The Thermal Behavior of Oscillating Squeeze Films

An analytical solution to the energy equation is provided for oscillating squeeze film flow, such as that which occurs in squeeze film damper bearings. Assumptions are: (a) the usual lubrication conditions for two-dimensional flow, (b) small oscillations, and (c) constant viscosity. Specific conditions are established for the latter assumption, which may be in force for stably operated squeeze film bearings. Relatively simple expressions are presented for the thermal performance variables (temperature field, average temperature, Nusselt number) for a variety of cases. The results are interesting from a heat transfer point of view in that the proper energy balance consists of dissipation, conduction, and storage terms, rather than convection terms as is usual in lubrication studies. Thus inferences drawn from other thermal analyses may be in error. Both average cross-film temperature rise and heat transfers are seen to increase from zero Pe´cle`t number and asympotically approach constant values. Due to the negligible convection conditions, the conventional definitions of bulk temperature, Nusselt number, and Pe´cle`t number are not appropriate. As a result of the thermal storage effect, interesting temporal phase-shift and temperature swing effects are exhibited.