Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

TL;DR

This study numerically investigates heat transfer and turbulence onset in fluid flows between heated rotating and cooled stationary cylinders, providing a criterion to determine when the infinite-cylinder approximation is valid.

Contribution

The paper introduces a simple linear criterion incorporating cylinder curvature to assess the validity of the infinite-cylinder assumption in heat transfer analysis.

Findings

Derived a linear criterion involving curvature, slope, and additive constant.

Identified a critical Rayleigh number for transition from laminar to convective flow.

Criterion remains robust across different Reynolds and Prandtl numbers.

Abstract

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction, in which cases heat transfer occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. We obtain a simple linear criterion that determines whether the infinite-cylinder assumption can be employed. The curvature of the cylinders enters this linear relationship through the slope and additive constant. For a given length-to-gap aspect ratio there is a critical Rayleigh number beyond which the laminar flow in the finite system is convective and so the behaviour is entirely different from the periodic case. The criterion does not depend on the Prandtl number and appears quite robust with respect to the Reynolds number. In particular, it continues to work reasonably in the turbulent regime.