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.
Asymptotic Approximation of Laminar Lubrication Thermal Field at Low Reduced Peclet and Brinkman Number
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.
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Johansen, P., Roemer, D. B., Andersen, T. O., and Pedersen, H. C. (July 29, 2014). "Asymptotic Approximation of Laminar Lubrication Thermal Field at Low Reduced Peclet and Brinkman Number." ASME. J. Tribol. October 2014; 136(4): 041706. https://doi.org/10.1115/1.4027957
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