Maged A. I. El-Shaarawi

Free convection in vertical eccentric annuli with a uniformly heated boundary

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.

Transient forced convection in the entrance region of concentric annuli

Abstract The paper presents a finite-difference scheme to solve the transient laminar forced convection problem in the entry region of a concentric annulus with sumultaneously developing hydrodynamic and thermal boundary layers. Four initial conditions are considered for the creation of thermal transients. These correspond to either a step change in temperature at one of the annulus boundaries or to a simultaneous step change in temperature at both the inlet cross-section and one of the annulus boundaries, the other annulus boundary is kept adiabatic in all cases. Numerical results are presented for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5.

Limiting Values for Free-Convection Induced Flow Rates in Vertical Eccentric Annuli with an Isothermal Boundary

Fully developed laminar natural convection in vertical eccentric annuli has been investigated under fundamental thermal boundary conditions of the first and third kinds. For conditions of the first kind, numerical solutions are presented showing the effect of eccentricity on the velocity profiles and the local Nusselt number in an annulus of radius ratio 0.5. Limiting values for the induced flow rate and the average Nusselt numbers are presented for a fluid of Pr = 0.7 over wide ranges of eccentricity and annulus radius ratio (0.1-0.9). Closed-form analytical solutions are obtained for fundamental conditions of the third kind and the corresponding variations in the limiting induced flow rates with eccentricity are presented.Fully developed laminar natural convection in vertical eccentric annuli has been investigated under fundamental thermal boundary conditions of the first and third kinds. For conditions of the first kind, numerical solutions are presented showing the effect of eccentricity on the velocity profiles and the local Nusselt number in an annulus of radius ratio 0.5. Limiting values for the induced flow rate and the average Nusselt numbers are presented for a fluid of Pr = 0.7 over wide ranges of eccentricity and annulus radius ratio (0.1-0.9). Closed-form analytical solutions are obtained for fundamental conditions of the third kind and the corresponding variations in the limiting induced flow rates with eccentricity are presented.

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

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 Nussel...

Critical conductivity ratio for conjugate heat transfer in eccentric annuli

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.

Boundary Layer Flow About and Inside a Liquid Sphere

A finite-difference scheme has been developed to solve the boundary-layer equations governing laminar flows around and inside a spherical fluid droplet moving steadily in another immiscible fluid. Using this scheme, results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ * ) and large values of the external flow Reynolds number (Re). Detailed results over the range 1.01 ≤ μ * ≤ ∞ (solid sphere) and 100 ≤ Re ≤ 10000 are presented for the velocity profiles outside and inside the droplet, the interface shear stress, the external flow separation angle, the droplet surface velocity and the drag coefficient.

Analytical solution for transient laminar fully developed free convection in vertical channels

Using Greens function method, analytical solutions for transient fully developed natural convection in open-ended vertical circular and two-parallel-plate channels are presented. Different fundamental boundary conditions for these two configurations have been investigated and the corresponding fundamental solutions are obtained. These fundamental solutions may be used to obtain solutions satisfying more general thermal boundary conditions. In terms of the obtained unsteady temperature and velocity profiles, the transient volumetric flow rate, mixing cup emperature and local nusselt number are estimated.ZusammenfassungFür oben und unten offene vertikale Kanäle mit Kreisquerschnitt bzw. als Parallelplattenanordnung werden unter Verwendung der Methode der Greenschen Funktionen analytische Lösungen für die nichtstationäre, vollausgebildete, natürliche Konvektion gefunden und zwar unter Zugrundelegung verschiedener Fundamental-Randbedingungen bezüglich beider Konfigurationen. Die so ermittelten Fundamentallösungen können zur Gewinnung von Lösungen für allgemeine Randbedingungen dienen. Der zeitlich veränderliche Volumenstrom, die Mischtemperatur und die Nusselt-Zahl werden mit Bezug auf die erhaltenen nichtstationären Profile für Temperatur und Geschwindigkeit näher analysiert.

Transient conjugated heat transfer in concentric annuli

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.

Transient conduction in eccentrically hollow cylinders

Abstract Transient heat conduction with uniform rate of internal heat generation has been numerically investigated in infinitely long eccentrically hollow cylinders. Two combinations of boundary conditions of the first and second kinds have been considered. The first of these combinations corresponds to the case of one surface being heated isothermally while the opposite surface is maintained at ambient temperature. The second combination of boundary conditions is with one surface maintained isothermal while the opposite surface is adiabatic. Results are presented for a radius ratio 0.5 with dimensionless eccentricities ranging from 0.1 to 0.8 and various values of internal heat generation.

Combined forced convection and surface radiation between two parallel plates

Purpose – This papers aim is to investigate the effect of surface radiation on the developing laminar forced convection flow of a transparent gas between two vertical parallel plates. The walls are heated asymmetrically, this enhances the effect of radiation even with the two walls having low values of emissivity.Design/methodology/approach – Numerical techniques were used to study the effect of the controlling parameters on wall temperatures, fluid temperature profiles, and Nusslet number.Findings – The values of the radiation number at which surface radiation can engender symmetric heating (and hence maximum average Nusslet number on the heated wall and maximum reduction in the maximum heated wall temperature are achieved) are obtained. Threshold values of the radiation number at which radiation effects can be neglected are obtained.Research limitations/implications – Boundary‐layer flow model is used.Practical implications – The implications include design of high‐temperature gas‐cooled heat exchanger...