatment, a part or most of second phases were dissolved in α-Mg matrix, except for Mg–Ce alloys. The thermal conductivity of as-cast and as-solutionized Mg–RE alloys decreased with the increase of concentrations. The thermal conductivity of as-solutionized Mg–Nd,Mg–Y and Mg–Gd alloys was lower than that of as-cast alloys. Thermal conductivity of as-solutionized Mg–Ce alloys was higher than that of as-cast alloys, because of the elimination of lattice defects and fine dispersed particles during solutionizing treatment. Different RE elements have different influences on the thermal conductivity of Mg alloys in the following order： Ce 〈 Nd 〈 Y 〈 Gd. Ce has the minimum effect on thermal conductivity of Mg alloys, because of the very low solubility of Ce in the α-Mg matrix. The variations in the atomic radius of the solute elements with Mg atom（ r）, valence, configuration of extranuclear electron of the solute atoms, and the maximum solid solubility of elements in the α-Mg matrix were suggested to be the main reasons for the differences in thermal conductivity of resulting Mg–RE alloys.