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Article
Publication date: 19 June 2007

Maged A.I. El‐Shaarawi, Esmail M.A. Mokheimer and Ahmad Jamal

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal…

659

Abstract

Purpose

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.

Design/methodology/approach

A finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.

Findings

Numerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR2 and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.

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 results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR2=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 2005

Esmail M.A. Mokheimer and Maged El‐Shaarawi

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…

386

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 27 March 2009

Maged A.I. El‐Shaarawia and Ali A. Al‐Ugla

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…

384

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 1995

M.A.I. El‐Shaarawi, M.A. Al‐Nimr and M.A. Hader

The paper presents a finite‐difference scheme to solve thetransient conjugated heat transfer problem in a concentricannulus with simultaneously developing hydrodynamic and…

109

Abstract

The paper presents a finite‐difference scheme to solve the transient conjugated heat transfer problem in a concentric annulus with simultaneously developing hydrodynamic and thermal boundary layers. The annular forced flow is laminar with constant physical properties. Thermal transient is initiated by a step change in the prescribed isothermal temperature of the inner surface of the inside tube wall while the outer surface of the external tube is kept adiabatic. The effects of solid‐fluid conductivity ratio and diffusivity ratio on the thermal behaviour of the flow have been investigated. Numerical results are presented for a fluid of Pr = 0.7 flowing in an annulus of radius ratio 0.5 with various values of inner and outer solid wall thicknesses.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 1992

M.A.I. EL‐SHAARAWI and M.A. AL‐ATTAS

A finite‐difference scheme is developed for solving the boundary layer equations governing the unsteady laminar free convection flow in open ended vertical concentric annuli. The…

88

Abstract

A finite‐difference scheme is developed for solving the boundary layer equations governing the unsteady laminar free convection flow in open ended vertical concentric annuli. The initial condition considered for the creation of the thermal transient corresponds to a step change in temperature at the inner annulus boundary while the outer wall is maintained adiabatic. Numerical results for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 are presented. The results show the developing velocity and pressure fields with respect to space and time. Also, the important relationship between the annulus height and the induced flow rate is presented for various values of the time parameter starting from quiescence to the final steady state.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 2001

M.A.I. El‐Shaarawi and S.A. Haider

Conjugate laminar forced convection heat transfer in the entry region of eccentric annuli is numerically investigated. Heat transfer parameters are presented for a fluid of Pr …

505

Abstract

Conjugate laminar forced convection heat transfer in the entry region of eccentric annuli is numerically investigated. Heat transfer parameters are presented for a fluid of Pr = 0.7 flowing in an annulus of radius ratio 0.5 for four values of dimensionless eccentricity ranging from 0.1 to 0.7. Solid‐fluid conductivity ratio (KR) is varied to cover the range for practical cases with commonly encountered inner and outer tube thickness. Boundary conditions applied are isothermal heating of the inner surface of the core tube, while the outer surface of the external tube is maintained at the inlet fluid temperature. Limits for KR above which the conjugation can be neglected are obtained.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 August 1998

Maged A.I. El‐Shaarawi and Esmail M. A. Mokheimer

The paper utilizes a boundary‐layer model in bipolar coordinates to study the developing laminar free convection in vertical open‐ended eccentric annuli with one of the boundaries…

503

Abstract

The paper utilizes a boundary‐layer model in bipolar coordinates to study the developing laminar free convection in vertical open‐ended eccentric annuli with one of the boundaries uniformly heated while the other boundary is cooled and kept isothermal at the ambient temperature. This model has been solved numerically using finite‐difference techniques. Results not available in the literature are presented for a fluid of Prandtl number 0.7 in an annulus of radius ratio 0.5 for three values of the dimensionless eccentricity, namely, 0.1, 0.5 and 0.7. These results include the developing velocity profiles and the pressure along the annulus, the channel heights required to naturally induce different flow rates and the variation of the total heat absorbed by the fluid with the channel height.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 15 May 2009

Mohamed A. Antar and Maged A.I. El‐Shaarawi

The purpose of this paper is to investigate the problem of entropy generation around a spinning/non‐spinning solid sphere subjected to uniform heat flux boundary condition in the…

370

Abstract

Purpose

The purpose of this paper is to investigate the problem of entropy generation around a spinning/non‐spinning solid sphere subjected to uniform heat flux boundary condition in the forced‐convection regime.

Design/methodology/approach

The governing continuity, momentum, energy and entropy generation equations are numerically solved for a wide range of the controlling parameters; Reynolds number and the dimensionless spin number.

Findings

The dimensionless overall total entropy generation increases with the dimensionless spin number. The effect of increasing the spin number on the fluid‐friction component of entropy generation is more significant compared to its effect on heat transfer entropy generation.

Research limitations/implications

Since the boundary‐layer analysis is used, the flow is presented up to only the point of external flow separation.

Practical implications

Entropy generation analysis can be used to evaluate the design of many heat transfer systems and suggest design improvements.

Originality/value

A review in the open literature indicated that no study is available for the entropy generation in the unconfined flow case about a spinning sphere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 3/4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 1999

M.A.I. El‐Shaarawi, M.A. Al‐Nimr and M.M.K. Al Yah

Transient conjugated forced convection in the thermal entry region of a thick‐walled annulus, filled with a homogeneous and isotropic porous medium, has been numerically…

411

Abstract

Transient conjugated forced convection in the thermal entry region of a thick‐walled annulus, filled with a homogeneous and isotropic porous medium, has been numerically investigated using finite‐difference techniques. Non‐Darcian effects as well as axial conduction of heat have been considered. The flow is assumed to be hydrodynamically fully developed and steady but thermally developing and transient. The thermal transient is initiated by a step change in the prescribed isothermal temperature on the outer surface of the external tube of the annulus while the inner surface of the internal tube is kept adiabatic. A parametric study is carried out to explore the effects of the Darcy number, the inertia term, the Peclet number and the porous medium heat capacity ratio on the transient thermal behavior in a given annulus.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 November 2002

M.A. Antar and M.A.I. El‐Shaarawi

Boundary‐layer flow around a spinning liquid sphere moving steadily in a gas stream is investigated numerically. The shear stress exerted on the sphere's surface results in…

399

Abstract

Boundary‐layer flow around a spinning liquid sphere moving steadily in a gas stream is investigated numerically. The shear stress exerted on the sphere's surface results in surface rotation in the meridional direction in addition to the azimuthal velocity resulting from the spinning of the liquid sphere. The parameters controlling the flow around the sphere are the external flow Reynolds number (Re), the liquid‐to‐gas viscosity ratio (μ*) and the spinning parameter (Rer/Re)2. The effect of these parameters on the velocity components (namely the meridional, radial and azimuthal velocity components) and on the shear stress is shown. Moreover, their effect on the location of external flow point of separation is also demonstrated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 12 no. 7
Type: Research Article
ISSN: 0961-5539

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