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.

References

References
1.
Kudish
,
I. I.
, and
Covitch
,
M. J.
,
2010
,
Modeling and Analytical Methods in Tribology
,
Chapman & Hall/CRC
,
Boca Raton, FL
.
2.
Kudish
,
I. I.
,
2013
,
Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches
,
CRC Press
,
Boca Raton, FL
.
3.
Laraqi
,
N.
,
Rashidi
,
M.
,
de Maria
,
J. G.
, and
Baïri
,
A.
,
2011
, “
Analytical Model for the Thermo-Hydrodynamic Behaviour of a Thin Lubricant Film
,”
Tribol. Int.
,
44
(
9
), pp.
1083
1086
.10.1016/j.triboint.2011.04.012
4.
Khonsari
,
M. M.
, and
Wang
,
S. H.
,
1992
, “
Notes on Transient THD Effects in a Lubricating Film
,”
Tribol. Trans.
,
35
(
1
), pp.
177
183
.10.1080/10402009208982106
5.
Kim
,
H. J.
,
Ehret
,
P.
,
Dowson
,
D.
, and
Taylor
,
C. M.
,
2001
, “
Thermal Elastohydrodynamic Analysis of Circular Contacts Part 1: Newtonian Model
,”
Proc. Inst. Mech. Eng., Part J
,
215
(
4
), pp.
339
352
.10.1243/1350650011543583
6.
Lee
,
R.-T.
,
Hsu
,
C.-H.
, and
Kuo
,
W.-F.
,
1995
, “
Multilevel Solution for Thermal Elastohydrodynamic Lubrication of Rolling/Sliding Circular Contacts
,”
Tribol. Int.
,
28
(
8
), pp.
541
552
.10.1016/0301-679X(96)85542-3
7.
Salehizadeh
,
H.
, and
Saka
,
N.
,
1991
, “
Thermal Non-Newtonian Elastohydrodynamic Lubrication of Rolling Line Contacts
,”
ASME J. Tribol.
,
113
(
3
), pp.
481
491
.10.1115/1.2920649
8.
Szeri
,
A. Z.
,
2011
,
Fluid Film Lubrication
,
Cambridge University Press
,
Cambridge, UK
.
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