Erratum: “A Scattering-Mediated Acoustic Mismatch Model for the Prediction of Thermal Boundary Resistance” [ASME J. Heat Transfer, 123, No. 1, pp. 105–112]

Abstract Solid-solid thermal boundary resistance (Rb) plays an important role in determining the heat flow between materials. The acoustic mismatch model (AMM) and the diffuse mismatch model (DMM), work pretty well in describing and predicting the thermal energy transport at solid-solid interface at very low temperatures (in the range of few Kelvin). At moderate cryogenic temperatures they do not perform that well, and the reason may be attributed to the dominance of scattering in determining Rb. Scattering mediated acoustic mismatch model (SMAMM) was developed on this principle. Though SMAMM works well, it has some fundamental problems. SMAMM’s assumption of U-processes, for amorphous layer formed between materials, is physically unexplainable. It also assumes unrealistically small scattering time. We propose a modified version of SMAMM called Amorphous SMAMM, which takes into account amorphous material properties for the interstitial layer formed, to find the scattering time to be used in SMAMM. This model performs better than all the models in the range of 25 to 60 K in predicting Rb. Above this temperature, original SMAMM performs better, but Amorphous SMAMM always performs better than the AMM. Amorphous SMAMM does not run into any physical problems with the assumptions made, hence the results have a better physical significance than SMAMM’s.

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Heat Transfer at Aluminum–Water Interfaces: Effect of Surface Roughness

Journal of Nanotechnology in Engineering and Medicine ◽

10.1115/1.4007584 ◽

2012 ◽

Vol 3 (3) ◽

Cited By ~ 4

Author(s):

H. Sam Huang ◽

Vikas Varshney ◽

Jennifer L. Wohlwend ◽

Ajit K. Roy

Keyword(s):

Heat Transfer ◽

Surface Roughness ◽

Finite Element ◽

Md Simulations ◽

Boundary Resistance ◽

Thermal Boundary Resistance ◽

Mesoscopic Scale ◽

Macroscopic Scale ◽

Microscopic Scale ◽

Thermal Boundary Conductance

In this paper, we studied the effect of microscopic surface roughness on heat transfer between aluminum and water by molecular dynamic (MD) simulations and macroscopic surface roughness on heat transfer between aluminum and water by finite element (FE) method. It was observed that as the microscopic scale surface roughness increases, the thermal boundary conductance increases. At the macroscopic scale, different degrees of surface roughness were studied by finite element method. The heat transfer was observed to enhance as the surface roughness increases. Based on the studies of thermal boundary conductance as a function of system size at the molecular level, a procedure was proposed to obtain the thermal boundary conductance at the mesoscopic scale. The thermal boundary resistance at the microscopic scale obtained by MD simulations and the thermal boundary resistance at the mesoscopic scale obtained by the extrapolation procedure can be included and implemented at the interfacial elements in the finite element method at the macroscopic scale. This provides us a useful model, in which different scales of surface roughness can be included, for heat transfer analysis.

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Measurement and Prediction of the Contact Conductance Across Epoxied Copper Contacts at Cryogenic Temperatures

10.1115/imece2000-1386 ◽

2000 ◽

Author(s):

Lisa De Bellis ◽

Patrick E. Phelan

Keyword(s):

Experimental Data ◽

Thermal Conductivity ◽

Boundary Resistance ◽

Thermal Boundary Resistance ◽

Cryogenic Temperatures ◽

Contact Conductance ◽

Acoustic Mismatch ◽

Model Predictions ◽

Experimental Values ◽

Scattering Time

Abstract Literature has demonstrated that the investigation of the contact conductance (hc) across epoxied joints at cryogenic temperatures is important to the microelectronic, satellite and other space industries. The accurate theoretical prediction of the hc arising across a metal-epoxy interface is still being researched. Several researchers have shown that the acoustic mismatch and other theories do not agree well with experimental data. This paper presents the results of an experimental and theoretical investigation of the hc across copper/epoxy/copper contacts. From the hc data, it was possible to extract the thermal conductivity (k) of the epoxy and the thermal boundary resistance (Rb) between the epoxy and copper. The Rb extracted from the experimental data was compared to model predictions made by the Acoustic Mismatch Model (AMM) and the Scattering Mediated Acoustic Mismatch Model (SMAMM). In the case of the AMM, the predictions underestimated the experimental values significantly. This finding is consistent with many investigations to date. The SMAMM was able to predict the experimental data very well when using an extremely small scattering time of 5×10−18 s.

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A Scattering-Mediated Acoustic Mismatch Model for the Prediction of Thermal Boundary Resistance

Journal of Heat Transfer ◽

10.1115/1.1338138 ◽

2000 ◽

Vol 123 (1) ◽

pp. 105-112 ◽

Cited By ~ 74

Author(s):

Ravi S. Prasher ◽

Patrick E. Phelan

Keyword(s):

Large Scale ◽

Dominant Role ◽

Phonon Transport ◽

Boundary Resistance ◽

Thermal Boundary Resistance ◽

Dielectric Substrates ◽

Solid Interface ◽

The Past ◽

Acoustic Mismatch ◽

Integrated Circuitry

Solid-solid thermal boundary resistance Rb plays an important role in determining heat flow, both in cryogenic and room-temperature applications, such as very large scale integrated circuitry, superlattices, and superconductors. The acoustic mismatch model (AMM) and the related diffuse mismatch model (DMM) describe the thermal transport at a solid-solid interface below a few Kelvin quite accurately. At moderate cryogenic temperatures and above, Rb is dominated by scattering caused by various sources, such as damage in the dielectric substrates and formation of an imperfect boundary layer near the interface, making Rb larger than that predicted by AMM and DMM. From a careful review of the literature on Rb, it seems that scattering near the interface plays a far more dominant role than any other mechanism. Though scattering near the interface has been considered in the past, these models are either far too complicated or are too simple (i.e., inaccurate) for engineering use. A new model, called the scattering-mediated acoustic mismatch model (SMAMM), is developed here that exploits the analogy between phonon and radiative transport by developing a damped wave equation to describe the phonon transport. Incorporating scattering into this equation and finding appropriate solutions for a solid-solid interface enable an accurate description of Rb at high temperatures, while still reducing to the AMM at low temperatures, where the AMM is relatively successful in predicting Rb.

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