Transient moment to rotate inner walls of vertical concentric annuli in the natural convection regime

Abstract

Purpose

The paper seeks to focus on obtaining the transient torque required to rotate the inner cylinder in open ended vertical concentric annuli for a fluid of Pr = 0.7 in the laminar natural convection flow regime over a wide range of the controlling parameter Gr²/Ta. The inner wall is heated and subjected to an impulsive rotation while the outer one is stationary and maintained adiabatic.

Design/methodology/approach

The governing transient boundary‐layer equations are numerically solved using an iterative linearized finite‐difference scheme.

Findings

The transient induced flow rate and absorbed heat for different annulus heights are presented. High rotational speed (i.e. low values of Gr²/Ta) increases the flow rate and heat absorbed in short annuli. However, for considerably tall annuli, Gr²/Ta has slight effect on the flow and heat absorbed. The steady‐state time is tangibly influenced by Gr²/Ta in considerably short annuli and very slightly affected for considerably tall annuli.

Practical implications

The investigated problem can simulate the start‐up period of naturally cooled small vertical electric motors.

Originality/value

The paper presents results not available in the literature for the effect of Gr²/Ta on the developing velocities, pressure, flow‐rate induced, absorbed heat by fluid and required torque in vertical concentric annuli with impulsively rotated inner walls under the transient free‐convection heat transfer mode.

Citation

El‐Shaarawia, M.A.I. and Al‐Ugla, A.A. (2009), "Transient moment to rotate inner walls of vertical concentric annuli in the natural convection regime", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 19 No. 2, pp. 201-222. https://doi.org/10.1108/09615530910930973