Material Distribution Optimization in a Metal Matrix Heat Sink Using a Constructal-Design Inspired Unit T-Cell

2017 ◽  
Author(s):  
Jacob Kephart ◽  
G. F. Jones
Keyword(s):  
T Cell ◽  
Heat Sink ◽  
Metal Matrix ◽  
Unit Cell ◽  
Material Distribution ◽  
Two Dimensional ◽  
Aspect Ratios ◽  
The Matrix ◽  
Unit Cells ◽  
Matrix Heat

Constructal principles are used to investigate the optimization of material utilization in a metal matrix heat sink that maximizes the total heat transfer rate through the base of heat sink. This approach utilizes a two-dimensional geometry to examine spatial heat flow and optimal material distribution in a metal matrix in the plane perpendicular to the coolant flow direction. The matrix is composed of multiple layers of conductive tees built up from the smallest constituent, the unit T-cell. The unit cell consists of a conductive tee-shaped geometry with the two rectangular void regions each making up half of a cooling channel. The horizontal boundaries must match the temperature and heat flux at the boundaries of the neighboring unit cells as this is a conjugate conduction/convection problem. The geometry of the unit cell is characterized by aspect ratios of channel width to height, overall cell width to height, and channel height to cell height. The matrix structure is assembled by stacking unit cells into multiple layers where the number of cells in each layer is an integer multiple of the cells contained in the lower layer. The solution is obtained for optimal T-cell geometric parameters under a set of predetermined constraints including overall volume, solid fill fraction, and number of layers. When a large number of stacked unit cells are considered, the results describe the ideal spatial distribution of porosity and pore sizes for two dimensional functionally graded metal-matrix heat sink. These results will lead to a better understanding of the role played by the porosity distribution in a metal-matrix heat sink and may be applied to the analysis, optimization, and design of more effective heat sinks.

Optimizing a Functionally Graded Metal-Matrix Heat Sink Through Growth of a Constructal Tree of Convective Fins

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Jacob Kephart ◽  
G. F. Jones
Keyword(s):  
Heat Sink ◽  
Metal Matrix ◽  
Heated Surface ◽  
Electronics Cooling ◽  
Functionally Graded ◽  
Aspect Ratios ◽  
Volume Porosity ◽  
Convective Fin ◽  
Matrix Heat ◽  
Fin Shape

Optimal material utilization in metal-matrix heat sink is investigated using constructal design (CD) in combination with fin theory to develop a constructal tree of optimally shaped convective fins. The structure is developed through systematic growth of constructs, consisting initially of a single convective fin enveloped in a convective medium. Increasingly complex convective fin structures are created and optimized at each level of complexity to determine optimal fin shapes, aspect ratios, and fin-base thickness ratios. One result of the optimized structures is a functional grading of porosity. The porosity increases as a function of distance from the heated surface in a manner ranging from linear to a power function of distance with exponent of about 2. The degree of nonlinearity in this distribution varies depending on the volume of the heat sink and average packing density and approaches a parabolic shape for large volume. For small volume, porosity approaches a linear function of distance. Thus, a parabolic (or least-material) fin shape at each construct level would not necessarily be optimal. Significant improvements in total heat transfer, up to 55% for the cases considered in this work, were observed when the fin shape is part of the optimization in a constructal tree of convective fins. The results of this work will lead to better understanding of the role played by the porosity distribution in a metal-matrix heat sink and may be applied to the analysis, optimization, and design of more effective heat sinks for electronics cooling and related areas.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals Two-Dimensional Composite Acoustic Metamaterials of Rectangular Unit Cell from Pentamode to Band Gap

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1457
Author(s):  
Qi Li ◽  
Ke Wu ◽  
Mingquan Zhang
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Band Gap ◽  
Unit Cell ◽  
The Other ◽  
Two Dimensional ◽  
Acoustic Metamaterials ◽  
Acoustic Wave Propagation ◽  
Theoretical Support ◽  
Unit Cells

Pentamode metamaterials have been receiving an increasing amount of interest due to their water-like properties. In this paper, a two-dimensional composite pentamode metamaterial of rectangular unit cell is proposed. The unit cells can be classified into two groups, one with uniform arms and the other with non-uniform arms. Phononic band structures of the unit cells were calculated to derive their properties. The unit cells can be pentamode metamaterials that permit acoustic wave travelling or have a total band gap that impedes acoustic wave propagation by varying the structures. The influences of geometric parameters and materials of the composed elements on the effective velocities and anisotropy were analyzed. The metamaterials can be used for acoustic wave control under water. Simulations of materials with different unit cells were conducted to verify the calculated properties of the unit cells. The research provides theoretical support for applications of the pentamode metamaterials.

scholarly journals An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films

2020 ◽  
Vol 76 (3) ◽  
pp. 345-357 ◽  
Author(s):  
Josef Simbrunner ◽  
Benedikt Schrode ◽  
Jari Domke ◽  
Torsten Fritz ◽  
Ingo Salzmann ◽  
...  
Keyword(s):  
Rotational Symmetry ◽  
Grazing Incidence ◽  
Unit Cell ◽  
Structure Identification ◽  
X Ray Diffraction ◽  
Cell Parameters ◽  
Lattice Constants ◽  
The Matrix ◽  
Unit Cells ◽  
Complex Scenario

Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.

scholarly journals Bio-Inspired Active Skins for Surface Morphing

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Yujin Park ◽  
Gianmarco Vella ◽  
Kenneth J. Loh
Keyword(s):  
Deformation Mechanism ◽  
Unit Cell ◽  
Material Behavior ◽  
Two Dimensional ◽  
New Class ◽  
Mechanical Metamaterials ◽  
Unique Material ◽  
Out Of Plane ◽  
Unit Cells ◽  
Significant Attention

AbstractMechanical metamaterials that leverage precise geometrical designs and imperfections to induce unique material behavior have garnered significant attention. This study proposes a Bio-Inspired Active Skin (BIAS) as a new class of instability-induced morphable structures, where selective out-of-plane material deformations can be pre-programmed during design and activated by in-plane strains. The deformation mechanism of a unit cell geometrical design is analyzed to identify how the introduction of hinge-like notches or instabilities, versus their pristine counterparts, can pave way for controlling bulk BIAS behavior. Two-dimensional arrays of repeating unit cells were fabricated, with notches implemented at key locations throughout the structure, to harvest the instability-induced surface features for applications such as camouflage, surface morphing, and soft robotic grippers.

scholarly journals A multilevel fast spectral domain algorithm for electromagnetic analysis of infinite periodic arrays with large unit cells

2006 ◽  
Vol 4 ◽  
pp. 41-47 ◽  
Author(s):  
T. F. Eibert
Keyword(s):  
Fast Multipole Method ◽  
Boundary Integral ◽  
Unit Cell ◽  
Spectral Domain ◽  
Antenna Element ◽  
Large Unit ◽  
Periodic Arrays ◽  
The Matrix ◽  
Unit Cells ◽  
Unit Cell Dimensions

Abstract. A multilevel fast spectral domain algorithm (MLFSDA) is introduced for the efficient evaluation of the matrix vector products due to the boundary integral (BI) operator within a hybrid finite element - BI (FEBI) method for the analysis of infinite periodic arrays. The MLFSDA utilizes the diagonalization property of the spectral domain (SD) BI representation and handles the large numbers of Floquet modes required for large (with respect to wavelength) periodic unit cells by similar hierarchical techniques as applied in the multilevel fast multipole method/algorithm (MLFMM/MLFMA). With the capability of the MLFSDA to handle very large periodic unit cells, it becomes possible to model finite antennas and scatterers with the infinite periodic array model. For a cavity-backed antenna element and for a semi-finite array of 4 cavity-backed antenna elements in the finite direction, the dependence of the input impedances on the unit cell sizes is investigated and it is found that array resonances disappear for reasonably large unit cell dimensions. Finally, a semi-finite array of antipodal Vivaldi antenna elements is considered and simulation results for infinite periodic, finite, and semi-finite array configurations are compared to measured data.

scholarly journals Connectivity and formula-generating functions for sheet-silicate minerals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1089-C1089
Author(s):  
Frank Hawthorne
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Unit Cell ◽  
Two Dimensional ◽  
Silicate Minerals ◽  
Topological Features ◽  
Unit Cells ◽  
Sheet Silicate ◽  
Symmetry Operations

Silicate sheets may be described by two-dimensional nets in which the vertices of the net are occupied by tetrahedra, and the edges of the net represent linkages between tetrahedra. A plane net must contain 3-connected vertices, but not all vertices need to be 3-connected. Simple silicate structures may thus be generated from simple 3-connected plane nets (e.g. 63, 4.82, 4.6.8, (4.6.8)2(6.82)1, etc.). More complicated silicate nets may be generated by various "building operations": (1) Insertion: insertion of 2- and 4-connected vertices into 3-connected plane nets; (2) Repetition: generation of double (or triple) nets by topological symmetry operations that retain transitivity at the junction between the repeated elements. Diversity is also introduced within the sheets of tetrahedra by [1] adjacent apical tetrahedron vertices pointing in the same or different directions, and [2] by folding of the sheets. For simple structures, net type strongly affects the stoichiometry of the resultant structure as the unit cells of the various nets are of different sizes (and shapes), although the stoichiometry may also be affected by non-tetrahedral components. Building operations strongly affect the stoichiometry of the resultant sheet, and this effect may be quantified. We define a formula-generating function F(k,l,...) that generates the formula of a sheet with specific topological features denoted by the indices k,l,... . A simple 3-connected net results in sheets of the form (T2O5)n where n denotes the number of (T2O5)n in the unit cell of the underlying net (for 63, n = 1; for 4.82, n = 2; for (4.6.8)2(6.82)1, n = 3, etc). Plane nets with k 3-connected vertices and l inserted 2-connected vertices result in sheets of the form [T(k+l) O(2.5k+3l)], where (...) are subscripted. Single- and double-sheet structures may be generated from the function F(k,l) = T(N{k+l}) O(N{3k+2.5l}-n{N-1}) where N = 1 and 2 for single- and double-sheets, respectively, and (...) are subscripted.

Correlation averaging of two-dimensional crystals: basic strategy and refinements

1986 ◽  
Vol 44 ◽  
pp. 136-139
Author(s):  
W. Baumeister ◽  
R. Rachel ◽  
R. Guckenberger ◽  
R. Hegerl
Keyword(s):  
Low Dose ◽  
Signal To Noise Ratio ◽  
Real Space ◽  
Fourier Domain ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Unit Cells ◽  
Lateral Displacements ◽  
Established Technique ◽  
Crystalline Array

IntroductionCorrelation averaging (CAV) is meanwhile an established technique in image processing of two-dimensional crystals /1,2/. The basic idea is to detect the real positions of unit cells in a crystalline array by means of correlation functions and to average them by real space superposition of the aligned motifs. The signal-to-noise ratio improves in proportion to the number of motifs included in the average. Unlike filtering in the Fourier domain, CAV corrects for lateral displacements of the unit cells; thus it avoids the loss of resolution entailed by these distortions in the conventional approach. Here we report on some variants of the method, aimed at retrieving a maximum of information from images with very low signal-to-noise ratios (low dose microscopy of unstained or lightly stained specimens) while keeping the procedure economical.

Bayesian removal of noise for increased sensitivity in vector pattern recognition lattice imaging of interfaces

1993 ◽  
Vol 51 ◽  
pp. 994-995
Author(s):  
L. Fei ◽  
P. Fraundorf
Keyword(s):  
Pattern Recognition ◽  
Perfect Crystal ◽  
Unit Cell ◽  
Ion Milling ◽  
Beam Radiation ◽  
Major Interest ◽  
Unit Cells ◽  
Mapping Process ◽  
Increased Sensitivity ◽  
Electron Microscopes

Interface structure is of major interest in microscopy. With high resolution transmission electron microscopes (TEMs) and scanning probe microscopes, it is possible to reveal structure of interfaces in unit cells, in some cases with atomic resolution. A. Ourmazd et al. proposed quantifying such observations by using vector pattern recognition to map chemical composition changes across the interface in TEM images with unit cell resolution. The sensitivity of the mapping process, however, is limited by the repeatability of unit cell images of perfect crystal, and hence by the amount of delocalized noise, e.g. due to ion milling or beam radiation damage. Bayesian removal of noise, based on statistical inference, can be used to reduce the amount of non-periodic noise in images after acquisition. The basic principle of Bayesian phase-model background subtraction, according to our previous study, is that the optimum (rms error minimizing strategy) Fourier phases of the noise can be obtained provided the amplitudes of the noise is given, while the noise amplitude can often be estimated from the image itself.

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