Analytical and numerical investigation of viscous heating in parallel-plate Couette flow
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Abstract
This study investigates the heating problem occurring in viscous oils used as lubricants between moving machine elements, using the Couette flow model. A system consisting of two parallel plates, maintained at a constant temperature (20 °C), with one moving relative to the other at a constant velocity of 8 m/s, is considered. The lubricant fluid has a dynamic viscosity of 0.3 Ns/m² and a thermal conductivity of 0.13 W/mK. The distance between the plates is 1 mm, and the plate area is 0.1 m². The effect of viscous heating on the oil temperature was investigated using both analytical and numerical methods. Under the assumptions of steady-state, fully developed, incompressible, and Newtonian fluid flow, the momentum and energy equations were simplified to obtain analytical solutions. Equations predicting a linear velocity profile and a parabolic temperature profile were derived. Using these equations, the maximum oil temperature was calculated as 311.54 °C, and the power required to move the upper plate was found to be 1920 W. For the numerical solution, ANSYS Fluent, a finite-volume-based computational fluid dynamics solver, was utilized. A two-dimensional, structured mesh was employed, and the steady-state laminar flow and energy equations were solved using a pressure-based solver and the SIMPLE algorithm. The velocity and temperature profiles obtained from the numerical solution were compared with the analytical solutions. An almost perfect agreement was observed between the analytical and numerical results for the temperature profiles, while minor deviations were detected in the velocity profiles, especially in the middle region of the channel and near the upper plate. Observed deviations are likely due to numerical factors (mesh resolution, algorithm, boundary conditions). This study definitively shows that viscous heating significantly increases temperature in lubrication systems, a critical consideration for engineering design.
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