Thermal Characterization of High-Density Interconnects in the Form of Equivalent Thermal Conductivity

2009 ◽  
Author(s):  
Wataru Nakayama ◽  
Katsuhiro Koizumi ◽  
Takashi Fukue ◽  
Masaru Ishizuka ◽  
Tatsuya Nakajima ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Flow ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Thermal Characterization ◽  
High Density ◽  
Cooperative Effort ◽  
Equivalent Thermal Conductivity ◽  
Metal Pattern

The issue addressed in the present study is how to model wiring substrates to perform heat conduction analysis on moderate computational resource. Equivalent thermal conductivity is a convenient measure in thermal modeling. However, its notion needs re-examination where higher accuracy of heat conduction analysis is pursued. Proposed is a scheme where the indexed volumetric metal contents are used to estimate the equivalent conductivity of representative volume element (RVE). The index is designed to reflect the effect of metal pattern on heat flow through RVE. In order to illustrate the core concept we report the analysis performed on template models of high-density interconnect (HDI) substrates. The element of HDI contains copper in several forms; through-via, continuous plane, and cross wires. Five heat flow directions are assumed; two are linear and three are right-angled turn. From combinations of the metal pattern and the heat flow direction twenty five templates are created, then, they are subjected to detailed numerical analysis. The values of equivalent thermal conductivity derived from the numerical solutions reveal that the gross volumetric metal content is totally inadequate as a parameter of thermal characterization. The paper also outlines the overall organization of our analysis system which is being developed in an industry-academia cooperative effort under the auspices of JSME.

Algebraically Explicit Analytical Solutions of Unsteady Conduction With Variable Thermal Properties in Spheroidal Coordinates

2004 ◽  
Author(s):  
Ruixian Cai ◽  
Na Zhang
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Heat Conduction ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Spherical Coordinates ◽  
Rectangular Coordinates ◽  
Conduction Theory ◽  
Unsteady Heat Conduction ◽  
Spheroidal Coordinates

The analytical solutions of unsteady heat conduction with variable thermal properties (thermal conductivity, density and specific heat are functions of temperature or coordinates) are meaningful in theory. In addition, they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes, grid generation methods and so forth. Such solutions in rectangular coordinates have been derived by the authors; some other solutions for unsteady point symmetrical heat conduction in spherical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.

scholarly journals Calculation of Boil-Off Gas (BOG) Generation of KC-1 Membrane LNG Tank with High Density Rigid Polyurethane Foam by Numerical Analysis

2017 ◽  
Vol 24 (1) ◽  
pp. 100-114 ◽  
Author(s):  
Hyeonwon Jeong ◽  
W. Jaewoo Shim
Keyword(s):  
Thermal Conductivity ◽  
Polyurethane Foam ◽  
The United States ◽  
Coast Guard ◽  
High Density ◽  
Heat Transfer Analysis ◽  
Internal Boundary ◽  
Rigid Polyurethane Foam ◽  
Equivalent Thermal Conductivity ◽  
Lng Tank

Abstract Recently, a new type of LNG tank named “KC-1 membrane LNG tank” has been developed by Korean Gas Corporation (KOGAS), and Samsung Heavy Industries (SHI) is currently building KC-1 membrane type LNG carriers. Unlike other LNG tanks, the KC-1 membrane LNG tank has a single-insulation structure rather than a double-insulation structure. For a given tank’s boundary condition, heat transfer analysis is performed from the external to the internal environment of the LNG tank by numerical simulation for three tanks. In each tank, the main thermally resistant layer of insulation is assembled with a High density rigid Polyurethane Foam (H-PUF), which is blown with one of three different types of hydrofluorocarbons-namely-HFC-365mfc, 245fa, and 245fa-e (enhanced). Advantage of such blowing agents is that it has a lower Ozone Depletion Potential (ODP) than HCFC-141b or carbon dioxide (CO2) that has been used in the past as well as having low thermal conductivity. A Reduced Order Model is utilized to a 3-dimensional section of the insulation to calculate equivalent thermal conductivity. The equivalent thermal conductivity of the insulation is then applied to the rest of LNG tank, reducing the size of tank simulation domain as well as computation time. Tank’s two external and internal boundary conditions used are those defined by the International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk (IGC) and the United States Coast Guard (USCG) conditions. Boil-off Rate (BOR) of the tank that has the insulation with H-PUF blown with HFC-245fa resulted in 0.0927 %/day and 0.0745 %/day for IGC and USCG conditions, respectively.

scholarly journals Preparation of Anisotropic Aerogels with Pristine Graphene by Heat Flow and Study of Their Effects on Heat Transfer in Paraffin

Nanomaterials ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 1622 ◽  
Author(s):  
Jinhui Huang ◽  
Buning Zhang ◽  
Ming He ◽  
Xue Huang ◽  
Guoqiang Yin ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Flow ◽  
Flow Direction ◽  
Structural Characteristics ◽  
Low Cost ◽  
Microwave Treatment ◽  
Thermal Conductivity Enhancement ◽  
Graphene Sheets ◽  
Pristine Graphene ◽  
Conductivity Enhancement

In this study, anisotropic graphene/graphene oxide (GO) aerogels (AGAs) were obtained by freeze-drying after direct participation of pristine graphene in the self-assembly of anisotropic gel by the heat flow method. After vacuum microwave treatment, the physical, chemical and structural characteristics of the AGAs were investigated. The results show that AGAs, in which the internal graphene sheets are parallel to the heat flow direction, are successfully prepared. After microwave treatment, the amount of oxygen and nitrogen reduces significantly and the sp2 domain increases. However, at the same time, many fragments and holes are generated in the graphene sheets. The effects of AGAs on the phase transition of paraffin is studied, and the results show that the melting enthalpy, solidification enthalpy and initial melting temperature of AGA/paraffin composites decreases as the GO content in the AGAs increases, whereas the melting range, solidifying range and subcooling degree increases. The highest axial thermal conductivity of the AGA/paraffin composite is 1.45 W/(mK), and the thermal conductivity enhancement efficiency is 884% (AGA content was 0.53 vol %). Compared with previously investigated, similar AGA/paraffin composites, the aerogels fabricated in this study have the obvious advantages of a simple fabrication process, a low cost and a high thermal conductivity enhancement efficiency. These aerogels possess the potential for application in phase-change energy storage (PES), thermal energy management and other fields.

Umklapp collisions and thermal conductivity

2021 ◽  
pp. 309-321
Author(s):  
Geoffrey Brooker
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Flow ◽  
Group Velocity ◽  
Thermodynamic Equilibrium ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Momentum Balance ◽  
Lattice Vector ◽  
Phonon Group Velocity

“Umklapp collisions and thermal conductivity” deals with heat conduction in a dielectric solid. Collisions of phonons are divided into Umklapp and normal according as a reciprocal lattice vector is or is not involved in the phonon momentum balance. A local temperature is defined by appeal to local thermodynamic equilibrium. An equilibrium phonon distribution can be off-centred, yet non-decaying, if the only collisions are “normal”, conserving the total phonon momentum. Then heat flow does not decay, even if a representative collision reverses the phonon group velocity. Conversely, in an Umklapp collision it is the non-conservation of phonon momentum that causes heat flow to decay.

scholarly journals Stationary heat conduction in a solid with functionally graded thermal properties

2019 ◽  
Vol 28 (4) ◽  
pp. 539-546
Author(s):  
Vazgen Bagdasaryan ◽  
Jan Szołucha
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Heat Conduction ◽  
Finite Difference Method ◽  
Numerical Solutions ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Stationary Heat ◽  
Stationary Heat Conduction ◽  
The Finite Difference Method

In the paper the solutions for stationary heat conduction in a two dimensional composite with functionally graded heat properties were obtained. Numerical solutions for the taken boundary conditions are shown for several types of changes of composite’s thermal conductivity. The solutions were obtained with the use of the finite-difference method.

THERMAL PERFORMANCE OF PANELS WITH HIGH DENSITY, RANDOMLY ORIENTED STRAW BALES

2018 ◽  
Vol 13 (1) ◽  
pp. 31-55 ◽  
Author(s):  
Sarah Seitz ◽  
Kyle Beaudry ◽  
Colin MacDougall
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Heat Flow ◽  
Experimental Error ◽  
High Density ◽  
Normal Density ◽  
Wall Panels ◽  
Lime Plaster ◽  
Straw Bale ◽  
Measured Thermal Conductivity

This paper describes the hot-box testing (based on ASTM C1363-11) of seven straw bale wall panels to obtain their thermal conductivity values. All panels were constructed with stacked bales and cement-lime plaster skins on each side of the bales. Four panels were made with traditional, 2-string field bales of densities ranging from 89.5 kg/m3–131 kg/m3 and with the bales on-edge (fibres perpendicular to the heat flow). Three panels were made with manufactured high-density bales (291 kg/m3–372 kg/m3). The fibres of the manufactured bales were randomly oriented. The key conclusion of this paper is that within the experimental error, there is no difference in the thermal conductivity value for panels using normal density bales and manufactured high density bales up to a density of 333 kg/m3. However, because of lack of precision of the hot-box, no conclusions can be made on the true thermal conductivity of the high density bale panels. In addition, the panels tested were found to have significant voids between bales, and this is believed to have contributed to higher measured thermal conductivity values compared to those reported in the literature for normal density bale panels. Thermal properties may be affected for bales with higher densities than 333 kg/m3, therefore further testing is suggested.

Modeling of Two-Dimensional Orthotropic Heat Conduction in Porous Gypsum

2015 ◽  
Vol 820 ◽  
pp. 520-525
Author(s):  
Carlos R.N. Souza ◽  
José P. Alencar ◽  
Alan Christie Silva Dantas ◽  
Andrea V. Ferraz ◽  
Nelson C. Olivier
Keyword(s):  
Thermal Conductivity ◽  
Numerical Modeling ◽  
Heat Conduction ◽  
Steady State ◽  
Heat Flow ◽  
Computer Simulations ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Hot Plate ◽  
Plate Method

The gypsum is a versatile material that shows low thermal conductivity, which makes this material very suitable for application as thermal insulation. The increase of the porosity of gypsum bodies promotes a decrease on the thermal conductivity. This effect optimize the range of applications of gypsum on the thermal insulate field. The present study aimed the numerical modeling of two-dimensional heat conduction by finite differences in a steady state to evaluate the ortotrophy of the thermal conductivity of porous gypsum using the elements of the protected hot plate method. Computer simulations were performed using thermal conductivity of the gypsum equal to 0.35 W/m.K. This value was varied on the x and y directions by 5%, 10% and 15%. The heat flow applied to the numerical simulations were equal 75 W/m2, 100 W/m2 to 125 W/m2.It was possible to produce temperature profiles where is visible the displacement of isotherms as a function of the change in thermal conductivity in the x direction.

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