Circular Annulus Research Articles

Morphologic differences in atrial and ventricular secondary tricuspid regurgitation by computed tomography

Abstract Background Differences in the mechanism behind atrial (ASTR) and ventricular (VSTR) secondary tricuspid regurgitation cause distinct remodeling in the tricuspid valve annulus (TA), right atrium (RA) and right ventricle (RV). Although these morphological changes have been described by echocardiography, computed tomography (CT) can provide better spatial resolution and detailed anatomical information particularly when planning valvular interventions. Purpose To compare the morphologic characteristics of the TA, RA and RV between ASTR and VSTR as measured by CT. Methods Patients with at least moderate secondary TR and who underwent CT were selected as follows: for the ASTR group (n=32), patients referred for atrial fibrillation (AF) ablation; for the VSTR group, patients referred for transcatheter aortic valve implantation, and which were further subdivided according to the presence of AF (with AF [n=51] and without AF [n=68]). Multiparametric echocardiographic approach was used to define TR severity. CT dataset were analyzed in diastole using a dedicated software for the following parameters: TA area, perimeter, antero-posterior (AP) and septal-lateral (SL) diameters, eccentricity index, annulus depth (to assess TA saddle shape), and RA and RV dimensions and volumes (Fig. 1). Results TR was more severe in VSTR, as 55% and 43% of patients had severe to massive TR in the VSTR group with and without AF, respectively, as compared to 12% in the ASTR group (p<0.001). The TA area was significantly larger in the ASTR and VSTR with AF patients (Fig.2), with a trend towards a more circular annulus by eccentricity index. Annulus depth was lower (flatter) in ASTR compared to both VSTR groups. For the RA, annulus to roof distance was larger in VSTR patients with AF, but the diameter width was wider for both ASTR and VSTR with AF. Indexed RA volume was larger in the VSTR with AF compared to both ASTR and VFTR without AF. The RV, on the other hand, showed a wide base and narrow mid in the ASTR group, both a wide base and mid in the VSTR group with AF, and slightly narrower base and wider mid in the VSTR without AF. RV base-to-mid ratio was lower for both VSTR groups compared to ASTR, but volumes did not significantly differ. RA-to-RV-volume ratio, however, was higher for the ASTR and VSTR with AF. Conclusion Remodeling of the TA and right chambers differ significantly between TR etiologies. ASTR is characterized by a larger and flatter TA, a widened RA and RV base, narrow RV mid, and almost proportional RA-to-RV volumes. VSTR remodeling differs with the presence of AF, as those without AF have a smaller and deep TA, smaller RA, a proportional dilatation of RV diameters, and a larger RV compared to RA. Differentiating these patterns may be useful to guide future interventions.

Laminar convective heat transfer combining buoyancy and thermal radiation of Carreau fluid within a concentric and eccentric annulus

The present study concerns a steady-state laminar combined thermal radiation and buoyancy-driven conjugate magnetohydrodynamic (MHD) natural convective flow and heat transfer inside a fully porous medium eccentric circular annulus bounded by two infinite horizontal cylinders occupied by a Carreau fluid permeated by a uniform transverse magnetic field (B0 ) and inclined by an angle (α). The convective and thermal radiation are approximated by the Boussinesq and Roseland models, respectively. The numerical integration was performed using the implicit finite volume method. The convective terms in the momentum and energy equations were Discretized using the second-order upwind method. On the other hand, the diffusive terms were Discretized using the central difference scheme. The pressure-velocity coupling was solved using the SIMPLE approach. The findings suggest a clear trend of enhancement in the heat transfer rate when the aspect ratio and annulus eccentricity increase. This pattern is more pronounced in the negative vertical eccentricities. It is worth noting that the eccentric annulus, which has an annulus aspect ratio of 1.6 and a vertical eccentricity of −0.8, offers the best performance regarding the heat transfer mechanism inside the annulus gap. The heat transfer mechanism turns out to be strongly affected by thermal radiation, Hartmann number, and magnetic field inclination angle. The increased thermal radiation parameter and the decreased flow behavior index improve the heat transfer mechanism between the Carreau fluid and the inner cylinder in the annular gap. Furthermore, the average Nusselt number increases considerably as the induced magnetic field inclines.

Technique of corneal allogenic ring segment preparation using femtosecond laser: preclinical study on human corneal grafts.

To describe a new technique for preparing corneal allogenic ring segments (CAIRSs) using femtosecond laser technology. Hospital Foundation Adolphe de Rothschild-Noémie de Rothschild institute, Paris, France. Preclinical study conducted on human corneal grafts. The corneal grafts were mounted on an artificial chamber pressurizer (ACP) with preset constant pressure, and the FSL was used to create a circular annulus with specific dimensions. The resulting CAIRSs were analyzed for their thickness and width after air drying. A total of 25 CAIRSs were prepared using the FSL. The mean width and thickness of the CAIRSs were 803 ± 77 μm and 83 ± 16 μm, respectively. Statistical analysis revealed no significant differences in width among the various quadrants of each CAIRS or between different CAIRSs. Significantly thicker CAIRSs were obtained with a higher ACP pressure. The technique of CAIRS preparation using FSL technology and controlled artificial anterior chamber pressure demonstrated reproducibility and precision. This approach holds the potential for customizing and personalizing CAIRSs based on individual corneal characteristics.

Shape matters: Convection and entropy generation in magneto-hydrodynamic nanofluid flow in constraint-based analogous annular thermal systems

This work analyzes the performance of annular thermal systems of distinct geometries to understand their shape impacts using a novel constraint-based methodology. This research fills the gap in the literature by analyzing the geometrical shape impact of magnetohydrodynamic CuO/water nanofluid flow on fluid flow, heat transfer, and thermodynamic irreversibility. Through computational simulations, the outcome results demonstrate that the circular annuli (Case 1 and Case 2) outperform the analogous square system in terms of fluid velocity, heat transfer, and irreversibility. The analysis is carried out for a range of Rayleigh numbers (Ra = 103 to 106), nanoparticle concentrations (ζ = 0 to 4%), magnetic fields (Ha = 0 to 100), and magnetic field inclinations (γ = 0° to 180°). Additionally, a significant improvement in heat transfer is observed by augmenting nanoparticles of the working fluid, while the magnetic field intensity plays a crucial role in controlling fluid flow and heat transfer. The study provides valuable insights into how various parameters affect the nanofluidic heat and flow characteristics of equivalent annular geometries and contributes to the development of more efficient and effective designs of thermal systems. The novelty of the study lies in its comprehensive approach in the use of a constraint-based methodology that matches the flow areas or cooling lengths while maintaining the same heating length to analyze the impact of geometric shapes on heat transport and accompanying irreversibility during MHD nanofluid flow. Furthermore, the energy-flux vectors are utilized to delve into the insights. The maximum value of heat transfer noted for Case 1 and Case 2 is approximately 7% and 11%, respectively, compared to the square annulus (Base Case). The inclusion of nanoparticles in the carrier fluid causes a significant enhancement in heat transfer by up to 11%, compared to pure fluid (ζ = 0).

In Vitro Comparison of a Closed and Semi-closed Leaflet Design for Adult and Pediatric Transcatheter Heart Valves

Transcatheter heart valve replacements (TVR) are mostly designed in a closed position (c) with leaflets coaptating. However, recent literature suggests fabricating valves in semi-closed (sc) position to minimize pinwheeling. With about 100,000 children in need of a new pulmonary valve each year worldwide, this study evaluates both geometrical approaches in adult as well as pediatric size and condition. Three valves of each geometry were fabricated in adult (30 mm) and pediatric (15 mm) size, using porcine pericardium. To evaluate performance, the mean transvalvular pressure gradient (TPG), effective orifice area (EOA), and regurgitation fraction (RF) were determined in three different annulus geometries (circular, elliptic, and tilted). For both adult-sized valve geometries, the TPG (TPGC = 2.326 ± 0.115 mmHg; TPGSC = 1.848 ± 0.175 mmHg)* and EOA (EOAC = 3.69 ± 0.255 cm2; EOASC = 3.565 ± 0.025 cm2)* showed no significant difference. Yet the RF as well as its fluctuation was significantly higher for valves with the closed geometry (RFC = 12.657 ± 7.669 %; RFSC = 8.72 ± 0.977 %)*. Recordings showed that the increased backflow was caused by pinwheeling due to a surplus of tissue material. Hydrodynamic testing of pediatric TVRs verified the semi-closed geometry being favourable. Despite the RF (RFC = 7.721 ± 0.348 cm2; RFSC = 5.172 ± 0.679 cm2), these valves also showed an improved opening behaviour ((TPGC = 20.929 ± 0.497 cm2; TPGSC = 15.972 ± 1.158 cm2); (EOAC = 0.629 ± 0.017 cm2; EOASC = 0.731 ± 0.026 cm2)). Both adult and pediatric TVR with semi-closed geometry show better fluiddynamic functionality compared to valves with a closed design due to less pinwheeling. Besides improved short-term functionality, less pinwheeling potentially prevents early valve degeneration and improves durability. *Results are representatively shown for a circular annulus geometry.

Maximum-width rainbow-bisecting empty annulus

Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus A of a particular shape with maximum possible width such that A does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in O(n3) time using O(n) space, in O(k2n2log⁡n) time using O(nlog⁡n) space and in O(n3) time using O(n2) space respectively.

EFFECT OF INNER BOUNDARIES GEOMETRY ON NATURALCONVECTION HEAT TRANSFER IN HORIZONTAL ANNULI

An analytical modeling of natural convection in physically-based analysis is developed for investigate free convective heat transfer in horizontal eccentric annulus between a circular outer cylinder and heated different shape inner envelope with used four models of the shapes of the inner cross section of (circular, triangular, square and hexagon inner boundary). The main objective of this paper was taking a composite model based on asymptotic solutions for three limiting cases: pure conduction, laminar boundary layer convection and transition flow convection. Laminar conditions up to Rayleigh number RaPi of 5×104 were investigated. By using data from MATLAB simulations for a wide range of two cylinder temperature difference in order to study the effects of annulus diameter ratio, Rayleigh number, and the cross section geometries of inner cylinder on the Nusslte number and the ratio of thermal conductivity. The numerical result illustrated for the circular the increasing the Rayleigh number leading to slightly increasing the non-dimensional Nusslte number with various value of annulus diameter ratio and when used the high annulus perimeter ratio (Po/Pi( about (4.5,2.6,1.6 and 1.175). There is rapid increasing in the non-dimensional ratio of thermal conductivity with increasing the Rayleigh number at the high values of (Po/Pi(, and the result showed that the non-dimensional ratio of thermal conductivity and the Nusslte number values of the (triangular, square and hexagon) less than in the case of circular inner boundary, but the hexagon model showed the Nusslte number more that than in the (triangular and square). the mathematical results compared with model developed by pervious numerical the model and data are in good agreement, with an average RMS difference of 10.6% for the circular annulus of dimensional Nusselt number (NuPi) and less than 4.9 % and 9.8% for the square inner geometry non-dimensional ratio thermal conductivity.

Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular.

A ROTATING WAVY CYLINDER ON BIOCONVECTION FLOW OF NANOENCAPSULATED PHASE CHANGE MATERIALS IN A FINNED CIRCULAR CYLINDER: ISPH SIMULATIONS

The originality of this study is the introduction of numerical investigations on the bioconvection flow of nano-encapsulated phase change materials (NEPCMs) with oxytactic microorganisms in a new configuration of a circular annulus with a rotating wavy inner cylinder. The incompressible smoothed particle hydrodynamics (ISPH) method was applied to solve the governing partial differential equations for the velocity, temperature, concentration, and density of motile microorganisms. Compared with the conventional mesh-based method, this mesh-free, particle-based approach offers strong advantages in the simulation of complex problems with free surfaces and moving boundaries with large displacements. The pertinent parameters are the undulation number (<i>N<sub>und</sub></i> = 2-36), bioconvection Rayleigh number (<i>Ra<sub>b</sub></i> = 1-1000), Darcy parameter (Da = 10<sup>-5</sup>-10<sup>-2</sup>), length of the inner fin (<i>L<sub>Fin</sub></i> = 0.05-0.15), radius of the inner wavy cylinder (<i>R<sub>c</sub></i> = 0.05-0.25), Rayleigh number (Ra = 10<sup>3</sup>-10<sup>5</sup>), undulation amplitude of the inner wavy cylinder surface (<i>A</i> = 0.1-0.4), and frequency parameter (<i>ω </i>= 1-5). The undulation number of the inner wavy cylinder enhanced the flow of the oxytactic microorganisms and isotherms, whereas it had the reverse effect on the velocity, decreasing the maximum velocity by 26.56%. In addition, the comparatively high undulation amplitude and frequency increased the average Nusselt and Sherwood numbers. It was found that the embedded wavy cylinder interacting with fins plays an important role in enhancing heat transfer and the bioconvection flow within a closed domain.

Acute exercise has specific effects on the formation process and pathway of visual perception in healthy young men.

Visual perception is formed over time through the formation process and visual pathway. Exercise improves visual perception, but it is unclear whether exercise modulates nonspecifically or specifically the formation process and pathway of visual perception. Healthy young men performed the visual detection task in a backward masking paradigm before and during cycling exercise at a mild intensity or rest (control). The task presented gratings of a circular patch (target) and annulus (mask) arranged concentrically as a visual stimulus and asked if the presence and striped pattern (feature) of the target were detected. The relationship between the orientations of the gratings of the target and the mask included iso-orientation and orthogonal orientation to investigate the orientation selectivity of the masking effect. The masking effect was evaluated by perceptual suppressive index (PSI). Exercise improved feature detection (∆PSI; Exercise: -20.6%, Control: 1.7%) but not presence detection (∆PSI; Exercise: 8.9%, Control: 29.6%) compared to the control condition, and the improving effect resulted from the attenuation of the non-orientation-selective (∆PSI; Exercise: -29.0%, Control: 16.8%) but not orientation-selective masking effect (∆PSI; Exercise: -3.1%, Control: 11.7%). These results suggest that exercise affects the formation process of the perceptual feature of the target stimulus by suppressively modulating the neural networks responsible for the non-orientation-selective surround interaction in the subcortical visual pathways, whose effects are inherited by the cortical visual pathways necessary for perceptual image formation. In conclusion, our findings suggest that acute exercise improves visual perception transiently through the modulation of a specific formation process of visual processing.

Boundary Distortion and the Schwarzian Derivative of a Univalent Function in a Circular Annulus

Boundary Distortion and the Schwarzian Derivative of a Univalent Function in a Circular Annulus

Comparison between multimodality imaging approaches for measurement of the tricuspid annulus in severe tricuspid regurgitation

BackgroundTricuspid valve (TV) sizing is crucial for surgical or interventional procedures planning. Imaging TV is frequently challenging and often requires multimodal imaging techniques. Computed tomography (CT) is the gold standard for sizing. The authors compared measurements of the tricuspid annulus (TA) acquired using echocardiography and CT. MethodsThirty-six patients with severe symptomatic tricuspid regurgitation were included in this retrospective analysis. During mid-diastole, the maximal two-dimensional (2D) TA diameter was directly measured in multiple views using transthoracic echocardiography (TTE) and transesophageal echocardiography (TEE). Three-dimensional (3D) TA size was assessed using cross-sectional long-axis and short-axis diameters, areas, and perimeters measured in the projected plane. The TA diameter was quantified by the perimeter measured on the CT images (CT imaging_indirect) and compared with echocardiography measurements. Tenting height and tenting area were also measured using TTE at mid systole. ResultsThe long-axis dimensions measured using 3DTEE (3DTEE_direct) best correlated with the TA diameter (CT imaging_indirect) (R = 0.851, P = 0.0001) and the least discrepancies (difference 1.2 ± 2.4 mm, P = 0.012). The TA diameters quantified by the perimeters measured using 3DTEE (3DTEE_indirect) were smaller than the CT values (difference 2.5 ± 2.5 mm, P = 0.0001). The maximal dimensions directly measured by 2DTEE (2DTEE_direct) were modestly correlated with the CT values. Overall, the maximal dimensions by TTE_direct were less reliable than those by CT. TA eccentricity index correlated with the maximal tenting height and area. ConclusionThe patients with severe tricuspid regurgitation had a dilated and circular annulus. The long-axis TA dimensions (3DTEE_direct) were similar to the diameters (CT imaging_indirect).

Distribution of corneal densitometry in different grades of keratoconus.

To evaluate the use of Scheimpflug tomography in corneal densitometry (CD) in comparing the stages of keratoconic eyes. Keratoconic (KC) corneas (stages 1-3 classified according to the topographic parameters) were examined using the Scheimpflug tomographer (Pentacam, Oculus) using the CD software. CD was measured over three different depths (anterior stromal layer [120 μm], posterior stromal layer [60 μm], and middle stromal layer between these two layers), and concentric annular zones (0.0 to 2.0, 2.0 to 6.0, 6.0 to 10.0, and 10.0 to 12.0 mm diameter area). The study participants were divided into three groups: keratoconus (KC) stage 1 (KC1) with 64 participants, keratoconus stage 2 (KC2) with 29 participants, and keratoconus stage 3 (KC3) with 36 participants. Comparing CD of all three layers (anterior, central, and posterior) of the cornea over different circular annuli (0-2, 2-6, 6-10, and 10-12 mm) revealed a significant difference in the 6-10 mm annulus between all groups and in all layers (P = 0.3, 0.2, and 0.2, respectively). Area under curve (AUC) was done. It revealed that the central layer showed the highest specificity (93.8%) in comparing KC1 and KC2, whereas CD in the anterior layer between KC2 and KC3 had the highest specificity (86.2%). CD showed increased values in the anterior corneal layer and in the annulus 6-10 mm more than other locations in all stages of KC.

Order and Disorder in a Cyclically Competitive Ecological Community

We consider a deterministic model of a rock-paper-scissors cyclic ecological system. The model accounts for species mobility via Fickian diffusion, as well as interspecies interactions describing the cyclic competition scheme. The system admits both single-species equilibria (saddles) and a three-species coexistence equilibrium state. We focus on the regime where coexistence is unstable. When there is no spatial dependence, the solution of the corresponding ordinary differential equation system admits an attracting heteroclinic cycle consisting of orbits connecting the three single-species saddles in the sequence, to which most solutions with physical initial conditions asymptote. When there is spatial dependence (partial differential equation system), we consider mixed initial conditions (all species cohabit the same spatial region), as well as patch initial conditions, where each species is isolated from the other two, and show that, when interspecies competition is not strong, spatiotemporal chaotic behavior generally occurs. We propose a mechanism for the development of chaos—patch splitting—whereby sufficiently large patches are repeatedly split by the diffusion of competitors into the patch. However, when there is strong interspecies competition, ordered spatiotemporal patterns can occur. We consider both 1D patterns, corresponding to a community confined to a thin, circular annulus, and 2D geometries, simulating a petri dish. We show that, in 1 dimension, traveling arrays of single-species patches, as well as modulated traveling waves, consisting of patches which periodically expand and contract (breather modes), exist. In 2 dimensions, spirals, as well as localized patches chasing each other in the sequence, can occur. We consider length and temporal scales appropriate for a bacterial community in a laboratory setting, qualitatively modeling observed Escherichia coli cyclic bacterial systems.

Green energy of discrete signed measure on concentric circles

We show that the difference between the Green energy of a discrete signed measure relative to a circular annulus concentrated at some points on concentric circles and the energy of the signed measure at symmetric points is non-decreasing during the expansion of the annulus. As a corollary, generalizations of the classical Pólya-Schur inequality for complex numbers are obtained. Some open problems are formulated.

External Heating of a Circular Annulus Cavity filled with Nano Fluid.

Nowadays, progress in direct absorption solar collectors requires further investigations to realize heat transfer occurring in a horizontal annulus cavity exposed to external heat from different angles. An annulus cavity filled with nano-fluid is numerically simulated by using Ansys-Fluent for Rayleigh number equals 105. The external wall of two-dimensional model for the cavity is equally divided into six parts to simulate heating from isothermal walls placed in different angles. The internal wall has constant low temperature simulating a pipe conveys cold fluid and acting as heat sink. Hot isothermal walls set in different angles to simulate several heating cases according to hot element position. “Upper”, “lower”, “upper-right”, “lower-right”, “upper & upper-right”, “lower & lower-right”, “lower-right & upper-right”, “upper-half”, and “lower-half” are the cases investigated to assess heating effectiveness for all possible directions of heating. It is found that heating in “lower” and “lower-right” cases is about six time that of “upper” case. In addition, heating improves slightly in the case of “lower-right” compared with that of “lower” heating. Heating effectiveness from two or three parts in the upper side appears less than heating of two or three parts from the lower side. Enlarging heating area not always reflects multiplication of heat transfer amount, natural convection on the cold wall decreases significantly due to restricted or weakened stream of fluid motion near to cold wall in poor heating cases. In conclusion, choosing correct direction of heating in annulus cavity demonstrates effective heating compared to that earned by enlarging heating area.

Analysis on Couette flow of a micropolar fluid through a circular annulus filled with the porous medium

Analysis on Couette flow of a micropolar fluid through a circular annulus filled with the porous medium

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.

Numerical Analysis on Convective Heat Transfer of water Based Hybrid Nanofluid (Alumina-Copper) In a Horizontal Annulus

Numerical inspection of natural thermally induced flow in horizontal annulus has been carried out. The annulus taken under consideration is the circular annulus. By applying heat flux to the inner tube, the inner wall of the annulus is kept at high temperature and the outer wall of the annulus is maintained at constant low temperature. The numerical simulations were accomplished by varying concentrations of the hybrid nanofluid of a hybrid alumina-copper various for each Rayleigh number (4 x 104 < Ra < 4 x l05). Heat transmission through natural convection using air as convective fluid, in the body of horizontally placed annulus resided between two same hollow cylinders, is calculated. The influence of the Rayleigh number along with particle concentration on heat transmission characteristics, change in fluid flow and effective thermal conductivity of an annulus has been studied. The results showed a proportional rise in the heat transfer performance and effective thermal conductivity with the increasing particle concentration and Rayleigh numbers.

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.