Developing Laminar Free Convection in an Open Ended Vertical Annulus with a Rotating Inner Cylinder

Abstract

A finite-difference scheme is developed for solving the boundary layer equations governing the laminar free convection flow in open ended vertical concentric annuli with rotating inner walls. Numerical results are presented for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 under the thermal boundary conditions of one wall being isothermal and the opposite wall adiabatic. Comparing the present results for the development of δθ (tangential boundary layer displacement thickness) with those corresponding results of forced flows shows that heating the inner cylinder has always stabilizing effects while heating the outer cylinder has either destabilizing or stabilizing effects.

Induced Flow in Uniformly Heated Vertical Annuli With Rotating Inner Walls

“…Payne and Martin [3] investigated the forced-convection heat transfer to laminar axial flow in a concentric annulus from a rotating inner cylinider under the constant heat flux condition. To the authors' knowledge, the only study available to date on natural-convection heat transfer in vertical open-ended concentric annuli with rotating inner walls is that of El-Shaarawi and Sarhan [4]. They presented results for the natural convection problem under the thermal boundary conditions of one wall being isothermal while the opposite wall is adiabatic.…”

“…The lack of information on the development of the tangential boundary-layer displacement thick- In the present paper, natural-convection heat transfer in vertical annuli with rotating inner walls is investigated under two thermal boundary conditions: case 1, in which the inner cylinder is uniformly heated while the outer wall of the annulus is adiabatic; and case 0 , in which the outer wall is uniformly heated while the inner wall is adiabatic. Using appropriate nondimensional parameters, the governing boundary-layer equations have been transferred into nondimensional forms identical to those governinig the case with an isothermal boundary condition [4]. Thus, the finite-difference scheme of El-Shaarawi and Sarhan [4] could be used, and numerical results were obtained.…”

“…Using appropriate nondimensional parameters, the governing boundary-layer equations have been transferred into nondimensional forms identical to those governinig the case with an isothermal boundary condition [4]. Thus, the finite-difference scheme of El-Shaarawi and Sarhan [4] could be used, and numerical results were obtained. This paper presents such numerical results for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 over a wide range of controlling parameters, viz., Grashof number, Taylor number, and the dimensionless volumetric flow rate (0.…”

Simulation of laminar flow through eccentric annuli using isogeometric variational multiscale method

“…The annular geometry is also widely used in industrial applications: in heat exchangers, food processing, fluidized beds, pulp screening, extrusion, as well as in the domain of oil well construction which forms the motivation for this work. The developing laminar flow and heat transfer in the limiting case of concentric annular passages have been investigated by Heaton et al [1] Sparrow and Lin [2], Coney and El-Shaarawi [3] and El-Shaarawi and Sarhan [4]. For the eccentric annulus, most of the investigations available in the literature deals with rather simplified cases by assuming potential, slug or fully developed flows.…”

Effect of induced magnetic field on natural convection in vertical concentric annuli

“…Shaarawi and Sarhan [3] have studied the fully developed free convective flow in vertical annuli by considering isothermal heating or cooling of the inner cylinder and adiabatic condition on outer cylinder. Joshi [4] has investigated the fully developed free convective flow in vertical annuli with two isothermal boundaries.…”