Induced flow and heat transfer due to inner stretching and outer stationary coaxial cylinders

The current pioneering research explores the development of fluid flow and heat transfer between two cylinders. The flow is induced solely by the stretching of inner cylinder enclosed by the stationary outer cylinder. The physical phenomenon occurs in polymer extrusion in engineering applications. A mathematical formulation based on the mass conservation, Navier-Stokes and energy equations is designed which reveals after nondimensionalization that the motion is governed by the cylinder curvature, Prandtl number and distance/gap parameters between the concentric cylinders. Numerical simulations portray that deformation of the inner cylinder sets up a motion drifting axially the fluid above, which is compensated by a radial fluid to conserve the mass flow. When the gap limits to infinity, the model perfectly matches with the Crane's solution for vanishing curvature and with the Wang's solution for all curvature. An analytical flow/heat solution in the specific case of narrowing cylinders is also derived in elementary polynomial form, which shows up as stretching triggered Coutte-kind flow. Yet, another analytical solution of the flow in terms of rational function valid with a specific value of curvature parameter is detected when the flow over the inner cylinder expands to infinity. In particular, the gap size has prominent effect on the formation of momentum and thermal fields. Results also prove that a critical gap distance exist at which the heat transfer rate is at its minimum. From a pure mathematical point of view, the present authors believe that some of the published numerical results should be rechecked through comparisons with the exact solutions as provided here.

Automated summary

This research investigates the fluid flow and heat transfer development between two cylinders, induced solely by the stretching of the inner cylinder. The mathematical formulation based on mass conservation, Navier-Stokes, and energy equations reveals that the motion is governed by cylinder curvature, Prandtl number, and gap parameters. Numerical simulations show that deformation of the inner cylinder generates axial motion of the fluid above, compensated by radial fluid flow. Analytical solutions are derived for specific cases, demonstrating different flow patterns and the effect of the gap size on momentum and thermal fields. The authors suggest rechecking published numerical results against these exact solutions from a mathematical perspective.