Concentric Circular Annulus Research Articles

Experimental Investigation of The Influence of Modifying the Inner Tube Outer Surface on Free Convection in A Concentrated Double Pipe

ABSTRACT Convection across circular concentric gaps between cylinders is crucial in industrial applications, including electronic cooling, heat exchangers, and solar collectors. The effect of longitudinal and annular grooves on the outside surface of the inside tube on natural convective heat transmission in enclosure concentric circular annulus is experimentally investigated in the present work. Twin pairs of circular aluminum cylinders with the same radius ratio, length, and surface area were examined. Each one consists of two concentric circular cylinders. To maintain a steady heat flux, the inside cylinder of each pair has an electrical heater connected. The results indicate that the increases in the Nusselt number of around 25%, 43%, 67%, 123%, 142%, 157%, and 172% are seen for groove depths of 0.05 cm, 0.10 cm, 0.15 cm, 0.20 cm, 0.25 cm, 0.3 cm, 0.35 cm, and 0.4 cm. In addition, increasing the depth of the longitudinal groove raises the Nusselt number by roughly 33%, 51%, 79%, 99%, 136%, 153%, 173%, and 184%. The longitudinal grooves with a depth of 4.0 mm enable a 38% increase in free convection over prior research. An annular groove of 4.0 mm depth increases free convection by 36%. Furthermore, a further advancement over earlier research is attributable to the extensive surface contact area of the inner cylinder made possible by longitudinal or annular grooves.

A new analytical model for the conduction shape factor of annulus sectors

Heat transfer devices, such as heat pipes, vapor chambers, thermosiphons, microchannel heat sinks, and Peltier cooling plates, rely on two-dimensional steady heat conduction to thermally manage telecommunications, aerospace, and microelectronics heat-generating components. The conduction shape factor can evaluate these devices’ two-dimensional steady heat conduction. The geometry of the device’s annulus and its mechanical attachment to the heat-generating component can vary. Given the prominence of single-sided heating and cooling, the two-dimensional heat conduction is commonly through an annulus sector. For the first time, an analytical model is developed to predict the conduction shape factor of annulus sectors. The present model is an extension of the previously developed equivalent concentric circular annulus model and applies the equivalent concentric circular annulus sector. The model is validated with results from finite element modeling for parametric boundary geometries, capturing most of the data across a variety of sectors within a relative difference of 10%. The present model provides a simple, closed-form analytical solution for the shape factor of an annulus sector formed between concentric arbitrarily shaped isothermal boundaries. More importantly, it provides a unified platform for designing and optimizing novel heat transfer devices.

Effect of internal heat generation or absorption on conjugate thermal-free convection of a suspension of hybrid nanofluid in a partitioned circular annulus

This study aims to explain the impact of the presence of a solid conductive partition on the thermal-free convective motion mechanism and heat transmission process within a concentric circular annulus filled with a water-based hybrid nanoliquid containing Copper (Cu) and Alumina (Al2O3) nanoparticles. The thermal natural convective flow is formed within the annulus due to the temperature difference which is externally imposed between the internal heated cylinder and the external cooled one and internally generated by the interior heat generation/absorption (IHG/A) phenomenon. The technique of finite volume is applied to discretize and approximately solve the non-dimensional conservation equations. The influence of selected factors such as the nanoparticles concentration, Rayleigh number, fluid/solid heat conductivity ratio, and the IHG/A parameter on the thermo-hydrodynamic behavior and heat exchange rate is interpreted. The findings show that, in the presence of a conductive solid partition, the combined effects of the IHG/A phenomenon and the combined nanoparticles considerably modify the flow and heat exchange behaviors within the annulus. We also employed a new correlation to predict the mean heat exchange rate in the defined input parameter range.

Peristaltic pumping in thin non-axisymmetric annular tubes.

The two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube and a concentric circular annulus. Here, we study peristaltic flow in a non-axisymmetric annular tube: in this case, the flow is three-dimensional, with motions in the azimuthal direction. This type of geometry is motivated by experimental observations of the pulsatile flow of cerebrospinal fluid along perivascular spaces surrounding arteries in the brain, which is at least partially driven by peristaltic pumping due to pulsations of the artery. These annular perivascular spaces are often eccentric and the outer boundary is seldom circular: their cross-sections can be well matched by a simple, adjustable model consisting of an inner circle (the outer wall of the artery) and an outer ellipse (the outer edge of the perivascular space), not necessarily concentric. We use this geometric model as a basis for numerical simulations of peristaltic flow: the adjustability of the model makes it suitable for other applications. We concentrate on the general effects of the non-axisymmetric configuration on the flow and do not attempt to specifically model perivascular pumping. We use a finite-element scheme to compute the flow in the annulus driven by a propagating sinusoidal radial displacement of the inner wall. Unlike the peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional: azimuthal pressure variations drive an oscillatory flow in and out of the narrower gaps, inducing an azimuthal wiggle in the streamlines. We examine the dependence of the flow on the elongation of the outer elliptical wall and the eccentricity of the configuration. We find that the time-averaged volumetric flow is always in the same direction as the peristaltic wave and decreases with increasing ellipticity or eccentricity. The additional shearing motion in the azimuthal direction will increase mixing and enhance Taylor dispersion in these flows, effects that might have practical applications.

Experimental investigation of subcooled flow boiling in annuli with reference to thermal management of ultra-fast electric vehicle charging cables

Transportation industry is presently in fast track to transition from Internal Combustion Engine Vehicles (ICEVs) to Electrical Vehicles (EVs). One of the most pressing challenges to full adoption of EVs is very slow charging at the networks of charging stations proposed worldwide. Despite many recent so-called ‘ultra-fast’ charging methods, which capitalize on a variety of single-phase liquid schemes to cool the charging cable, thermal constraints limit the electrical current carrying capacity of the fastest commercial chargers to about 500 A. Achieving the faster charging time required for the anticipated proliferation of EVs will require increasing this current capacity to at least 2000 A, which poses formidable thermal challenges in design of the charging cable. This study explores the development of a vastly more powerful charging cable thermal management scheme to achieve this higher current threshold. Subcooled flow boiling is proposed as the primary means to dissipating the larger amounts of heat generated at higher currents. Experiments are performed by pumping highly subcooled dielectric liquid HFE-7100 though a concentric circular annulus mimicking a segment of an actual cable, with a uniformly heated 6.35-mm-diameter inner surface representing the electrical conductor and adiabatic 23.62-mm-diameter outer surface the external conduit. All experimental cases considered are conFig.d to ensure subcooled fluid conditions throughout the test module. It is shown the proposed cooling scheme is capable of tackling currents up to 2438 A, around four times higher than the present-day commercial maximum. With appropriate batteries and other ancillary components, this technology is expected to bring EV charging times down to less than 5 minutes. Aside from demonstrating this potential, an assessment of available subcooled boiling heat transfer coefficient correlations identified Moles and Shaw's to predict the new experimental data with an overall mean absolute error of only 11.68%. The flow and heat transfer physics are also explained in detail.

Dispersion as a waste-clearance mechanism in flow through penetrating perivascular spaces in the brain

Accumulation of metabolic wastes in the brain is correlated with several neurodegenerative disorders, including Alzheimer’s disease. Waste transport and clearance occur via dispersion, the combined effect of diffusion and advection by flow of fluid. We examine the relative contributions of diffusion and advection in the perivascular spaces (PVSs) that surround penetrating cortical blood vessels and are filled with cerebrospinal fluid (CSF). To do so, we adapt prior analytic predictions of dispersion to the context of PVSs. We also perform advection-diffusion simulations in PVS-like geometries with parameters relevant to transport of amyloid-beta (associated with Alzheimer’s) in a variety of flows, motivated by in vivo measurements. Specifically, we examine solute transport in steady and unsteady Poiseuille flows in an open (not porous) concentric circular annulus. We find that a purely oscillatory flow enhances dispersion only weakly and does not produce significant transport, whereas a steady flow component, even if slow, clears waste more effectively.

MHD natural convection of a CNT-based nanofluid-filled annular circular enclosure with inner heat-generating solid cylinder

The present work is dedicated to understanding the natural convective flow mechanism and heat exchange under magnetic field within a concentric circular annulus between a heat-generating conductive internal cylinder and an isothermally cold external cylinder filled with a CNTs-water-based nanoliquid. The free convective flow is generated by the temperature gradient created between the inner heat-generating solid cylinder and the outer cold cylinder. The flow equations in their dimensionless form are numerically solved via the technique of finite volume. The dependency of various factors and their interrelationships affecting the thermo-hydrodynamic behavior and heat exchange rate within the system has been delineated. The findings of this study emphasize the role of the considered control parameters with regards to the hydro-thermal characteristics and the heat exchange rate within the annulus.

Hydraulic resistance of periarterial spaces in the brain

BackgroundPeriarterial spaces (PASs) are annular channels that surround arteries in the brain and contain cerebrospinal fluid (CSF): a flow of CSF in these channels is thought to be an important part of the brain’s system for clearing metabolic wastes. In vivo observations reveal that they are not concentric, circular annuli, however: the outer boundaries are often oblate, and the arteries that form the inner boundaries are often offset from the central axis.MethodsWe model PAS cross-sections as circles surrounded by ellipses and vary the radii of the circles, major and minor axes of the ellipses, and two-dimensional eccentricities of the circles with respect to the ellipses. For each shape, we solve the governing Navier–Stokes equation to determine the velocity profile for steady laminar flow and then compute the corresponding hydraulic resistance.ResultsWe find that the observed shapes of PASs have lower hydraulic resistance than concentric, circular annuli of the same size, and therefore allow faster, more efficient flow of cerebrospinal fluid. We find that the minimum hydraulic resistance (and therefore maximum flow rate) for a given PAS cross-sectional area occurs when the ellipse is elongated and intersects the circle, dividing the PAS into two lobes, as is common around pial arteries. We also find that if both the inner and outer boundaries are nearly circular, the minimum hydraulic resistance occurs when the eccentricity is large, as is common around penetrating arteries.ConclusionsThe concentric circular annulus assumed in recent studies is not a good model of the shape of actual PASs observed in vivo, and it greatly overestimates the hydraulic resistance of the PAS. Our parameterization can be used to incorporate more realistic resistances into hydraulic network models of flow of cerebrospinal fluid in the brain. Our results demonstrate that actual shapes observed in vivo are nearly optimal, in the sense of offering the least hydraulic resistance. This optimization may well represent an evolutionary adaptation that maximizes clearance of metabolic waste from the brain.

Dynamic Bath Mixing during an Ingot Casting Process

This paper presents the results of a bath stirring investigation using a physical model for an uphill ingot casting process. A new method of mixing time measurement that overcomes the drawback of the conventional measurement method was developed. The method was used to investigate bath stirring for a dynamic-volume bulk bath in which the liquid volume increases over time during the teeming process. The results show that the new method can be successfully applied to reveal the relationship between gas blowing schemes, gas blowing flowrates, and bath depths. It is demonstrated that blowing bubbles causes the flow of the bath to increase when the bath depth is increased. By applying the new data analysis method, three different bottom blowing schemes were explored to study the mixing behaviors under different operating conditions. The results suggest that the concentric circular annulus is more favorable than both the eccentric blowing scheme and symmetrical scheme to achieve efficient mixing.

Hele-Shaw flows with time-dependent free boundaries involving a concentric annulus

We consider the classical Hele-Shaw situation with two parallel planes separated by a narrow gap. A blob of Newtonian fluid is sandwiched between the planes and, initially, its plan-view occupies a doubly connected region, so that we physically have a fluid surrounding what we will refer to as an air hole. We seek to predict the evolution of the plan-view of the blob as fluid is added to or removed from the blob at specific injection or suction points, or as air is added to or removed from the air hole. We suppose the relevant free boundary condition to be one of constant pressure, but allow different constant pressures to act along each free boundary. If we begin with a blob in the form of a concentric circular annulus, we obtain an analytic solution to describe its subsequent evolution when subjected to any pattern of injection or suction of fluid, or addition or removal of air, provided only that the plan-view of the blob either remains doubly connected or becomes simply connected as the air hole disappears. Since each state we can reach by this process may itself be regarded as an initial state for some subsequent motion, the class of problems we are thus able to solve is quite extensive. The solutions are expressed in terms of conformal maps that have an explicit analytic form incorporating a finite number of parameters; in general, these parameters must be determined numerically by solving a finite set of transcendental equations. The efficacy of the procedure is illustrated by means of specific examples, chosen to exhibit a number of features of physical interest. The development has an independent mathematical interest, for it involves the solution of a nonlinear functional equation; we here deal only with the particular form of equation that arises in the present application, but generalizations can be handled by similar techniques. Also, the solutions are expressed in terms of functions which themselves have interesting properties. However, we do not pursue these mathematical questions in this paper.

Free-solution electrophoresis with amplification of small mobility differences by helical flow

A description and theoretical analysis is given of a free-solution, three-dimensional electrophoretic field-flow fractionation separation in a concentric circular annulus, in which an axisymmetric swirl flow with velocity components in the axial and azimuthal directions is used to amplify a small difference between the electrophoretic mobilities of two species in a radial electric field. Separation is achieved in the azimuthal direction. The potential of this process is illustrated by calculations (neglecting diffusion) of azimuthal separations of β-lactoglobulins A and B, and racemic denopamine complexed to a stereoselective cyclodextrin. The relative mobility difference for the β-lactoglobulins is about 7%, while that the denopamine enantiomers (one of which is a potent cardiotonic agent) is about 2%. (Diffusionless) separations of 180° can be achieved with relatively modest angular rotation rates.

Symmetry theorems for some overdetermined boundary value problems on ring domains

In this paper we study various overdetermined boundary value problems for elliptic equations. In particular, we introduce overdetermined problems for the Saint-Venant equation whose only solution domain is the concentric circular annulus. The proofs depend on a generalisation of the reflection method of James Serrin. We then use these results to generalise, to the case of doubly connected “ring” domains, the recent work of L. Payne and G. Philippin for the Stekloff eigenvalue problem: we present overdetermining conditions which permit solution only when the domain is a concentric circular annulus. Here, the proof employs an integral characterisation of the annulus by harmonic functions.

Green's function of the clamped punctured disk

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.

Surface Waves Normally Incident on a Submerged Horizontal Cylinder

When small amplitude surface waves on infinitely deep water are normally incident on a submerged circular cylinder whose axis is horizontal, there is zero reflection at all frequencies (Ursell (1950)) and an exponentially small phase shift at high frequency (Davis (1974)). Here the latter result is generalized to finite depth and cylinders of arbitrary cross section, after which it is shown that zero reflection at all frequencies only occurs when the cross section of the fluid region can be mapped by a bilinear transformation into a concentric circular annulus, i.e., only for Ursell’s geometry.

A Simple Method of investigating the Creep of Metals under Simple Shear

DR. K. H. JOLLIFFE and I1 have investigated the creep of metals under simple shear by the use of a disk of the metal in question, in which is cut a concentric circular annulus, the metal external to the annulus being securely gripped, while that internal to the annulus is subjected to a constant torque. We have shown that the behaviour of the metal in these circumstances is in many ways simpler and more informative than that exhibited by wires or rods under tension.