Modeling Thermal Microspreading Resistance in Via Arrays

2016 ◽  
Vol 138 (1) ◽  
Author(s):  
Michael Fish ◽  
Patrick McCluskey ◽  
Avram Bar-Cohen
Keyword(s):  
Boundary Conditions ◽  
Effective Properties ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
Simulation Software ◽  
Electronic Packages ◽  
Isothermal Boundary ◽  
Unit Cells ◽  
Flow Through ◽  
Management Techniques

As thermal management techniques for three-dimensional (3D) chip stacks and other high-power density electronic packages continue to evolve, interest in the thermal pathways across substrates containing a multitude of conductive vias has increased. To reduce the computational costs and time in the thermal analysis of through-layer via (TXV) structures, much research to date has focused on defining effective anisotropic thermal properties for a pseudohomogeneous medium using isothermal boundary conditions. While such an approach eliminates the need to model heat flow through individual vias, the resulting properties are found to depend on the specific boundary conditions applied to a unit TXV cell. More specifically, effective properties based on isothermal boundary conditions fail to capture the local “microspreading” resistance associated with more realistic heat flux distributions and local hot spots on the surface of these substrates. This work assesses how the thermal microspreading resistance present in arrays of vias in interposers, substrates, and other package components can be properly incorporated into the modeling of these arrays. We present the conditions under which spreading resistance plays a major role in determining the thermal characteristics of a via array and propose methods by which designers can both account for the effects of microspreading resistance and mitigate its contribution to the overall thermal behavior of such substrate–via systems. Finite element modeling (FEM) of TXV unit cells is performed using commercial simulation software (ansys).

Modeling Thermal Spreading Resistance in Via Arrays

2015 ◽  
Author(s):  
Michael Fish ◽  
Patrick McCluskey ◽  
Avram Bar-Cohen
Keyword(s):  
Boundary Conditions ◽  
Effective Properties ◽  
Numerical Models ◽  
Thermal Characteristics ◽  
Simulation Software ◽  
Worst Case ◽  
Spreading Resistance ◽  
Isothermal Boundary ◽  
Unit Cells ◽  
Adjustment Factors

As thermal management techniques for 3D chip stacks and other high power density electronic packages continue to evolve, interest in the thermal pathways across substrates containing a multitude of conductive vias has increased. To facilitate the use of numerical models that can reduce computational costs and time in the thermal analysis of through-layer via (TXV) structures, much research to date has focused on defining effective anisotropic thermal properties for a pseudo-homogeneous TXV medium using isothermal boundary conditions. While such an approach eliminates the need to model heat flow through individual vias, the resulting properties can be shown to depend on the specific boundary conditions applied to a unit TXV cell. More specifically, effective properties based on isothermal boundary conditions fail to capture the local “micro-spreading” resistance associated with more realistic heat flux distributions and local hot spots on the surface of these substrates. This work assesses how the thermal spreading resistance present in arrays of vias in interposers, substrates, and other package components can be properly incorporated into the modeling of these arrays. We present the conditions under which spreading resistance plays a major role in determining the thermal characteristics of a via array and propose methods by which designers can both account for the effects of spreading resistance and mitigate its contribution to the overall thermal behavior of such substrate-via systems. Finite element modeling of TXV unit cells is performed using commercial simulation software (ANSYS). Compactly stated, micro-spreading contributes to the total resistance RT = R1d + (fu + fl)Rsp,max, where 0≤ f ≤ 1 are adjustment factors that depend on the conditions at the upper and lower surfaces of the via array layer and Rsp,max occurs under worst-case conditions.

Three Dimensional Thermoacoustic Oscillation in a Premix Combustor

2001 ◽  
Author(s):  
S. Akamatsu ◽  
A. P. Dowling
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Linear Equations ◽  
Three Dimensional ◽  
Total System ◽  
Mean Flow ◽  
Modal Coupling ◽  
Rate Of Heat Release ◽  
Flow Through ◽  
Combustion Processes

A theory is developed to describe high frequency three-dimensional thermoacoustic waves in a simplified geometry representing a typical premix combustor. The theory considers linear modes of frequency ω and circumferential mode number m i.e. proportional to eiωt+imθ. The radial and axial dependence is determined for a cylindrical combustor. Simple geometries are investigated systematically to analyze the effect of different inlet boundary conditions to the combustion chamber on the frequency of oscillation and on the susceptibility to instability, both near and away from the cut-off frequencies. The model includes a one-dimensional mean flow, radial mode coupling and idealized combustion processes, which are added in stages to build up an understanding of the complicated acoustics of the premix combustor geometry. It is demonstrated that the flow through the premix ducts provides a frequency-dependent boundary condition at combustor inlet and causes modal coupling. Generalized linear equations of conservation of mass, momentum and energy, together with boundary conditions, are solved to identify the eigenfrequencies, ω, of the total system. Then Real ω determines the frequency of the oscillation, while Imaginary ω indicates the growth rate of the disturbance. It is found that strong resonant peaks in the pressure waves exist close to the cut-off condition for acoustic waves and that the relationship between the unsteady rate of heat release and the flow significantly influences the instability of oscillation.

A Thermal Network Approach for Predicting Thermal Characteristics of Three-Dimensional Electronic Packages

2006 ◽  
Author(s):  
P. L. Chen ◽  
S. F. Chang ◽  
T. Y. Wu ◽  
Y. H. Hung
Keyword(s):  
Boundary Conditions ◽  
Thermal Analyses ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Electronic Packages ◽  
Network Approach ◽  
Electronic Package ◽  
Thermal Network ◽  
Network Method ◽  
Thermal Network Method

In the present study, a numerical approach for characterizing three-dimensional (3-D) electronic packages is presented, based on the steady-state solution of the thermal network method for generalized rectangular geometries, where boundary conditions are uniformly specified over specific regions of the package. As we know, the thermal-network method is very powerful on thermal analysis of electronic packaging because of its feasibility and flexibility. Accordingly, the numerical approach with thermal-network method to simulate heat transfer characteristics for 3-D package geometries becomes important in the modem microelectronic applications. The thermal analyses are presented with a general overview of the thermal network method, boundary conditions and solution procedures. Furthermore, the application of boundary conditions at the fluid-solid, package-board and layer-layer interfaces provides a means for obtaining a unique numerical result for 3-D complex electronic packages. The complex geometries found in most 3-D electronic package configurations are modeled using numerical method through the careful use of simplifying assumptions. Comparisons of the present numerical results with the existing experimental data for 3-D electronic package of pin grid arrays and multi-chip modules are made with a satisfactory agreement. Thus, the present study demonstrates that the numerical thermal-network approach can offer an accurate and efficient solution procedure for evaluating the thermal characterization of 3-D electronic packages.

scholarly journals Pulsatile flow in ventricular catheters for hydrocephalus

2017 ◽  
Vol 375 (2096) ◽  
pp. 20160294 ◽  
Author(s):  
Á. Giménez ◽  
M. Galarza ◽  
U. Thomale ◽  
M. U. Schuhmann ◽  
J. Valero ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Computational Study ◽  
Three Dimensional ◽  
Mathematical Methods ◽  
Basic Principles ◽  
Heart Beating ◽  
Ventricular Catheters ◽  
Flow Through ◽  
Three Dimensional Models ◽  
Previous Computational Study

The obstruction of ventricular catheters (VCs) is a major problem in the standard treatment of hydrocephalus, the flow pattern of the cerebrospinal fluid (CSF) being one important factor thereof. As a first approach to this problem, some of the authors studied previously the CSF flow through VCs under time-independent boundary conditions by means of computational fluid dynamics in three-dimensional models. This allowed us to derive a few basic principles which led to designs with improved flow patterns regarding the obstruction problem. However, the flow of the CSF has actually a pulsatile nature because of the heart beating and blood flow. To address this fact, here we extend our previous computational study to models with oscillatory boundary conditions. The new results will be compared with the results for constant flows and discussed. It turns out that the corrections due to the pulsatility of the CSF are quantitatively small, which reinforces our previous findings and conclusions. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

Thermal Characterization of Electronic Packages Using a Three-Dimensional Fourier Series Solution

2000 ◽  
Vol 122 (3) ◽  
pp. 233-239 ◽  
Author(s):  
J. R. Culham ◽  
M. M. Yovanovich ◽  
T. F. Lemczyk
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Series Solution ◽  
Analytical Approach ◽  
Printed Circuit Boards ◽  
Three Dimensional ◽  
Thermal Characterization ◽  
Steady State Solution ◽  
Electronic Packages

The need to accurately predict component junction temperatures on fully operational printed circuit boards can lead to complex and time consuming simulations if component details are to be adequately resolved. An analytical approach for characterizing electronic packages is presented, based on the steady-state solution of the Laplace equation for general rectangular geometries, where boundary conditions are uniformly specified over specific regions of the package. The basis of the solution is a general three-dimensional Fourier series solution which satisfies the conduction equation within each layer of the package. The application of boundary conditions at the fluid-solid, package-board and layer-layer interfaces provides a means for obtaining a unique analytical solution for complex IC packages. Comparisons are made with published experimental data for both a plastic quad flat package and a multichip module to demonstrate that an analytical approach can offer an accurate and efficient solution procedure for the thermal characterization of electronic packages. [S1043-7398(00)01403-1]

The Calculation of Three Dimensional Viscous Flow Through Multistage Turbomachines

1990 ◽  
Author(s):  
J. D. Denton
Keyword(s):  
Boundary Conditions ◽  
Unsteady Flow ◽  
Viscous Flow ◽  
Calculation Method ◽  
Three Dimensional ◽  
Mixing Process ◽  
Three Dimensional Flow ◽  
Flow Calculation ◽  
Dimensional Flow ◽  
Flow Through

The extension of a well established three dimensional flow calculation method to calculate the flow through multiple turbomachinery blade rows is described in this paper. To avoid calculating the unsteady flow, which is inherent in any machine containing both rotating and stationary blade rows, a mixing process is modelled at a calculating station between adjacent blade rows. The effects of this mixing on the flow within the blade rows may be minimised by using extrapolated boundary conditions at the mixing plane.

Streamwise Computation of Three-Dimensional Flows Using Two Stream Functions

1993 ◽  
Vol 115 (2) ◽  
pp. 233-238 ◽  
Author(s):  
M. S. Greywall
Keyword(s):  
Boundary Conditions ◽  
Stream Function ◽  
Potential Flow ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Spatial Coordinate ◽  
Independent Variables ◽  
Dependent Variables ◽  
Stream Functions ◽  
Flow Through

An approach to compute three-dimensional flows using two stream functions is presented. The independent variables used are χ, a spatial coordinate, and ξ and η, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since the value of a stream function is constant along the solid boundaries, this choice of variables makes it easy to satisfy the boundary conditions. To illustrate the approach, computations of incompressible potential flow through a circular-to-rectangular transition duct are also presented.

scholarly journals Influence of unit cell parameters of tetrachiral mechanical metamaterial on its effective properties

2021 ◽  
Vol 8 (1) ◽  
pp. 150-157
Author(s):  
Linar R. Akhmetshin ◽  
◽  
Igor Yu. Smolin ◽  
◽  
◽  
...  
Keyword(s):  
Rotation Angle ◽  
Effective Properties ◽  
Three Dimensional ◽  
Unit Cell ◽  
The Finite Element Method ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Chiral Structures ◽  
Unit Cells ◽  
Loading Axis

In the paper, we study the mechanical behavior of a three-dimensional chiral mechanical metamaterial using numerical modeling. A feature of chiral structures is that during their uniaxial loading a twisting is observed along the loading axis. A rod of the mechanical metamaterial composed of 3 × 3 × 9 unit cells along the corresponding three orthogonal axes. The relative strain of uniaxial compression of the sample in the simulation did not exceed 3.3%. The simulation was performed by the finite element method in a threedimensional case. Original results on the dependencies of the rotation angle and the reaction of the rigidly fixed support of the metamaterial sample on the parameters characterizing the structure of the unit cell of the metamaterial are presented in this context. All the dependencies, except one, are nonlinear with portions of large and small changes.

Non-Newtonian Computational Fluid Dynamics (CFD) Modeling on Left Coronary Artery with Multiple Blockages

2014 ◽  
Vol 592-594 ◽  
pp. 1924-1929
Author(s):  
Krishna Murari Pandey ◽  
Ritabrata Thakur ◽  
Abhinav Hazarika ◽  
Tarun Ashutosh ◽  
Dipankar Gogoi
Keyword(s):  
Coronary Artery ◽  
Static Pressure ◽  
Three Dimensional ◽  
Simulation Software ◽  
Cfd Modeling ◽  
Ansys Fluent ◽  
Viscous Losses ◽  
Computational Fluid Dynamics Cfd ◽  
Flow Through ◽  
Dimensional Section

The rate of mean blood flow through arteries depend on the resistance to flow presented by the blood vessels. Mean blood pressure decreases as the circulating blood moves away from the heart through arteries and capillaries due to viscous losses of energy. Atherosclerosis is a common phenomenon that is observed causing blockage in coronary arteries leading to cardiac arrest. This blockage is due to the deposition of cholesterol or plaque on the inner walls of the coronary artery. This paper provides an analytical study on the variation of static pressure with multiple blockages in the artery implementing the conventional simulation software. A general three dimensional section of the coronary artery was taken for the analysis and the variation of static pressure with increase in the number of blockages due to cholesterol deposition was studied. Meshing of the geometry and specification of the boundary types have been accomplished using GAMBIT 2.3.16 and the analysis has been carried out using ANSYS FLUENT 6.3.26.

Crystal Structure Analysis of Cu-Zr Alloys by Convergent Beam Diffraction

1981 ◽  
Vol 39 ◽  
pp. 354-355
Author(s):  
A. F. Marshall ◽  
J. W. Steeds ◽  
D. Bouchet ◽  
S. L. Shinde ◽  
R. G. Walmsley
Keyword(s):  
Crystal Structure ◽  
Point Group ◽  
Intermetallic Phase ◽  
Three Dimensional ◽  
Crystal Structure Analysis ◽  
Ion Milling ◽  
Composition And Structure ◽  
Unit Cells ◽  
Sputter Deposited ◽  
Convergent Beam

Convergent beam electron diffraction is a powerful technique for determining the crystal structure of a material in TEM. In this paper we have applied it to the study of the intermetallic phases in the Cu-rich end of the Cu-Zr system. These phases are highly ordered. Their composition and structure has been previously studied by microprobe and x-ray diffraction with sometimes conflicting results.The crystalline phases were obtained by annealing amorphous sputter-deposited Cu-Zr. Specimens were thinned for TEM by ion milling and observed in a Philips EM 400. Due to the large unit cells involved, a small convergence angle of diffraction was used; however, the three-dimensional lattice and symmetry information of convergent beam microdiffraction patterns is still present. The results are as follows:1) 21 at% Zr in Cu: annealed at 500°C for 5 hours. An intermetallic phase, Cu3.6Zr (21.7% Zr), space group P6/m has been proposed near this composition (2). The major phase of our annealed material was hexagonal with a point group determined as 6/m.

Sign in / Sign up

Export Citation Format

Share Document