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 ¼ 0.7 in the laminar natural convection flow regime over a wide range of the controlling parameter Gr 2 /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 Gr 2 /Ta) increases the flow rate and heat absorbed in short annuli. However, for considerably tall annuli, Gr 2 /Ta has slight effect on the flow and heat absorbed. The steady-state time is tangibly influenced by Gr 2 /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 Gr 2 /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.