Asymptotic approximation of laminar lubrication thermal field at low reduced peclet and Brinkman number

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7 Citations (Scopus)

Abstract

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.
Original languageEnglish
Article numberTRIB-13-1248
JournalJournal of Tribology
Volume136
Issue number4
Number of pages7
ISSN0742-4787
DOIs
Publication statusPublished - 2014

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Brinkman number
Peclet number
lubrication
Lubrication
convection
approximation
fluid films
conduction
Heat problems
perturbation
series expansion
simplification
heat transmission
engineers
Film thickness
Temperature distribution
temperature distribution
film thickness
Heat transfer
Engineers

Cite this

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title = "Asymptotic approximation of laminar lubrication thermal field at low reduced peclet and Brinkman number",
abstract = "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.",
author = "Per Johansen and Roemer, {Daniel Beck} and Andersen, {Torben Ole} and Pedersen, {Henrik C.}",
year = "2014",
doi = "10.1115/1.4027957",
language = "English",
volume = "136",
journal = "Journal of Tribology",
issn = "0742-4787",
publisher = "American Society of Mechanical Engineers",
number = "4",

}

Asymptotic approximation of laminar lubrication thermal field at low reduced peclet and Brinkman number. / Johansen, Per; Roemer, Daniel Beck; Andersen, Torben Ole; Pedersen, Henrik C.

In: Journal of Tribology, Vol. 136, No. 4, TRIB-13-1248, 2014.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Asymptotic approximation of laminar lubrication thermal field at low reduced peclet and Brinkman number

AU - Johansen, Per

AU - Roemer, Daniel Beck

AU - Andersen, Torben Ole

AU - Pedersen, Henrik C.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1115/1.4027957

DO - 10.1115/1.4027957

M3 - Journal article

VL - 136

JO - Journal of Tribology

JF - Journal of Tribology

SN - 0742-4787

IS - 4

M1 - TRIB-13-1248

ER -