Compact Thermal Representations for Several Fundamental Shapes in Natural Convection

2003 ◽  
Author(s):  
Kyle A. Brucker ◽  
Kyle T. Ressler ◽  
Joseph Majdalani
Keyword(s):  
Thermal Conductivity ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Heat Sink ◽  
Volume Of Fluid ◽  
Compact Representation ◽  
Canonical Forms ◽  
Design Engineers ◽  
Porous Block

In this article, general canonical forms for the effective thermal conductivities of compact heat sink models are derived using perturbation tools. The resulting approximations apply to a large number of fundamental heat sink shapes used in natural convection applications. The effective thermal conductivity is a property that can be assigned to the porous block (i.e., volume of fluid) above the heat sink base that was once occupied by the fins. The increased thermal conductivity of the fluid entering the porous block produces a reduced thermal resistance that matches that of the original heat sink. The use of a compact representation is accompanied by substantial computational savings that promote faster optimization and communication between simulation analysts and design engineers. The generalized approximations for the effective thermal conductivity presented here are numerically verified.

Compact Modeling of Unshrouded Plate Fin Heat Sinks

2003 ◽  
Author(s):  
Sridhar Narasimhan ◽  
Avram Bar-Cohen
Keyword(s):  
Thermal Conductivity ◽  
Pressure Drop ◽  
Effective Thermal Conductivity ◽  
Heat Sink ◽  
Heat Sinks ◽  
Compact Modeling ◽  
Base Temperature ◽  
Computational Domain ◽  
Porous Block ◽  
Compact Models

The present work considers the compact modeling of unshrouded parallel plate heat sinks in laminar forced convection. The computational domain includes three heat sinks in series, cooled by an intake fan. The two upstream heat sinks are represented as “porous blocks”, each with an effective thermal conductivity and a pressure loss coefficient, while the downstream heat sink, assumed to be the component requiring the most accurate characterization, is modeled in detail. A large parametric space covering three typical heat sink geometries, as well as a range of common inlet velocities, separation distances between the heat sinks, and bypass clearances is considered in the development and evaluation of the compact models. The current study uses a boundary layer-based methodology, accounting for both the viscous dissipation and form drag losses, to determine the pressure drop characteristics, and an effective conductivity methodology, using a flow bypass model and Nusselt number correlation, to determine the effective thermal conductivity, for the porous block representation of the heat sink. The results indicate that the introduction of compact heat sinks has little influence on the pressure drop of the critical heat sink. Good agreement in pressure drops, typically in the range of 5%, is also obtained between “detailed” heat sink models and their corresponding porous block representation. The introduction of the compact models is found to have little influence (typically less than 1°C) on the base temperature of the critical heat sinks. For the compact heat sinks, the agreement is again within a typical difference of 5% in thermal resistance. Dramatic improvements were observed in the mesh count (factor > 10X) and solution time (factor >20X) required to achieve a high-fidelity simulation of the velocity, pressure, and temperature fields.

Compact Thermal Representations for Several Fundamental Shapes in Forced Convection

2003 ◽  
Author(s):  
Kyle A. Brucker ◽  
Kyle T. Ressler ◽  
Joseph Majdalani
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Forced Convection ◽  
Heat Sink ◽  
Thin Sheet ◽  
Three Dimensional ◽  
Porous Space ◽  
Equivalent Thermal Conductivity ◽  
Porous Block ◽  
Dimensional Distribution

In the cooling of electronic packages, the task of simulating large arrays of heat sinks is often accomplished by the use of compact models. These simpler models attempt to capture the thermal and flow resistance characteristics of a representative heat sink while ignoring secondary detail. In the porous block model, an equivalent thermal conductivity is assigned to the fluid that enters the ‘porous’ space above the heat sink base that was once occupied by the fins. This artificially enhanced thermal conductivity enables the porous block of fluid to exhibit the same thermal resistance as that of the original heat sink. Due to the three-dimensional distribution of the thermal resistance in space, temperature maps associated with the resulting model provide better agreement with detailed numerical simulations than is possible with other models based on two-dimensional flat plate or thin sheet approximations. In this paper, we present closed-form expressions for the equivalent thermal conductivity associated with a large number of heat sink shapes in a forced convection environment.

Determining the thermal resistance of a highly insulated wall containing vacuum insulation panels through experimental, calculation and numerical simulation methods

2020 ◽  
pp. 174425912098003
Author(s):  
Travis V Moore ◽  
Cynthia A. Cruickshank ◽  
Ian Beausoleil-Morrison ◽  
Michael Lacasse
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Edge Effect ◽  
3D Simulation ◽  
Simulation Methods ◽  
Zone Method ◽  
Vacuum Insulation ◽  
Thermal Bridges ◽  
Wall Assembly

The purpose of this paper is to investigate the potential for calculation methods to determine the thermal resistance of a wall system containing vacuum insulation panels (VIPs) that has been experimentally characterised using a guarded hot box (GHB) apparatus. The VIPs used in the wall assembly have not been characterised separately to the wall assembly, and therefore exact knowledge of the thermal performance of the VIP including edge effect is not known. The calculations and simulations are completed using methods found in literature as well as manufacturer published values for the VIPs to determine the potential for calculation and simulation methods to predict the thermal resistance of the wall assembly without the exact characterisation of the VIP edge effect. The results demonstrate that disregarding the effect of VIP thermal bridges results in overestimating the thermal resistance of the wall assembly in all calculation and simulation methods, ranging from overestimates of 21% to 58%. Accounting for the VIP thermal bridges using the manufacturer advertised effective thermal conductivity of the VIPs resulted in three methods predicting the thermal resistance of the wall assembly within the uncertainty of the GHB results: the isothermal planes method, modified zone method and the 3D simulation. Of these methods only the 3D simulation can be considered a potential valid method for energy code compliance, as the isothermal planes method requires too drastic an assumption to be valid and the modified zone method requires extrapolating the zone factor beyond values which have been validated. The results of this work demonstrate that 3D simulations do show potential for use in lieu of guarded hot box testing for predicting the thermal resistance of wall assemblies containing both VIPs and steel studs. However, knowledge of the VIP effective thermal conductivity is imperative to achieve reasonable results.

Effective Thermal Conductivity of Functionally Graded Particulate Nanocomposites With Interfacial Thermal Resistance

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
H. M. Yin ◽  
G. H. Paulino ◽  
W. G. Buttlar ◽  
L. Z. Sun
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Functionally Graded ◽  
Interfacial Thermal Resistance ◽  
Conductivity Distribution ◽  
Consistent Model ◽  
The Matrix ◽  
Graded Material ◽  
Perfect Interface

By means of a fundamental solution for a single inhomogeneity embedded in a functionally graded material matrix, a self-consistent model is proposed to investigate the effective thermal conductivity distribution in a functionally graded particulate nanocomposite. The “Kapitza thermal resistance” along the interface between a particle and the matrix is simulated with a perfect interface but a lower thermal conductivity of the particle. The results indicate that the effective thermal conductivity distribution greatly depends on Kapitza thermal resistance, particle size, and degree of material gradient.

scholarly journals Effective thermal conductivity of complicated hierarchic multilayer fabric

2014 ◽  
Vol 18 (5) ◽  
pp. 1613-1618 ◽  
Author(s):  
Jie Fan ◽  
Na Zhu ◽  
Zhi Liu ◽  
Qian Cheng ◽  
Yong Liu
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Geometric Feature ◽  
Retention Efficiency

Warm retention property of fabric is one of the most important factors for clothing comfortability. The worm retention efficiency of a multilayer fabric with hierarchic inner structure was investigated based on its geometric feature. The thermal resistance of the multilayer fabric increases as the layer of the fabric increases.

Integration of Silver Heat Spreaders in LTCC utilizing Thick Silver Tape in the Co-fire Process

2015 ◽  
Vol 2015 (CICMT) ◽  
pp. 000062-000066 ◽  
Author(s):  
T. Welker ◽  
S. Günschmann ◽  
N. Gutzeit ◽  
J. Müller
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Heat Sink ◽  
Junction Temperature ◽  
Large Area ◽  
Heat Spreader ◽  
Integration Density ◽  
Heat Spreaders ◽  
Cte Mismatch ◽  
Pattern Resolution

The integration density in semiconductor devices is significantly increased in the last years. This trend is already described by Moore's law what forecasts a doubling of the integration density every two years. This evolution makes greater demands on the substrate technology which is used for the first level interconnect between the semiconductor and the device package. Higher pattern resolution is required to connect more functions on a smaller chip. Also the thermal performance of the substrate is a crucial issue. The increased integration density leads to an increased power density, what means that more heat has to dissipate on a smaller area. Thus, substrates with a high thermal conductivity (e. g. direct bonded copper (DBC)) are utilized which spread the heat over a large area. However, the reduced pattern resolution caused by thick metal layers is disadvantageous for this substrate technology. Alternatively, low temperature co-fired ceramic (LTCC) can be used. This multilayer technology provides a high pattern resolution in combination with a high integration grade. The poor thermal conductivity of LTCC (3 … 5 W*m−1*K−1) requires thermal vias made of silver paste which are placed between the power chip and the heat sink and reduce the thermal resistance of the substrate. The via-pitch and diameter is limited by the LTCC technology, what allows a maximum filling grade of approx. 20 to 25 %. Alternatively, an opening in the ceramic is created, to bond the chip directly to the heat sink. This leads to technological challenges like the CTE mismatch between the chip and the heat sink material. Expensive materials like copper molybdenum composites with matched CTE have to be used. In the presented investigation, a thick silver tape is used to form a thick silver heat spreader through the LTCC substrate. An opening is structured by laser cutting in the LTCC tape and filled with a laser cut silver tape. After lamination, the substrate is fired using a constraint sintering process. The bond strength of the silver to LTCC interface is approx. 5.6 MPa. The thermal resistance of the silver structure is measured by a thermal test chip (Delphi PST1, 2.5 mm × 2.5 mm) glued with a high thermal conducting epoxy to the silver structure. The chip contains a resistor and diodes to generate heat and to determine the junction temperature respectively. The backside of the test structure is temperature stabilized by a temperature controlled heat sink. The resulting thermal resistance is in the range of 1.1 K/W to 1.5 K/W depending on the length of silver structure (5 mm to 7 mm). Advantages of the presented heat spreader are the low thermal resistance and the good embedding capability in the co-fire LTCC process.

Effective Thermal Conductivity of Submicron Powders: A Numerical Study

2016 ◽  
Vol 846 ◽  
pp. 500-505
Author(s):  
Wei Jing Dai ◽  
Yi Xiang Gan ◽  
Dorian Hanaor
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Gas Phase ◽  
Numerical Study ◽  
Transfer Model ◽  
Size Of Particles ◽  
Contact Unit

Effective thermal conductivity is an important property of granular materials in engineering applications and industrial processes, including the blending and mixing of powders, sintering of ceramics and refractory metals, and electrochemical interactions in fuel cells and Li-ion batteries. The thermo-mechanical properties of granular materials with macroscopic particle sizes (above 1 mm) have been investigated experimentally and theoretically, but knowledge remains limited for materials consisting of micro/nanosized grains. In this work we study the effective thermal conductivity of micro/nanopowders under varying conditions of mechanical stress and gas pressure via the discrete thermal resistance method. In this proposed method, a unit cell of contact structure is regarded as one thermal resistor. Thermal transport between two contacting particles and through the gas phase (including conduction in the gas phase and heat transfer of solid-gas interfaces) are the main mechanisms. Due to the small size of particles, the gas phase is limited to a small volume and a simplified gas heat transfer model is applied considering the Knudsen number. During loading, changes in the gas volume and the contact area between particles are simulated by the finite element method. The thermal resistance of one contact unit is calculated through the combination of the heat transfer mechanisms. A simplified relationship between effective thermal conductivity and loading pressure can be obtained by integrating the contact units of the compacted powders.

Effective Thermal Conductivity of Composites with Contact Thermal Resistance between the Inclusions and the Matrix

2020 ◽  
Vol 40 (8) ◽  
pp. 622-627
Author(s):  
I. V. Lavrov ◽  
A. A. Kochetygov ◽  
V. V. Bardushkin ◽  
A. P. Sychev ◽  
V. B. Yakovlev
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Contact Thermal Resistance ◽  
The Matrix

Advanced Thermal Interface Materials

2006 ◽  
Vol 968 ◽  
Author(s):  
Yimin Zhang ◽  
Allison Xiao ◽  
Jeff McVey
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Thermal Energy ◽  
Heat Sink ◽  
Electronic Device ◽  
Thermal Interface Materials ◽  
Thermal Interface ◽  
Current State ◽  
Interface Materials ◽  
State Of Art

ABSTRACTThermal interface materials (TIMs) are used to dissipate thermal energy from a heat-generating device to a heat sink via conduction. The growing power density of the electronic device demands next-generation high thermal conductivity and/or low thermal resistance TIMs. This paper discusses the current state-of-art TIM solutions, particularly fusible particles for improved thermal conductivity. The paper will address the benefits and limitations of this approach, and describe a system with unique filler morphology. Thermal resistance and diffusivity/conductivity characterization techniques are also discussed.

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