Slip flow between corotating disks with heat transfer

Purpose

This study aims to explore the hydrodynamic and thermal behavior of an incompressible fluid flowing between uniformly corotating disks with finite radii. The narrow gap between the disks necessitates accounting for slip flow in the radial direction, departing from the classic no-slip model.

Design/methodology/approach

The author uses a perturbation approach and derives full analytical approximations to the Navier–Stokes and energy equations up to the second order. Higher-order truncations require significant numerical effort due to the complexity of the resulting expressions.

Findings

For the no-slip case, the momentum solutions perfectly match those found in the literature. The author then demonstrates the convergence of the series solutions with slip for selected specific parameter sets. Finally, the author investigates the impact of both slip and Reynolds number on the velocity field, pressure and temperature field between the inlet and outlet positions.

Originality/value

The key finding is that both factors lead to thinner momentum and thermal boundary layers within the corotating finite disk setup, resulting in cooler disk surfaces.