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In this study, an investigation was conducted on four distinct configurations, designated as Case-1, Case-2, Case-3, and Case-4, focusing on parametric analysis. Each configuration features a cylindrical enclosure containing pure Gallium, a phase change material (PCM). The solid-to-liquid phase transition of the encapsulated material was examined using a 2D CFD methodology. Additionally, the effect of applying three temperatures, T1=32∘C, T2=39∘C, and T3=42∘C, along the generator of the enclosure, with or without fins, was also studied. To accurately model the melting process of the PCM, the Enthalpy- Porosity Method was employed, and meticulous detailing of underlying assumptions was under- taken to ensure precise representation. The validation process involved comparing outcomes of the physical solidification/melting model with reference data from a state-of-the-art study. The specific cases comprised Case-1 - a slender finless cylinder; Case-2 - a thin finned cylinder (l=10mm, t=0.6mm); Case-3 - featuring larger fins (l=20mm, t=0.6mm); and Case-4 - incorporating the largest fins (l=30mm, t=0.6mm). Strategically incorporating thin fins accelerates Gallium melting significantly, reducing times by up to 89%. This enhancement is driven by a 96% increase in the heat transfer coefficient (h), leading to faster melting rates. In addition, fins boost the Nusselt number (Nu) by 91%, indicating improved convective heat transfer and enhanced melting. Melting rates increase by around 30%, notably in Case-3. Temperature T1 shifts dominant heat transfer from convection to conduction, as seen in 2D CFD contours with stratified patterns in Case-3 at t=240s and Case-4 at t=240s and t=300s. A localized cold spot at t = 300s in Case-4 signals localized heat transfer effects.

An optical-thermal-stress coupled analysis model of the Parabolic Trough Receiver (PTR) was built based on the Monte Carlo Ray Tracing method and Computational Fluid Dynamics. The temperature field and stress field of the PTR were studied by numerical simulation, and the absorber deformation and the Kovar ring failure were analyzed. Furthermore, the effects of the aperture width (W) and focal length (f) across the entire receiver temperature gradient and thermal stress field were studied. The results showed that the effect of width and focal length on the temperature field was mainly reflected in the change in the high-temperature distribution of the absorber. The maximum collector efficiency were 81.02% and 70.4% when W = 13 m and f = 1.84 m, respectively. The maximum deformation on the absorber reached 17.85 mm at W = 7 m. High deformation and high Von Mises stress were maintained with f from 3.5 m to 5.5 m. The trends of maximum temperature difference and average temperature on bellows, Kovar ring and glass tube were similar. The results also showed that width and focal length mainly affected the axial stress on Kovar rings and bellows. • Three-dimensional coupled optical-thermal-stress model of PTR was established. • The MCRT-FVM-FEM coupled method was used to analysis the proposed model. • The effect of aperture width and focal length on PTR performance was studied. • Temperature and stress of bellows, glass tube and Kovar ring were specially analyzed. • It is unreasonable to ignore bellows and Kovar rings in simulating PTR. [ABSTRACT FROM AUTHOR]

The problem of uniqueness of universal formulae for (quantum) dimensions of simple Lie algebras is investigated and connection of some of these functions with geometrical configurations, such as the famous Pappus–Brianchon–Pascal (9 3) 1 configuration of points and lines, is established by proposing some generic functions, which multiplied by a universal (quantum) dimension formula, preserve both its structure and its values at the points from Vogel’s table. We deduce, that the appropriate realizable configuration (144 3 36 12) (yet to be found) will provide a symmetric non-uniqueness factor for any universal dimension formula. [ABSTRACT FROM AUTHOR]

A cyclic (n 3) configuration is a combinatorial configuration whose automorphism group contains a cyclic permutation of the points of the configuration; that is, the points of the configuration may be considered to be elements of Z n , and the lines of the configuration as cyclic shifts of a single fixed starting block [0, a, b], where a , b ∈ Z n . We denote such configurations as Cyc n (0 , a , b) . One of the fundamental questions in the study of configurations is that of geometric realizability. In the case where n = 2 m , it is combinatorially possible to divide the points and lines of the configuration into two classes according to parity, so it is natural to ask whether the configuration can be realized using those classes. We provide methods for producing geometric realizations of configurations Cyc 2 m (0 , a , b) that have two symmetry classes under the maximal rotational subgroup of the geometric symmetry group (that is, chiral astral realizations), and we provide a number of constraints on a and b that guarantee such a realization exists. Experiments on up to 500 points suggest that, with the exception of some small sporadic examples and a single infinite family Cyc 2 (k + 1) (0 , 1 , k) , k ≥ 3 and k odd, all cyclic (2 m 3) configurations are realizable as geometric chiral astral configurations using the methods described in this paper. [ABSTRACT FROM AUTHOR]

Torpedo anchors are an innovative and cost-effective technology in marine foundation engineering; however, there is a lack of systematic and comprehensive studies on the influence of torpedo anchor geometry on its hydrodynamic characteristics, especially the effect of anchor fin configuration on the hydrodynamic characteristics is rarely reported in the existing literature. Therefore, this study investigates the influence of geometric characteristics of both finless and finned torpedo anchors on their terminal velocity, drag coefficient and installation directional stability in water through CFD numerical analysis in a systematical manner. The considered geometric characteristics include the center of gravity position, shape and angle of anchor tip, shaft and fin aspect ratio, fin number, fin thickness, fin shape, fin position and fin area. Based on the obtained numerical results, some practical design recommendations and impact weighting charts of different anchor geometric factors are provided, which enables a quick qualitative and quantitative assessment of torpedo anchors. In addition, a simple weight-based approach for estimation of terminal velocity and drag coefficient of torpedo anchors considering multiple geometric configuration factors is proposed, which may provide some reference and scientific guidance for experimental and engineering design of torpedo anchors. • The effect of torpedo anchor geometry configuration on its hydrodynamic performance was systematically investigated. • Some practical design recommendations and impact weighting charts of different anchor geometric factors were provided. • A simple weight-based approach for estimation of terminal velocity and drag coefficient of torpedo anchors was proposed. [ABSTRACT FROM AUTHOR]

A geometric 4 -configuration is a collection of points and straight lines with the property that every point lies on exactly four lines in the collection and every line passes through exactly four points in the collection. This paper describes a method for constructing a large number of new infinite families of rotationally symmetric geometric 4-configurations which are movable; that is, there is at least one continuous parameter which preserves the symmetry of the configuration. In fact, the configurations in this paper have 2 q continuous parameters for any integer $$q \ge 2$$ ; previously the known classes of movable 4-configurations had only one or two degrees of freedom. The construction is extended to produce movable 4-configurations with dihedral symmetry. The paper ends with a number of open questions. [ABSTRACT FROM AUTHOR]

Recently, a curvature theory for polyhedral surfaces has been established that associates with each face a mean curvature value computed from areas and mixed areas of that face and its corresponding Gaussian image face. Therefore, a study of constant mean curvature (cmc) surfaces requires studying pairs of polygons with some constant nonvanishing value of the discrete mean curvature for all faces. We focus on meshes where all faces are planar quadrilaterals or planar hexagons. We show an incidence geometric characterization of a pair of parallel quadrilaterals having a discrete mean curvature value of −1. This characterization yields an integrability condition for a mesh being a Gaussian image mesh of a discrete cmc surface. Thus, we can use these geometric results for the construction of discrete cmc surfaces. In the special case where all faces have a circumcircle, we establish a discrete Weierstrass-type representation for discrete cmc surfaces. [ABSTRACT FROM AUTHOR]

Recently a curvature theory for polyhedral surfaces has been established, which associates with each face a mean curvature value computed from areas and mixed areas of that face and its corresponding Gauss image face. Therefore a study of minimal surfaces requires studying pairs of polygons with vanishing mixed area. We show that the mixed area of two edgewise parallel polygons equals the mixed area of a derived polygon pair which has only the half number of vertices. Thus we are able to recursively characterize vanishing mixed area for hexagons and other n-gons in an incidence-geometric way. We use these geometric results for the construction of discrete minimal surfaces and a study of equilibrium forces in their edges, especially those with the combinatorics of a hexagonal mesh. [ABSTRACT FROM AUTHOR]

This paper introduces a reasoning system based on a previously developed model for ternary projective relations between spatial objects. The model applies to spatial objects of the kind point and region is based on basic projective invariants and takes into account the size and shape of the three objects that are involved in a relation. The reasoning system proposes a set of permutation and composition rules, which allow the inference of unknown relations from given ones. [ABSTRACT FROM AUTHOR]

[Display omitted] • 3D coarse-grid CFD for pilot-scale biomass pyrolysis VPU reactor. • Sub-grid models incorporated into CFD model for meso-scale structure. • Study of extensive types of different gas inlet, catalyst feed and outlet structures. • The effect of geometric configurations on RTD and temperature is complex. The effect of geometric configurations on flow hydrodynamics, heat transfer, and residence time distribution (RTD) in a pilot-scale biomass pyrolysis vapor phase upgrading (VPU) reactor is comprehensively studied by numerical simulations. More specifically, three types of carrier gas structure, three types of particle feed structure, and five types of outlet structure are included in the present study. The results demonstrate that the effect of geometric configurations on heat transfer and RTD is much more pronounced than that on flow hydrodynamics such as the axial particle distribution, probably due to the low particle inventory. In this case, it is necessary to verify the difference of the temperature field in the grid independence analysis in addition to flow dynamics. Furthermore, we find that the carrier gas inlet and particle feed have an important influence on the particle distribution at the bottom of the reactor and thus affect the back-mixing behavior at both the bottom and outlet. As a consequence, such back-mixing flows further affect the temperature field and RTD substantially. Moreover, reducing the abrupt structure contributes to the catalyst particles well-distributed at the bottom of the reactor. This can reduce the mean residence time and variance, thereby decreasing the particle and gas temperature in the reactor. This work has a potential to provide a feasible guideline for biomass pyrolysis VPU reactor design and optimization. [ABSTRACT FROM AUTHOR]

Laser radiation can be used to reshape cartilage tissue into new morphologic configurations. When a critical temperature is attained, mechanically deformed cartilage becomes malleable and may be reshaped into new geometric configurations that harden as the tissue cools. This temperature dependent process results in mechanical stress relaxation and is characteristic of a phase transformation. The principal advantages of using laser radiation for the generation of thermal energy in tissue are precise control of both the space-time temperature distribution and time-dependent thermal denaturation kinetics. We illustrate the utility of laser mediated cartilage reshaping in ex vivo porcine model of reconstructive nasal and laryngeal surgery, and attempt to determine the temperature range in which accelerated stress relaxation occurs during laser mediated cartilage reshaping. Optimization of the reshaping process requires identification of the temperature dependence of this phase transformation and its relationship to observed changes in cartilage optical (diffuse scattering), mechanical (internal stress), and thermodynamic properties (heat capacity). Light scattering, infrared radiometry, and modulated differential scanning calorimetry were used to measure temperature-dependent changes in the biophysical properties of cartilage tissue during fast (laser mediated) and slow heating (conventional calorimetric beating). Our studies using MDSC and laser probe techniques have identified changes in tissue thermodynamic and optical properties suggestive of a phase transformation occurring near 60°C. Clinically, reshaped cartilage tissue can be used to recreate the underlying cartilaginous framework of structures in the head and neck such as the ear, larynx, trachea, and nose [ABSTRACT FROM PUBLISHER]