Thermal contact conductance of elastically deforming nominally flat surfaces using fractal geometry

Abstract

Purpose -This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact. Design/methodology/approach -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. Findings -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. Originality/value -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.

Fractal model of thermal contact conductance of rough surfaces based on cone asperity

“…Thermal contact conductance (TCC) widely exists in engineering applications such as machinery manufacturing, aircraft connection structures, low-temperature superconductivity and heat exchangers (Antonetti and Yovanovich, 1988; Abuzeida and Alnumanb, 2013). Many researchers have carried out lots of studies and developed many prediction models based on sphere asperity to calculate the TCC of rough surfaces.…”

Fractal model of thermal contact conductance of rough surfaces based on elliptical asperity

“…The TCC of the joint surfaces plays a vital role in heat transfer efficiency and thermal coupling and, in extreme cases, will affect the reliability of the thermal control system and machine operation. The prediction of TCC has become a key link in many engineering fields such as mechanical manufacturing, low-temperature superconductivity, aircraft connection structures and heat exchangers (Antonetti and Yovanovich, 1988; Abuzeida and Alnumanb, 2013). Therefore, it is of great theoretical significance and practical value to acquire an ideal prediction model of the TCC of rough surfaces.…”

Fractal model of thermal contact conductance of micro-segment gear considering friction coefficient

“…Thermal contact conductance (TCC) plays a crucial role in various fields, including mechanical manufacturing, low-temperature superconductivity, aircraft connection structures and heat exchanger design (Abuzeid and Alnuman, 2013; Antonetti and Yovanovich, 1988; Zou et al , 2008; Siddappa and Tariq, 2020). Inadequate consideration of its influence may lead to inaccurate predictions of temperature distribution and thermal deformation in certain cases.…”