Fractal network model for contact conductance

Journal Article · Thu Aug 01 04:00:00 EDT 1991 · Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States)

DOI:https://doi.org/10.1115/1.2910594· OSTI ID:5697114

Majumdar, A ^[1]; Tien, C L ^[2]

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1. Arizona State Univ., Tempe (United States)
2. Univ. of California, Berkeley (United States)

The topography of rough surfaces strongly influences the conduction of heat and electricity between two surfaces in contact. Roughness measurements on a variety of surfaces have shown that their structure follows a fractal geometry whereby similar images of the surface appear under repeated magnification. Such a structure is characterized by the fractal dimension D, which lies between 2 and 3 for a surface and between 1 and 2 for a surface profile. This paper uses the fractal characterization of surface roughness to develop a new network model for analyzing heat conduction between two contacting rough surfaces. The analysis yields the simple result that the contact conductance h and the real area of contact A{sub t} are related as h {approximately} A{sub t}{sup D/2} where D is the fractal dimension of the surface profile. Contact mechanics of fractal surfaces has shown that A{sub t} varies with the load F as A{sub t} {approximately} F{sup {eta}} where {eta} ranges from 1 to 1.33 depending on the value of D. This proves that the ocnductance and load are related as h {approximately} F{sup {eta}D/2} and resolves the anomaly in previous investigations, which theoretically and experimentally obtained different values for the load exponent. The analytical results agreed well with previous experiments although there is a tendency for overprediction.

• OSTI ID: 5697114
• Journal Information: Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States), Journal Name: Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States) Vol. 113:3; ISSN 0022-1481; ISSN JHTRA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY TRANSFER
FRACTALS
FRICTION
HEAT TRANSFER
LUBRICATION
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
ROUGHNESS
SEALS
SURFACE PROPERTIES
SURFACES
THERMAL CONDUCTION
WEAR