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

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 these cases heat transfer in the laminar regime 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. The influence of the geometric parameters is comprehensively studied by varying the radius ratio (0.1 <= eta <= 0.99) and the length-to-gap aspect ratio (5 <= Gamma <= 80). Similarly, a wide range of Prandtl, Rayleigh, and Reynolds numbers is explored (0.01 <= sigma <= 100, Ra <= 30,000, and Re <= 1000, respectively). We obtain a simple criterion, Ra which determines whether the infinite-cylinder assumption can be employed. The coefficient a is well approximated by a cubic fit over the whole n-range. Noteworthy the criterion is independent of the Prandtl number and appears robust with respect to Reynolds number even beyond the laminar regime. (C) 2015 Elsevier Ltd. All rights reserved.Postprint (published version

Stability analysis between two concentric rotating cylinders with heat and mass transfer

“…Fu et al read the heat/mass movement effect on the interface with the rotation of the outer cylinder, but the fluid taken by them was nonviscous. Lopez examined the linear stability in laterally heated and rotating flows via direct numerical simulation. Awasthi and Awasthi et al studied the interface of two viscous liquids in an annular region, where the outer cylinders rotated.…”

Dielectrophoretic force-driven convection in annular geometry under Earth’s gravity

“…Since stable flow is referred to unicellular laminar (natural) free convection the criterion found by Gill and Davey (1969) and recently extended by Lopez et al (2015) seems also valid. Interestingly, the break-up of the line of marginal stability occurs in close proximity to the criterion.…”

“…Elder (1965b) found the empirical relation Ra C = 8 · 10 8 Pr 1/2 /Γ. Rearranging the relation and substitution of Ra C found with the criterion from Lopez et al (2015) yields to Γ C ≥ 66.5. From all the considerations we draw the following conclusions.…”

“…In absence of an electric potential, they found for Ra = 5.009 · 10 4 (∆T = 14.64 K) critical modes in the form of oscillatory axisymmetric vortices (vertical wavenumber k C ≈ 2.5) of the thermal instability (see also Bahloul et al, 2000). They considered the temperature profile and the vertical velocity profile, which corresponds to the conductive regime (Choi and Korpela, 1980;Lopez et al, 2015;Meyer et al, 2017). Near the midheight the flow is parallel to the vertical sidewalls.…”

nsCouette – A high-performance code for direct numerical simulations of turbulent Taylor–Couette flow

“…In this simple case, termed basic state, the governing equations admit simple analytic solutions for u θ (r) and T (r), which only depend on r. The heat transfer can be enhanced by either increasing Re i (forced convection) or by increasing Ra (natural convection). In both cases, the basic state exhibits a sequence of distinct instabilities ultimately leading to turbulent heat transfer [14]. A measure of the efficiency is given by the Nusselt number (Nu i ), which is the ratio of total heat transfer at the inner cylinder wall, normalized by that of the basic state at the same temperature difference.…”