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Abstract
This paper introduces the modelling of two-dimensional laminar flow of Newtonian fluid in a system of concentric or eccentric rotating cylinders with regards to viscous dissipation. Viscous dissipation is a main part, where the viscosity is large for example in oils. The dependence of the Nusselt number on the ratio of the radius of the inner cylinder to the radius of the external cylinder for the selected distance of the cylinder axes was investigated. In order to determine the velocity fields and the temperature distribution, the boundary element method was used. The results of the calculations were presented in the form of diagrams.
Highlights
IntroductionThe viscosity dissipation in the flows between the rotating cylinders is usually neglected
The flow of viscous fluid in the space between cylinders is a three-dimensional flow, assuming a considerable length of cylinders, a sufficient approximation is the adoption of the two-dimensional flow model described in the Stokes equations and continuity for a viscous, incompressible fluid
The energy dissipation function from equation (1) is determined, which is the condition for equation (2)
Summary
The viscosity dissipation in the flows between the rotating cylinders is usually neglected. Flows between rotating cylinders are solved by analytical [1, 5, 6] or numerical [7,8,9,10,11] methods. Considerations of viscous dissipation for flows with a small Reynolds number usually relate to flows in microchannels [12,13,14]. Examples of the application of the boundary element method for solving the viscous dissipation effect for laminar flow in straight ducts were presented in [15, 16]. Examples of viscous dissipation solutions in flows between rotating cylinders can be found in the literature [17-19]
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