Analytical Thermal Field Theory Applicable to Oil Hydraulic Fluid Film Lubrication

An analytical thermal field theory is derived by a perturbation series expansion solution to the energy conservation equation. The theory is valid for small values of the Brinkman number and the modified Peclet number. This condition is sufficiently satisfied for hydraulic oils, whereby the analytical approach provides an alternative to existing computationally expensive numerical methods. The paper presents the dimensional analysis, which provides the foundation for the derivation of the analytical approximation. Subsequently, the perturbation method is applied in order to find an asymptotic expansion of the thermal field. The series solution is truncated at first order in order to obtain a closed form approximation. Finally a numerical thermohydrodynamic simulation of a piston-cylinder interface is presented, and the results are used for a comparison with the analytical theory in order to validate the modelling approach.