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Research Papers: Hydrodynamic Lubrication

Asymptotic Approximation of Laminar Lubrication Thermal Field at Low Reduced Peclet and Brinkman Number

[+] Author and Article Information
Per Johansen

Fluid Power and Mechatronic Systems,
Department of Energy Technology,
Aalborg University,
Aalborg East, 9220, Denmark
e-mail: pjo@et.aau.dk

Daniel B. Roemer

Fluid Power and Mechatronic Systems,
Department of Energy Technology,
Aalborg University,
Aalborg East, 9220, Denmark
e-mail: dbr@et.aau.dk

Torben O. Andersen

Professor
Fluid Power and Mechatronic Systems,
Department of Energy Technology,
Aalborg University,
Aalborg East, 9220, Denmark
e-mail: toa@et.aau.dk

Henrik C. Pedersen

Associate Professor
Fluid Power and Mechatronic Systems,
Department of Energy Technology,
Aalborg University,
Aalborg East, 9220, Denmark
e-mail: hcp@et.aau.dk

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received December 9, 2013; final manuscript received June 16, 2014; published online July 29, 2014. Assoc. Editor: Mihai Arghir.

J. Tribol 136(4), 041706 (Jul 29, 2014) (7 pages) Paper No: TRIB-13-1248; doi: 10.1115/1.4027957 History: Received December 09, 2013; Revised June 16, 2014

A conventional simplification of the thermal problem in fluid film lubrication analysis is performed by assuming that the main direction of heat flow is conduction through the film thickness, and thereby neglecting convection. However, in a significant amount of applications, convection is not negligible, whereby the majority of design engineers exclusively use numerical solvers. This paper presents a perturbation series expansion of the temperature field for small values of the Brinkman number. The derived perturbation solution and the more conventional analytical solution, where convection is neglected, are compared to a numerical test case. The comparison shows a significant improvement in the region where the convection term and conduction term are of the same order.

Copyright © 2014 by ASME
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References

Figures

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Fig. 1

Lubrication interface coordinate axes and length scales

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Fig. 2

Tilted piston test case

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Fig. 20

Temperature in Kelvin at x = 1

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Fig. 19

Temperature in Kelvin at x = 7/8

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Fig. 18

Temperature in Kelvin at x = 6/8

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Fig. 17

Temperature in Kelvin at x = 5/8

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Fig. 16

Temperature in Kelvin at x = 4/8

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Fig. 15

Temperature in Kelvin at x = 3/8

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Fig. 14

Temperature in Kelvin at x = 2/8

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Fig. 13

Temperature in Kelvin at x = 1/8

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Fig. 12

Temperature in Kelvin at x = 0

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Fig. 11

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 1

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Fig. 10

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 7/8

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Fig. 9

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 6/8

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Fig. 8

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 5/8

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Fig. 7

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 4/8

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Fig. 6

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 3/8

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Fig. 5

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 2/8

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Fig. 4

Ratio of mean and maximum temperature deviation to the temperature range in the cross section at x = 1/8

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Fig. 3

Tilted piston test case cross sections

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