On the Use of Point Source Solutions for Forced Air Cooling of Electronic Components—Part I: Thermal Wake Models for Rectangular Heat Sources

2003 ◽  
Vol 125 (2) ◽  
pp. 226-234 ◽  
Author(s):  
Alfonso Ortega ◽  
Shankar Ramanathan
Keyword(s):  
Temperature Field ◽  
Point Source ◽  
Three Dimensional ◽  
Air Cooling ◽  
Heat Sources ◽  
Multiple Sources ◽  
One Dimensional ◽  
Forced Air ◽  
The Individual ◽  
Thermal Wake

Analytical solutions are presented for the temperature field that arises from the application of a source of heat on an adiabatic plate or board when the fluid is represented as a uniform flow with an effective turbulent diffusivity, i.e., the so-called UFED flow model. Solutions are summarized for a point source, a one-dimensional strip source, and a rectangular source of heat. The ability to superpose the individual kernel solutions to obtain the temperature field due to multiple sources is demonstrated. The point source solution reveals that the N−1 law commonly observed for the centerline thermal wake decay for three-dimensional arrays is predicted by the point source solution for the UFED model. Examination of the solution for rectangular sources shows that the thermal wake approaches the point source behavior downstream from the source, suggesting a new scaling for the far thermal wake based on the total component power and a length scale given by ε/U. The new scaling successfully collapses the thermal wake for several sizes of components and provides a fundamental basis for experimental observations previously made for arrays of three-dimensional components.

Three-Dimensional Steady and Oscillatory Natural Convection in a Rectangular Enclosure With Heat Sources

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Amin Bouraoui ◽  
Rachid Bessaïh
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Three Dimensional ◽  
Air Cooling ◽  
Heat Sources ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Simpler Algorithm ◽  
Strong Relation

In this paper, a numerical study of three-dimensional (3D) natural convection air-cooling of two identical heat sources, simulating electronic components, mounted in a rectangular enclosure was carried out. The governing equations were solved by using the finite-volume method based on the SIMPLER algorithm. The effects of Rayleigh number Ra, spacing between heat sources d, and aspect ratios Ax in x-direction (horizontal) and Az in z-direction (transversal) of the enclosure on heat transfer were investigated. In steady state, when d is increased, the heat transfer is more important than when the aspect ratios Ax and Az are reduced. In oscillatory state, the critical Rayleigh numbers Racr for different values of spacing between heat sources and their aspect ratios, at which the flow becomes time dependent, were obtained. Results show a strong relation between heat transfers, buoyant flow, and boundary layer. In addition, the heat transfer is more important at the edge of each face of heat sources than at the center region.

A Model for Bending, Torsional, and Axial Vibrations of Micro- and Macro-Drills Including Actual Drill Geometry—Part I: Model Development and Numerical Solution

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Sinan Filiz ◽  
O. Burak Ozdoganlar
Keyword(s):  
Cross Section ◽  
Model Development ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Three Dimensional Model ◽  
Axial Thrust ◽  
One Dimensional ◽  
Three Dimensional Models ◽  
The Individual ◽  
Actual Geometry

Part I of this work presents a combined one-dimensional/three-dimensional approach for obtaining a unified model for the dynamics of micro- and macro-drills. To increase the numerical efficiency of the model, portions of the drill with circular cross-section (shank, extension, and tapered sections) are modeled using one-dimensional beam models without compromising model accuracy. A three-dimensional model is used for an accurate representation of the fluted section, considering the actual geometry with the pretwisted shape and axially varying (nonaxisymmetric) cross-section. The actual cross-section of the drills is incorporated to the model through a polynomial mapping while the pretwist effect is captured by defining a rotating reference frame. The boundary-value problem for both one- and three-dimensional models are derived using a variational approach, based on the extended Hamilton’s principle, and are subsequently solved by applying the spectral-Tchebychev technique. A component-mode synthesis is used for connecting the individual sections to obtain the dynamic model for the entire drill. Convergence of the model is studied by varying the number of polynomials for each section. The experimental validation of the model is included in Part II for both macro- and micro-drills. Also included in Part II is an analysis of drill dynamics for varying drill-geometry parameters and axial (thrust) force.

Analysis of the Heat Transfer Within Combustor Liners Using a Combined Monte Carlo and Two-Flux Method

2020 ◽  
Author(s):  
Andressa L. Johnson ◽  
Xinyu Zhao
Keyword(s):  
Monte Carlo ◽  
Gas Turbine ◽  
Three Dimensional ◽  
Radiative Energy ◽  
Air Cooling ◽  
Gas Turbine Combustor ◽  
Eddy Simulation ◽  
Model Gas Turbine Combustor ◽  
Forced Air ◽  
Cold Metal

Abstract One of the consequences of increasing the efficiency of gas turbine combustors is the higher combustion temperatures within the chamber. Advances on managing larger heat loads have been made to protect the combustor wall and turbines. Among those are thermal barrier coatings (TBCs) deposited on metal walls and forced air cooling such as through effusion holes. Historically, both the flame and TBCs have received a simplified gray treatment using effective absorptivities and emissivities. However, studies have shown that the gray analysis can considerably under-predict the cold metal side temperature resulting in misguided combustor life estimates. In this study, non-gray radiation is compared to gray and black radiation by combining three-dimensional Monte Carlo Ray Tracing (MCRT) solution of non-gray flames in a model gas turbine combustor to one-dimensional energy balance within combustor liners. A recent large eddy simulation (LES) of a gas turbine combustor is analyzed, where both gray and non-gray models are exercised. A two-band spectral model is employed for the TBC, where a translucent band and an opaque band are identified. A line-by-line treatment for gas-phase radiation is adopted, and the incident radiative energy on the combustor wall is collected using the MCRT solver, where the fraction of radiative energy within the translucent band is collected and compared with those obtained from the blackbody assumption. The temperature distributions along the multi-layered combustor wall are computed and parametric comparison is conducted. The effects of the nongray flame radiation are more prominent at elevated pressures than at atmospheric pressure, leading to a difference of approximately 150 K in the prediction of peak temperature on the hot side of the TBC. The gray model is found to over-predict the TBC temperature at downstream locations, but under-predict the TBC temperature near the flame locations. The present study proposes a methodology to estimate the wall temperatures when radiation within the TBC is considered. Future work includes application of the methodology to more realistic combustors where both radiative fluxes and convective fluxes can be accurately captured.

Multidimensional Water Flow in Variably Saturated Soils

2003 ◽  
Author(s):  
Arthur W. Warrick
Keyword(s):  
Point Source ◽  
Three Dimensional ◽  
Practical Interest ◽  
Two Dimensions ◽  
Point Sources ◽  
Radial Coordinate ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Divergent Flow ◽  
Suction Sampler

Chapters 4 and 5 dealt with one-dimensional rectilinear flow, with and without the effect of gravity. Now the focus is on multidimensional flow. We will refer to two- and three-dimensional flow based on the number of Cartesian coordinates necessary to describe the problem. For this convention, a point source emitting a volume of water per unit time results in a three-dimensional problem even if it can be described with a single spherical coordinate. Similarly, a line source would be two-dimensional even if it could be described with a single radial coordinate. A problem with axial symmetry will be termed a three-dimensional problem even when only a depth and radius are needed to describe the geometry. The pressure at a point source is undefined. But more generally, three-dimensional point sources refer to flow from finite-sized sources into a larger soil domain, such as infiltration from a small surface pond into the soil. Often, the soil domain can be taken as infinite in one or more directions. Also, a point sink can occur with flow to a sump or to a suction sampler. In two dimensions, the same types of example can be given, but we will refer to them as line sources or sinks. Practical interest in point sources includes analyses of surface or subsurface leaks and of trickle (drip) irrigation. The desirability of determining soil properties in situ has provided the impetus for a rigorous analysis of disctension and borehole infiltrometers. Also, environmental monitoring with suction cups or candles, pan lysimeters, and wicking devices all include convergent or divergent flow in multidimensions. There are some conceptual differences between line and point sources and one-dimensional sources. For discussion, consider water supplied at a constant matric potential into drier surroundings. For a one-dimensional source, the corresponding physical problem includes a planar source over an area large enough for “edge” effects to be negligible. For two dimensions, the source might be a long horizontal cylinder or a furrow of finite depth from which water flows. For three dimensions, the source could be a small orifice providing water at a finite rate or a small, shallow pond on the soil surface.

Three-Dimensional Forced Air Cooling System Analysis of a Scooter Engine

2002 ◽  
Author(s):  
Ennio Carnevale ◽  
Giacomo Migliorini ◽  
Stefano Zecchi ◽  
Bart Olmi
Keyword(s):  
Mass Flow ◽  
Noise Level ◽  
Cooling System ◽  
Three Dimensional ◽  
Low Noise ◽  
Air Cooling ◽  
Air Mass ◽  
Air Cooling System ◽  
Flow Demand ◽  
Forced Air

Internal combustion engines must match several requirements such as good efficiency and low fuel consumption rate; when they are applied on scooter they are subject to some other restrictions. Nowadays, both low pollutant emissions and low noise level are requested for this engine since scooters are usually city vehicles. To match these requirements several aspects must be investigated: one of these may be the cooling system. There are usually three cooling methods, i.e. free stream air cooling, liquid cooling and forced air cooling. The first one is usually not employed in scooter engines because of its arrangement inside the scooter body (due to functionality and aestheticism). The second one may present some plant complications caused by the heat exchanger and ducts. A forced air cooling system presents usually lower complication, lower weight and greater reliability. Nevertheless, in order to keep engine temperatures below lubricant and structural limit, high mass flow rate may be necessary since air has smaller coolant efficiency compared to liquids. Moreover cooling air, supplied by a fan, requires high pumping power which may be excessive at high rotational speed; the fan itself may produce excessive noise reducing comfort. Sometimes, it may be hard to define the air flow demands in order to properly cool the critical parts (i.e. cylinder head); poor design may result in an excessive air mass flow demand and high pressure losses. Consequently the fan requires an excessive power and emits high noise level. Proper coolant distribution around the cylinder and the engine head reduces the overall air mass flow demand, rising indirectly engine efficiency. Usually the geometry of a forced air cooled engine is quite complex because of fins and other internal passages. To study coolant distribution and heat transfer a three-dimensional approach is then required. Computational fluid dynamic calculations, provided by commercial codes, can give useful suggestions about flow distribution around a finned cylinder. This paper will show an analysis of a typical air cooled scooter engine. Air mass flows and cooling efficiency are shown at several engine rotational speeds.

Influence of the Crystallization Solvent on the Molecular Structures of Copper(II) Saccharinato Complexes with Pyridazine: Synthesis, X-Ray Crystallography, Spectroscopy, Photoluminescence, and Thermal Properties

2008 ◽  
Vol 61 (8) ◽  
pp. 634 ◽  
Author(s):  
Veysel T. Yilmaz ◽  
Evrim Senel ◽  
Canan Kazak
Keyword(s):  
Thermal Properties ◽  
Three Dimensional ◽  
Chain Structure ◽  
Molecular Structures ◽  
One Dimensional ◽  
X Ray ◽  
X Ray Crystallography ◽  
Reaction Solution ◽  
Strong Exchange ◽  
The Individual

X-Ray structural analysis has shown that the products of the reaction of [Cu(sac)2(H2O)4]·2H2O (sac = saccharinate) with pyridazine (pydz) are markedly dependent on the solvent used in the crystallization. The mononuclear complex [Cu(sac)2(H2O)(pydz)2] is obtained by slow evaporation of a 1:2 H2O/methanol solution at room temperature, whereas liquid-phase diffusion of diethyl ether into the same reaction solution produces the polymeric complex [Cu(μ-OH)(μ-sac)(μ-pydz)]n. The individual molecules of [Cu(sac)2(H2O)(pydz)2] are doubly bridged into dimers by O–H…O hydrogen bonds. All ligands in [Cu(sac)2(H2O)(pydz)2] are monodentate, whereas copper(ii) ions in [Cu(μ-OH)(μ-sac)(μ-pydz)]n are triply bridged by all ligands, leading to a one-dimensional chain structure, which is further assembled to form a three-dimensional framework by non-covalent π–π and CH–π stacking interactions. Complex [Cu(sac)2(H2O)(pydz)2] is paramagnetic, whereas complex [Cu(μ-OH)(μ-sac)(μ-pydz)]n exhibits a significantly low μeffective value due to very strong exchange coupling between the copper atoms with a relatively short Cu–Cu distance of 3.360(3) Å. In addition, the full spectroscopic, luminescence, and thermal properties of the complexes are reported.

TRAVELLING WAVES IN A CIRCULAR ARRAY OF CHUA’S CIRCUITS

1996 ◽  
Vol 06 (03) ◽  
pp. 473-484 ◽  
Author(s):  
VLADIMIR I. NEKORKIN ◽  
VICTOR B. KAZANTSEV ◽  
MANUEL G. VELARDE
Keyword(s):  
Differential Equations ◽  
Periodic Orbits ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Dimensional System ◽  
Circular Array ◽  
One Dimensional ◽  
Numerical Studies ◽  
The Individual ◽  
Three Dimensional System

The possibility of travelling waves in a one-dimensional circular array of Chua's circuits is investigated. It is shown that the problem can be reduced to the analysis of the periodic orbits of a three-dimensional system of ordinary differential equations (ODEs) describing the individual dynamics of Chua's circuit. The results of analytical and numerical studies of the bifurcation associated with the appearance of the periodic orbits are presented. A criterion for stability of the travelling waves is also provided.

On the Eshelby’s Inclusion Problem for Ellipsoids With Nonuniform Dilatational Gaussian and Exponential Eigenstrains

2003 ◽  
Vol 70 (3) ◽  
pp. 418-425 ◽  
Author(s):  
P. Sharma ◽  
R. Sharma
Keyword(s):  
Point Source ◽  
Material Science ◽  
Elastic Strain ◽  
Three Dimensional ◽  
Spherical Shape ◽  
Inclusion Problem ◽  
Elastic State ◽  
One Dimensional ◽  
Source Type ◽  
Limited Degree

This work investigates the three-dimensional elastic state of inclusions in which the prescribed stress-free transformation strains or eigenstrains are spatially nonuniform and distributed either in a Gaussian, or an exponential manner. The prescribed eigenstrain distributions are taken to be dilatational. Typical research in the micromechanics of inclusions and inhomogeneities has dealt, by and large, with spatially uniform eigenstrains and, to some limited degree, with polynomial distributions. Solutions to Eshelby’s inclusion problem, where eigenstrains are Gaussian and exponential in nature, do not exist. Such eigenstrain distributions arise naturally due to highly localized point-source type heating (typical in electronic chips), due to compositional differences, and those due to diffusion related mechanisms among others. The current paper provides such a solution for ellipsoidal shaped inclusions located in an infinite isotropic elastic matrix. It is shown, similar to the much-discussed uniform eigenstrain problem, that the elastic state is completely determined in closed form save for some simple one-dimensional integrals that are evaluated trivially using numerical quadrature. For the specialized case of a spherical shape, solutions in terms of known functions are derived and numerical results are presented. The elastic state both within and outside the inclusion is investigated. For the specific case of a sphere, the elastic strain energies are given in terms of simple formulas. Some applications of the current work in various areas such as electronics, micromechanics of composites, and material science are also discussed.

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