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Maximum possible induced flow rates in open‐ended vertical eccentric annuli with uniform heat flux

Esmail M.A. Mokheimer (Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia)
Maged El‐Shaarawi (Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 March 2005

382

Abstract

Purpose

Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature). Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature).

Design/methodology/approach

The fully‐developed laminar free convection momentum equation has been solved numerically using an analytical solution of the governing energy equation.

Findings

Results are presented to show the effect of the annulus radius ratio and the dimensionless eccentricity on the induced flow rate, the total heat absorbed by the fluid, and the fully developed Nusselt numbers on the two boundaries of the annulus for a fluid of Prandtl number 0.7.

Practical implications

Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.

Originality/value

The paper presents a solution that is not available in the literature for the problem of fully developed free convection in open‐ended vertical eccentric annular channels under thermal boundary conditions of the fourth kind. Also presents the maximum possible induced flow rates, the total heat absorbed by the fluid, and the Nusselt numbers on the two boundaries of the annulus. The effects of N and E (the radius ratio and eccentricity, respectively) on these results are presented. Such results are very much needed for design purposes of heat transfer equipment.

Keywords

Citation

Mokheimer, E.M.A. and El‐Shaarawi, M. (2005), "Maximum possible induced flow rates in open‐ended vertical eccentric annuli with uniform heat flux", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 15 No. 2, pp. 161-182. https://doi.org/10.1108/09615530510578438

Publisher

:

Emerald Group Publishing Limited

Copyright © 2005, Emerald Group Publishing Limited

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