Micro- and Nanoscale Conductive Tree-Structures for Cooling a Disk-Shaped Electronic Piece

In this research, we consider the generation of conductive heat trees at microscales and nanoscales for cooling electronics which are considered as heat-generating disk-shaped solids. With the advent of nanotechnology and the production of electronics in micro- and nanoscales in recent years, designing workable systems for cooling them is considered widely. Therefore, tree-shape conduction paths of highly conductive material including radial patterns, structures with one level of branching, tree-with-loop architectures, and combination of structures with branching and structures with loops are generated for cooling such electronic devices. Furthermore, constructal method which is used to analytically generate heat trees for cooling a disk-shaped body is modified in the present work, that we call it modified analytical method. Moreover, every feature of the tree architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. Since there are some constructal tree architectures which are not possible to be generated analytically, numerical approach is used for optimization. When the smallest features of the internal structure are smaller than mean free path of the energy carriers, heat conductivity is no longer a constant and becomes a function of the smallest dimension of the structure. Therefore, we consider models which were proposed for estimating conductivity of small scale bodies.

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Design and Optimization of Conductive Heat Trees at Micro and Nanoscales for Cooling Electronics

Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer ◽

10.1115/ht2012-58512 ◽

2012 ◽

Author(s):

Masoud Daneshi ◽

Ebrahim Shirani

Keyword(s):

Electronic Devices ◽

Mean Free Path ◽

Small Scale ◽

Conductive Heat ◽

Structural Dimension ◽

Cooling Systems ◽

Nano Technology ◽

Conductive Material ◽

Design And Optimization ◽

The Mean

In this research, we consider the generation of conductive heat trees at micro and nano scales for cooling electronics which are considered as heat-generating disc-shaped solids. Due to the development of nano technology and its role in the production of small scale electronics in recent decades, the necessity of designing cooling systems for them will be revealed more than any other time. Therefore, tree-shape conduction paths of highly conductive material including radial patterns, structures with one level of branching, tree-with-loop architectures, and combination of structures with branching and structures with loop are generated for cooling such electronic devices. Furthermore, Constructal method which is used to analytically generate heat trees for cooling a disk-shaped body is modified in the present work, that we call it modified analytical method. Moreover, every feature of the tree-shaped architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. When the smallest features of the internal structure are so small, the conventional description of conduction breaks down. Hence, the effective thermal conductivity exhibits the “size effect”, and is governed by the smallest structural dimension which is comparable with the mean free path of the energy carriers. Therefore, we consider a model which was proposed for small-scale bodies in order to evaluate conductivity of heat trees.

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Molecular Dynamics for Near Surface Flows in Nano Liquid and Micro Gas Systems

ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, Parts A and B ◽

10.1115/icnmm2006-96170 ◽

2006 ◽

Author(s):

Graham B. Macpherson ◽

Jason M. Reese

Keyword(s):

Molecular Dynamics ◽

Fluid Mechanics ◽

Free Path ◽

Stokes Equations ◽

Computational Cost ◽

Surface Effects ◽

Mean Free Path ◽

Small Scale ◽

Near Surface ◽

Non Equilibrium

Conventional fluid mechanics (Navier–Stokes equations with linear constitutive relations) is, on the whole, applicable for simulating very small scale liquid and gas systems. This changes (for simple fluids) only in the vicinity of solid surfaces (approximately 5 molecular diameters for liquids, or one mean free path for gases) or under very high temperature or velocity gradients. It is shown that typical experimental conditions in practical systems do not give rise to gradients of this magnitude. Therefore, only surface effects cause significant deviation from results expected by conventional fluid mechanics. In micro and nano systems, however, large surface area to volume ratio means that the detail of boundary conditions and near surface dynamics can dominate the flow characteristics. In this paper, the use of non–equilibrium molecular dynamics (NEMD) to study these fluid mechanics problems in an engineering simulation context is discussed. The extent of systems that can be studied by NEMD, given current computational capabilities, is demonstrated. Methods for reducing computational cost, such as hybridisation with continuum based fluid mechanics and extracting information from a small representative systems are also discussed. Non–equilibrium surface effects in gas micro systems may also been studied using NEMD. These occur at boundaries in the form of discontinuities (velocity slip and temperature jump) and within approximately one mean free path of a surface, in the form of a Knudsen layer. The distributions of molecular velocities, free path between collisions and time spent in collision have been calculated for an unbounded equilibrium fluid. The influence of a solid surface on the state of a fluid or flow can be investigated by measuring how these fundamental properties are affected.

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A SIMPLE ANALYTICAL METHOD TO DETERMINE SOLAR ENERGETIC PARTICLES’ MEAN FREE PATH

The Astrophysical Journal ◽

10.1088/0004-637x/730/1/46 ◽

2011 ◽

Vol 730 (1) ◽

pp. 46 ◽

Cited By ~ 11

Author(s):

H.-Q. He ◽

G. Qin

Keyword(s):

Free Path ◽

Analytical Method ◽

Mean Free Path ◽

Energetic Particles ◽

Solar Energetic Particles ◽

Simple Analytical Method

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Umklapp Scattering and Heat Conductivity of Superlattices

MRS Proceedings ◽

10.1557/proc-626-z9.5 ◽

2000 ◽

Vol 626 ◽

Author(s):

M.V. Simkin ◽

G.D. Mahan

Keyword(s):

Free Path ◽

Heat Conductivity ◽

Mean Free Path ◽

The Mean ◽

Superlattice Period ◽

Umklapp Scattering

ABSTRACTThe mean free path of phonons in superlattices is estimated. It is shown to be strongly dependent on the superlattice period due to the Umklapp scattering in subbands. It first falls with increasing the superlattice period until it becomes comparable with the latter after what it rises back to the bulk value. Similar behavior is expected of heat conductivity, which is proportional to the mean free path.

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Progress of discrete unified gas-kinetic scheme for multiscale flows

Advances in Aerodynamics ◽

10.1186/s42774-020-00058-3 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Zhaoli Guo ◽

Kun Xu

Keyword(s):

Free Path ◽

Spatial Scales ◽

Mesh Size ◽

Kinetic Scheme ◽

Mean Free Path ◽

Numerical Approach ◽

Time Step ◽

Flow Problems ◽

A Cell ◽

Unified Gas Kinetic Scheme

AbstractMultiscale gas flows appear in many fields and have received particular attention in recent years. It is challenging to model and simulate such processes due to the large span of temporal and spatial scales. The discrete unified gas kinetic scheme (DUGKS) is a recently developed numerical approach for simulating multiscale flows based on kinetic models. The finite-volume DUGKS differs from the classical kinetic methods in the modeling of gas evolution and the reconstruction of interface flux. Particularly, the distribution function at a cell interface is reconstructed from the characteristic solution of the kinetic equation in space and time, such that the particle transport and collision effects are coupled, accumulated, and evaluated in a numerical time step scale. Consequently, the cell size and time step of DUGKS are not passively limited by the particle mean-free-path and relaxation time. As a result, the DUGKS can capture the flow behaviors in all regimes without resolving the kinetic scale. Particularly, with the variation of the ratio between numerical mesh size scale and kinetic mean free path scale, the DUGKS can serve as a self-adaptive multiscale method. The DUGKS has been successfully applied to a number of flow problems with multiple flow regimes. This paper presents a brief review of the progress of this method.

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