A numerical study has been performed for the flow and heat transfer in the space between a pair of coaxial cylinders with the outer one fixed and the inner one rotating. Of special interest is the case where either one of the cylinders has an axially grooved surface resulting in twelve circumferentially periodic cavities embedded in it. The ends of the cylinder are bounded by flat impermeable walls that are either fixed to the outer cylinder or rotate with the inner one. Such a geometry is common in electric motors where an improved understanding of thermophysical phenomena is essential for analysis and design. Discretized transport equations are solved for two-dimensional and three-dimensional, steady, constant property laminar flow using a second-order accurate finite volume scheme within the context of a SIMPLER-based iterative methodology. The two-dimensional calculations reveal a shear-induced recirculating flow in the cavities. For supercritical values of the Reynolds number, the three-dimensional calculations show how the flow in a cavity interacts with Taylor vortices in the annular space to enhance heat transfer. Relative to coaxial cylinders with smooth surfaces, for the conditions of this study the transport of momentum and heat is raised by a factor of 1.2 in the case of cavities embedded in the inner cylinder and by a factor of 1.1 in the case of cavities embedded in the outer cylinder.

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