Review of Thermal Joint Resistance Models for Nonconforming Rough Surfaces

2006 ◽  
Vol 59 (1) ◽  
pp. 1-12 ◽  
Author(s):  
M. Bahrami ◽  
J. R. Culham ◽  
M. M. Yananovich ◽  
G. E. Schneider
Keyword(s):  
Experimental Data ◽  
Flux Tube ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Thermal Analyses ◽  
Theoretical Models ◽  
Empirical Correlations ◽  
Data Points ◽  
The Mean ◽  
Circular Heat

The thermal contact resistance (TCR) in a vacuum is studied. The TCR problem is divided into three different parts: geometrical, mechanical, and thermal. Each problem includes a macro- and microscale subproblem; existing theories and models for each part are reviewed. Empirical correlations for microhardness, and the equivalent (sum) rough surface approximation, are discussed. Suggested correlations for estimating the mean absolute surface slope are summarized and compared with experimental data. The most common assumptions of existing thermal analyses are summarized. As basic elements of thermal analyses, spreading resistance of a circular heat source on a half-space and flux tube are reviewed; also existing flux tube correlations are compared. More than 400 TCR data points collected by different researchers during the last 40years are grouped into two limiting cases: conforming rough and elastoconstriction. Existing TCR models are reviewed and compared with the experimental data at these two limits. It is shown that the existing theoretical models do not cover both of the above-mentioned limiting cases. This review article cites 58 references.

Review of Thermal Joint Resistance Models for Non-Conforming Rough Surfaces in a Vacuum

2003 ◽  
Author(s):  
M. Bahrami ◽  
J. R. Culham ◽  
M. M. Yovanovich ◽  
G. E. Schneider
Keyword(s):  
Experimental Data ◽  
Thermal Analysis ◽  
Flux Tube ◽  
Thermal Contact ◽  
Theoretical Models ◽  
Size Number ◽  
Data Points ◽  
Contact Models ◽  
The Mean ◽  
Contact Parameters

The thermal contact resistance (TCR) problem is categorized into three different problems: geometrical, mechanical, and thermal. Each problem includes a macro and micro scale sub-problem; existing theories and models for each part are reviewed. Empirical correlations for microhardness, and the equivalent (sum) rough surface approximation are discussed. Suggested correlations for estimating the mean absolute surface slope are summarized and compared with experimental data. The classical conforming rough contact models, i.e elastic and plastic, as well as elastoplastic models are reviewed. A set of scale (dimensionless) relationships are derived for the contact parameters, i.e. the mean microcontact size, number of micro-contacts, density of microcontacts, and the external load as functions of dimensionless separation, for the above models. These scale relationships are plotted; it is graphically shown that the behavior of these models, in terms of the contact parameters, are similar. The most common assumptions of existing thermal analysis are summarized. As basic elements of thermal analysis, spreading resistance of a circular heat source on a half-space and flux tube are reviewed, also existing flux tube correlations are compared. More than 400 TCR data points collected by different re-searchers during last forty years are grouped into two limiting cases: conforming rough, and elasto-constriction. Existing TCR models are reviewed and compared with the experimental data at these two limits. It is shown that the existing theoretical models do not cover both of the above-mentioned limiting cases.

A Scale Analysis Approach to Thermal Contact Resistance

2003 ◽  
Author(s):  
M. Bahrami ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
Contact Resistance ◽  
Entire Range ◽  
Thermal Contact Resistance ◽  
Present Model ◽  
Thermal Contact ◽  
Scale Analysis ◽  
Metal Contacts ◽  
Novel Approach ◽  
Wide Range ◽  
Data Points

A new analytical model is developed for predicting thermal contact resistance (TCR) of non-conforming rough contacts of bare solids in a vacuum. Instead of using probability relationships to model the size and number of microcontacts of Gaussian surfaces, a novel approach by employing the “scale analysis methods” is taken. It is shown that the mean size of the microcontacts is proportional to the surface roughness and inversely proportional to the surface asperity slope. A general relationship for determining TCR is derived by superposition of the macro and the effective micro thermal resistances. The present model allows TCR to be predicted over the entire range of non-conforming rough contacts from conforming rough to smooth Hertzian contacts. It is demonstrated that the geometry of heat sources on a half-space for microcontacts is justifiable and that effective micro thermal resistance is not a function of surface curvature. A comparison of the present model with 604 experimental data points, collected by many researchers during the last forty years, shows good agreement for the entire range of TCR. The data covers a wide range of materials, mechanical and thermophysical properties, micro and macro contact geometries, and similar and dissimilar metal contacts.

Statistical and Theoretical Models of Ingestion Through Turbine Rim Seals

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Kunyuan Zhou ◽  
Simon N. Wood ◽  
J. Michael Owen
Keyword(s):  
Experimental Data ◽  
Statistical Model ◽  
Flow Parameter ◽  
Likelihood Estimation ◽  
Theoretical Models ◽  
Operating Conditions ◽  
Data Points ◽  
Effects Of Rotation ◽  
Effectiveness Data ◽  
Good Agreement

In recent papers, orifice models have been developed to calculate the amount of ingestion, or ingress, that occurs through gas-turbine rim seals. These theoretical models can be used for externally induced (EI) ingress, where the pressure differences in the main gas path are dominant, and for rotationally induced (RI) ingress, where the effects of rotation in the wheel space are dominant. Explicit “effectiveness equations,” derived from the orifice models, are used to express the flow rate of sealing air in terms of the sealing effectiveness. These equations contain two unknown terms: Φmin, a sealing flow parameter, and Γc, the ratio of the discharge coefficients for ingress and egress. The two unknowns can be determined from concentration measurements in experimental rigs. In this paper, maximum likelihood estimation is used to fit the effectiveness equations to experimental data and to determine the optimum values of Φmin and Γc. The statistical model is validated numerically using noisy data generated from the effectiveness equations, and the simulated tests show the dangers of drawing conclusions from sparse data points. Using the statistical model, good agreement between the theoretical curves and several sets of previously published effectiveness data is achieved for both EI and RI ingress. The statistical and theoretical models have also been used to analyze previously unpublished experimental data, the results of which are included in separate papers. It is the ultimate aim of this research to apply the effectiveness data obtained at rig conditions to engine-operating conditions.

A Unified Microscopic and Macroscopic Thermal Contact Resistance Model

2006 ◽  
Author(s):  
Ravi Prasher ◽  
Patrick Phelan
Keyword(s):  
Contact Resistance ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Mean Free Path ◽  
Characteristic Dimension ◽  
Constriction Resistance ◽  
Acoustic Mismatch ◽  
The Mean ◽  
Two Sides ◽  
Heat Carriers

There are two types of thermal contact resistance at the interface of two solids. One of them is due to the constriction of heat flow lines at the interface, commonly known as thermal contact resistance. The other type of constriction resistance is microscopic in nature. If the characteristic dimension of the constriction becomes comparable to the mean free path of the heat carriers then there is a ballistic component to the constriction resistance. For different materials on the two sides, thermal boundary resistance due to acoustic mismatch becomes important. In this paper a unified model is developed which accounts for both microscopic and macroscopic contact resistances.

Surface Chemistry and Characteristics Based Model for the Thermal Contact Resistance of Fluidic Interstitial Thermal Interface Materials

2001 ◽  
Vol 123 (5) ◽  
pp. 969-975 ◽  
Author(s):  
Ravi S. Prasher
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Contact Resistance ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Thermal Interface Materials ◽  
Heat Spreader ◽  
Thermal Interface ◽  
Thermal Solution ◽  
Interface Materials

Microprocessor powers are increasing at a phenomenal rate, which requires very small thermal resistance between the die (chip) and the ambient, if the current economical methods of conduction and convection cooling are to be utilized. A typical thermal solution in flip chip technology utilizes two levels of thermal interface materials: between the die and the heat spreader, and between the heat spreader and the heat sink. Phase change materials and thermal greases are among the most prominent interstitial thermal interface materials (TIM) used in electronic packaging. These TIMs are typically polymeric matrix loaded with highly conducting filler particles. The dwindling thermal budget has necessitated a better understanding of the thermal resistance of each component of the thermal solution. Thermal conductivity of these particle-laden materials is better understood than their contact resistance. A careful review of the literature reveals the lack of analytical models for the prediction of contact resistance of these types of interstitial materials, which possess fluidic properties. This paper introduces an analytical model for the thermal contact resistance of these types of interstitial materials. This model is compared with the experimental data obtained on the contact resistance of these TIMs. The model, which depends on parameters such as, surface tension, contact angle, thermal conductivity, roughness and pressure matches very well with the experimental data at low pressures and is still within the error bars at higher pressures.

Modeling Thermal Contact Resistance: A Scale Analysis Approach

2004 ◽  
Vol 126 (6) ◽  
pp. 896-905 ◽  
Author(s):  
M. Bahrami ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
Contact Resistance ◽  
Contact Pressure ◽  
Thermal Contact Resistance ◽  
Present Model ◽  
Thermal Contact ◽  
Scale Analysis ◽  
Novel Approach ◽  
Wide Range ◽  
Applicable Range ◽  
Data Points

A compact analytical model is developed for predicting thermal contact resistance (TCR) of nonconforming rough contacts of bare solids in a vacuum. Instead of using probability relationships to model the size and number of microcontacts of Gaussian surfaces, a novel approach is taken by employing the “scale analysis method.” It is demonstrated that the geometry of heat sources on a half-space for microcontacts is justifiable for an applicable range of contact pressure. It is shown that the surface curvature and contact pressure distribution have no effect on the effective microthermal resistance. The present model allows TCR to be predicted over the entire range of nonconforming rough contacts from conforming rough to smooth Hertzian contacts. A new nondimensional parameter, i.e., ratio of the macro- over microthermal resistances, is introduced as a criterion to identify three regions of TCR. The present model is compared to collected TCR data for SS304 and showed excellent agreement. Additionally, more than 880 experimental data points, collected by many researchers, are summarized and compared to the present model, and relatively good agreement is observed. The data cover a wide range of materials, mechanical and thermophysical properties, micro- and macrocontact geometries, and similar and dissimilar metal contacts.

Thermal Resistance of Pressed Contacts between Steel Surfaces: Influence of Oxide Films

1979 ◽  
Vol 21 (3) ◽  
pp. 159-166 ◽  
Author(s):  
M. N. Mian ◽  
F. R. Al-Astrabadi ◽  
P. W. O'Callaghan ◽  
S. D. Probert
Keyword(s):  
Surface Roughness ◽  
Statistical Analysis ◽  
Film Thickness ◽  
Thermal Resistance ◽  
Applied Load ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Experimental Measurements ◽  
The Mean ◽  
Steel Surfaces

Flat, rough surfaces of steel specimens were oxidized and subsequently pressed into contact. From a statistical analysis of the experimental measurements for freshly-assembled contacts, an expression has been established relating the loading pressure, mean roughness of the two surfaces and oxide film thicknesses to the thermal resistance of the contacts in high vacua. The thermal contact resistance increased with (i) the film thickness and (ii) the ratio of the total film thickness to the mean surface roughness, and decreased with the loading pressure and the mean surface roughness. Increasing and decreasing the applied load revealed a slight hysteresis effect.

scholarly journals Estimating the Maximum Splat Diameter of a Solidifying Droplet

1999 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Contact Angle ◽  
Simple Model ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Simple Analytical Model ◽  
Droplet Spreading ◽  
Isothermal Model ◽  
High Reynolds

Abstract We present a simple analytical model for the estimation of the maximum splat diameter of an impacting droplet on a subcooled target. This work is an extension of the isothermal model of Pasandideh-Fard et al. (1996). The model uses an energy conservation argument, applied between the initial and final drop configurations, to approximately capture the dynamics of spreading. The effects of viscous dissipation, surface tension, and contact angle are taken into account. Tests against limited experimental data at high Reynolds and Weber numbers indicate that an accuracy of the order of 5% is achieved with no adjustable parameters required. Agreement with experimental data in the limit We → ∞ is also very good. We additionally propose a simple model for the estimation of the thickness of the freezing layer developed at the droplet-substrate contact during droplet spreading. This model accounts for the effect of thermal contact resistance and its predictions compare favorably with experimental data.

scholarly journals Effect of Compression on the Effective Thermal Conductivity and Thermal Contact Resistance in PEM Fuel Cell Gas Diffusion Layers

2010 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Ned Djilali ◽  
Majid Bahrami
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Fuel Cell ◽  
Contact Resistance ◽  
Effective Thermal Conductivity ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Pem Fuel Cell ◽  
Gas Diffusion ◽  
Analytical Models

Heat transfer through the gas diffusion layer (GDL) of a PEM fuel cell is a key process in the design and operation a PEM fuel cell. The analysis of this process requires determination of the effective thermal conductivity as well as the thermal contact resistance between the GDL and adjacent surfaces/layers. In the present study, a guarded-hot-plate apparatus has been designed and built to measure the effective thermal conductivity and thermal contact resistance in GDLs under vacuum and atmospheric pressure. Toray carbon papers with the porosity of 78% and different thicknesses are used in the experiments under a wide range of compressive loads. Moreover, novel analytical models are developed for the effective thermal conductivity and thermal contact resistance and compared against the present experimental data. Results show good agreements between the experimental data and the analytical models. It is observed that the thermal contact resistance is the dominant component of the total thermal resistance and neglecting this phenomenon may result in enormous errors.

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