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This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact.

The rough surfaces, known to be physical fractal, are modelled using a deterministic Cantor structure. Such structure shows several levels of imperfections and including, therefore, several scales in the constriction of the flux lines. The proposed model will study the effect of the deformation (approach) of the two rough surfaces on the TCC as a function of the remotely applied load.

An asymptotic power law, derived using approximate iterative relations, is used to express the area of contact and, consequently, the thermal conductance as a function of the applied load. The model is valid only when the approach of the two surface in contact is of the order of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results both in trend and the numerical values.

The model obtained provides further insight into the effect that surface texture has on the heat conductance process. The proposed model could be used to conduct an analytical investigation of the thermal conductance of rough surfaces in contact. This model, although simple (composed of springs), nevertheless works well.

The purpose of this study is to establish a thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory.

The effects of contact load, inclination angle, fractal dimensional and fractal roughness on thermal contact conductance of rough surfaces were studied using numerical simulation.

The results show that the thermal contact conductance of the rough surface increases with the increase of contact load and fractal dimension and decreases with the increase of fractal roughness and inclination angle. The inclination angle of the rough surface has an important influence on the thermal contact conductance of the rough, and it is a factor that cannot be ignored in the study of the thermal contact conductance of rough surfaces.

A thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory was established in this study. The achievements of this study provide some theoretical basis for the investigation of the thermal contact conductance of rough surfaces.

The purpose of this study is to present a fractal model of thermal contact conductance of rough surfaces based on elliptical asperity.

The effects of contact load, fractal dimensional, fractal roughness and eccentricity on thermal contact conductance of rough surfaces were investigated by using numerical simulation.

The results indicate that the thermal contact conductance of rough surfaces increases with the increase of the contact load, increases with the increase of the fractal dimension and decreases with the increase of the fractal roughness. The thermal contact conductance of rough surfaces increases with the increase of eccentricity. The shape of the asperity of rough surfaces has an important influence on the thermal contact conductance of rough surfaces.

A fractal model of thermal contact conductance of rough surfaces based on elliptical asperity was established in this study. The achievements of this study provide some theoretical basis for the investigation of thermal contact conductance of bolted joint surfaces.

The purpose of this study is to propose a fractal model of thermal contact conductance of rough surfaces based on axisymmetric cosinusoidal asperity.

The effects of contact load, fractal dimension, fractal roughness and friction coefficient on the thermal contact conductance of rough surfaces were investigated in this study.

The findings suggest that as the contact load increases, the thermal contact conductance of rough surfaces also increases. In addition, an increase in the fractal dimension corresponds to an increase in the thermal contact conductance. Conversely, an increase in fractal roughness leads to a decrease in thermal contact conductance. The smaller the friction coefficient, the lower the thermal contact conductance of the rough surface. In practical engineering applications, it is possible to achieve the desired thermal contact conductance of rough surfaces by selecting surfaces with appropriate roughness.

A fractal model of thermal contact conductance of rough surfaces based on axisymmetric cosinusoidal asperity was established in this study. The findings of this study offer a theoretical foundation for investigating the thermal contact conductance of rough surfaces.

The purpose of this study is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces considering substrate deformation. Three deformation modes of the asperity of the rough surface are considered, including elastic deformation, elastic–plastic deformation and full plastic deformation.

The influences of contact load, fractal dimension and fractal roughness on the TCC of the rough surface were studied.

The results show that the TCC of the rough surface increases with the increase of contact load. When D > 2.5, the larger the fractal dimension, the higher the increased rate of the TCC of the rough surface with the increase of contact load. The TCC of the rough surface increases with the increase of fractal dimension and decreases with the increase of fractal roughness. The TCC of the rough surface can be achieved by selecting a contact surface with roughness.

A fractal model of TCC of rough surfaces considering substrate deformation was established in this study. The achievements of this study provide some theoretical basis for the investigation of TCC of rough surfaces.

The purpose of this paper is to simulate in the time domain three‐dimensional electrical, thermal, mechanical coupled contact problems arising in electric resistance welding (ERW) processes.

A three‐dimensional multiphysical numerical model for analyzing contact problems is proposed. Electrical and thermal field equations in bulk domains are discretized with the cell method (CM). Welding resistance at contact interfaces is described locally by synthetic statistic parameters and contacting domains are matched together by a non‐overlapping domain decomposition method. Contact pressure distribution is resolved by a finite‐element procedure. The model is validated with 3D FEM software package.

The semi‐analytical model describing the electric and thermal resistances at contact interfaces can be easily embedded in CM formulations, where problem variables are expressed directly in integral form. Compatibility conditions between contact members are enforced by a domain decomposition approach. System conditioning and computing time are improved by a solution strategy based on the Schur complement method.

The electrical‐thermal analysis is not coupled strongly with the mechanical analysis and contact pressure distribution is assumed to be not depending on thermal stresses, which can be considerable near the contact area where localized joule heating occurs.

Resistance welding processes involve mechanical, electrical, and thermal non‐linear coupled effects that cannot be simulated by standard commercial software packages. The proposed numerical model can be used instead for designing and optimizing ERW processes.

The paper shows that numerical modeling of ERW processes requires a careful prediction of the localized joule heating occurring at the electrode‐material interface. This effect is reconstructed by the proposed approach simulating coupled electrical, thermal, and mechanical effects on different spatial scales.

The purpose of the present research is to examine very small-sized samples of approximately 2-mm diameters. For samples of this size, the holder must make contact with the entire perimeter surface of the sample, and the sample is held in place by friction. This necessitates a mathematical model for the direct solution which accommodates the holder and a contact resistance between the holder and the sample.

Most flash diffusivity testing is performed on samples which are nominally 12-13 mm in diameter and are held by only a small contact area around the perimeter of the sample in a holder. With an experiment set up in this way, the effects of conduction between the sample and the holder are normally ignored.

This research examines the effects of the holder and the contact resistance on the measured thermal diffusivity of the sample and includes experimental results from laboratory measurements.

This work provides a method for finding thermal diffusivity for extremely small samples. This capability is important in cases involving precious materials or highly toxic materials where only small samples are available.

The purpose of this paper is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces based on cone asperity.

A detailed numerical study is conducted to examine the effects of contact load, fractal dimensional, fractal roughness and material properties on the TCC of rough surfaces.

The results indicate that when the fractal dimension D is less than 2.5, the TCC of rough surfaces increases nonlinearly with the increase of the contact load. However, when the fractal dimension D is greater than or equal to 2.5, the TCC of rough surfaces increases linearly with the increase of the contact load; the TCC of the rough surfaces increases with the increase of the fractal dimension D and the decrease of the fractal roughness G; the material parameters also have an influence on the TCC of the rough surfaces, and the extent of the effect on the TCC is related to the fractal dimension D.

A fractal model of TCC of rough surfaces based on cone asperity is established in this paper. Some new results and conclusions are obtained from this work, which provides important theoretical guidance for further study of TCC of rough surfaces.

Surface configuration at the interface between two materials makes a huge difference on thermal resistance. Thermal transient analysis is a powerful tool for thermal characterization of complex structures like LEDs. The purpose of this paper is to report the influence of surface finish on thermal resistance.

Surface of heat sink was modified into two categories: machined as channel like structure; and polished using mechanical polisher and tested with 3W green LED for thermal resistance analysis.

The observed surface roughness of rough and polished surface was 44 nm and 4 nm, respectively. Structure function analysis was used to determine the thermal resistance between heat sink and MCPCB board. The observed thermal resistance from junction to ambient (R_thJA) value measured with thermal paste at 700 mA was lower (34.85 K/W) for channel like surface than rough surface (36.5 K/W). The calculated junction temperature (T_J) for channel like surface and polished surface was 81.29°C and 85.24°C, respectively.

Channelled surface aids in increasing bond line thickness. Surface polishing helps to reduce the air gaps between MCPCB and heat sink and also to increase the surface contact conductance.

The proposed method of surface modification can be easily done at laboratory level with locally available techniques.

Much of the available literature is only concentrating on the design modification and heat transfer from fins to ambient. There was little research on modification of top surface of the heat sink and the proposed concept would give good results and also it will make the material cost reduction as well as material too.

The purpose of this study is to propose a fractal model of thermal contact conductance (TCC) of two spherical joint surfaces, considering friction coefficient based on the three-dimensional fractal theory.

The effects of friction coefficient, fractal parameters, radius of curvature and contact type on TCC were analyzed using numerical simulation.

The results indicate that the TCC decreases with the increase of friction coefficient and fractal roughness and increases with the increase of fractal dimension and radius of curvature; the contact type of two spherical joint surfaces has an important influence on the TCC, and the TCC of external contact is smaller than that of internal contact under the same contact load.

A fractal model of TCC of two spherical joint surfaces considering friction coefficient is proposed in this paper. Achievements of this work provide some theoretical basis for the research of TCC of bearings and other curved surfaces.