Non-circular Cross-section Research Articles

Computational Framework Development for Heat Transfer Studies in Liquid Metal-Cooled Small-Scale Heat Sinks With Non-Circular Cross Sections

Abstract The present work provides a reliable computational framework to investigate the laminar and turbulent forced convection of sodium and sodium–potassium (Na, NaK) in small-scale heat sinks with hydraulic diameters between 1 mm and 5 mm. Na and NaK flow and heat transfer are studied numerically for a wide range of Reynolds numbers from 600 to 9000 in three sharp-cornered miniature heat sinks with rectangular, pentagonal, and hexagonal cross sections. For a fixed surface area to volume ratio, it is observed that the rectangular minichannel heat sink provides the highest convective heat transfer rates. The rectangular miniature heat sink is shown to provide 280% higher convective heat transfer rates in comparison with the pentagonal heat sink. Moreover, the obtained convective heat transfer coefficients for NaK are almost 20% higher than the ones for Na in the investigated pentagonal heat sink. For the same flow Peclet number in the rectangular and hexagonal heat sinks, both Na and NaK provide nearly identical average Nusselt numbers. However, NaK shows greater local and average Nusselt numbers compared to Na at the same Reynolds number.

A novel auto-gaping magnetic pole system for inner surface finishing of non-circular pipes using magnetic abrasive finishing process

This study explored the design of a novel auto-gaping magnetic pole system for finishing the inner surface of non-circular pipes using a magnetic abrasive finishing (MAF) process. Non-circular pipes are widely used for the transportation of ultra-high purity substances, including gases and fluids in many industries for semiconductor, medical, and aerospace applications. MAF process typically utilizes non-movable magnetic poles. However, due to the noncircular cross-section of the pipe, the magnetic flux density, produced by non-movable magnetic poles, across the polishing surface will exhibit huge variations, resulting in uneven and poor finish at some areas. The proposed auto-gaping magnetic pole system allows the magnetic poles to move so that they can track the workpiece surface to keep the gap between the magnetic pole and workpiece’s external surface constant. As a result, the magnetic densities can be maintained at desired values to achieve even and effective finishing by MAF process. Elliptical pipes were used as the non-circular pipes for experimental validation under different MAF process parameters. The results showed that this novel technique for inner surface finishing of a non-circular pipe is capable of improving the surface roughness, reducing the Ra values from over 0.20 μm to 0.05 μm or lower, across the entire inner surface of the elliptical pipe. In addition, superior material removal efficiency was achieved. The results demonstrate that the MAF process combined with a novel auto-gaping magnetic pole system is feasible to produce the ultra-smooth inner surface of non-circular pipe.

Entropy Generation-Based Analysis of Laminar Magneto-Convection in Different Cross-Section Channel Filled with Ferrofluid and Subjected to Partial and Full Magnetic Fields

Heat transfer and entropy generation of laminar flow of a ferrofluid in different cross-section channel subjected to partial and full magnetic field are investigated in this study. A constant heat flux condition was applied on the external surface. The conservation equations (mass, momentum, and energy) are solved numerically via the finite volume method with a second-order precision. The effects of fully or partially applying a magnetic field with different directions and intensities on thermodynamic features, heat transfer, and entropy generation have been investigated. Analyses were carried out in four different cross-section channels, namely triangular, rectangular, circular, and elliptical. Results indicate that the circular cross-section channel provides higher heat transfer rates and lower entropy generation than non-circular cross-section channels.

Trajectory deflection of noncircular cross-section projectile penetrating into metal targets

To analyze the trajectory deflection of a noncircular cross-section projectile penetrating into multiple metal targets, numerical simulations with different impact velocities, projectile tip height and charge geometry are conducted. The simulation model is established using the finite element software LS-DYNA and verified based on the experiment carried out by a single-stage light gas gun. The results show that the impact velocity significantly affects the trajectory deflection of noncircular cross-section projectile. Although the deflections may be different in direction, the magnitudes exhibit decreasing trends with the increasing impact velocity. Besides, the trajectory varies from downward deflection to upward deflection with the increase of projectile tip height, and changes significantly with the tip height ranging from 0.8mm to 1.1mm. Further, as the geometry profile of projectile remains unchanged, the ones with noncircular charge exhibit better ballistic stability as compared with the circular charge projectile. This is mainly related to the variation in projectile mass instead of the variation in moment of inertia.

Axisymmetric oscillatory modes in cylindrical magnetized plasma bounded by a conducting wall

A comparison between analytic theory and numerical simulations of axisymmetric modes in magnetically confined, cylindrical plasma with non-circular cross-section bounded by a conducting wall is presented. If the wall is close to the plasma, modes are oscillatory, with frequency scaling with the Alfvén frequency. The two frequencies differ when the plasma cross-section is elongated, but they become equal in the circular limit. The mechanism for oscillatory behavior is a consequence of the currents induced on the perfectly conducting wall when the plasma is displaced from its equilibrium positions. The induced currents exert a restoring force on the plasma, and the oscillation frequency is a combination of the strength of this force and the plasma mass density. An additional parameter, depending on the distance between the wall and the plasma boundary, also affects the oscillation frequency so that the frequency becomes large when the wall-plasma boundary distance approaches zero.

Elementary Liber Fibres Characterisation: Bias from the Noncylindricity and Morphological Evolution along the Fibre

In this work, we investigate the influence of noncircularity along with cross-sectional area evolution on the measurement of the mechanical properties of elementary fibres. First, we focus on the cross-sectional area measurement and compare the circular assumption with the elliptical one using an ombroscopic device that allows the measurement of the projected diameters along the fibre as the fibre rotates around its axis, the fibre dimensional analysis system (FDAS). The results highlight important approximations to the cross-sectional area evaluation for fibres with noncircular cross sections, leading to reduced elastic modulus and stress at failure evaluated by the standard method. Additionally, results from the FDAS are used to evaluate the twist inside an individual fibre when the cross sections are sufficiently elliptical. A numerical model based on the real measured dimensions of the fibres is developed to illustrate and visualize this nonuniformity and to more accurately identify the elastic modulus. The results obtained lead us to an analytical approach that takes into account the evolution of the cross-sectional area along the fibre for a better identification of the stiffness and modulus of elasticity, which maximizes the identified mechanical properties on average by 12% for the modulus and 200% for the stress at failure. Finally, recommendations are formulated to better account for the variability along a fibre in order to evaluate the cross-sectional area.

Semi-Analytical Solution of Transverse Vibration of Cylinders with Non-Circular Cross-Section Partially Submerged in Water

The free transverse vibration of a surface-piercing, vertical cylinder partially submerged in water was studied. The cylinder had an arbitrary non-circular, but symmetric, cross-section in the vibration direction. The water was assumed to be an incompressible and inviscid fluid. The effect of the surface waves of water was neglected in the analysis. The exact solution of velocity potential of water was derived by the method of separation of variables. The unknown coefficients in the solution of the velocity potential were expressed in the form of integral equations, including the dynamic deformation of the beam. Then, the governing differential equation of bending vibration of the cylinder under the hydrodynamic pressure was obtained. The Galerkin method was used to obtain the eigenvalue equation by expanding the wet modes of the cylinder into a series of dry modes. The elliptical cylinders partially submerged in water were taken as the numerical example. The accuracy of the proposed method was evaluated by the convergence studies. As a consequent result, the non-dimensional added virtual mass incremental (NAVMI) factor solutions were compared to the present Galerkin solutions, which can be used as a benchmark test for more sophisticated numerical simulations of computational fluid dynamics.

A numerical approach to the stability analysis of growing cylindrical tubes and spherical tissues

In this paper, the effect of growth on the stability of elastic materials is examined through a numerical approach. Growth and resorption are considered to have two main effects from the stability standpoint. Corresponding to the change in mass, the geometry of a system changes, and the critical length of the system can be modified. In addition, the growth of the material may be affected by the stress, yet it may also impose residual stresses. As a result, the material is either stabilized or destabilized by these stresses. As a general framework for the description of elastic properties, the theory of finite elasticity is employed to investigate the growth of elastic materials. Growth is taken into account through matrix multiplication of the deformation gradient. The formalism of incremental deformation is adopted to consider growth effects. Using this formalism, the stability of growing neo-Hookean incompressible cylindrical and spherical shells under external pressure is considered. Firstly, the incremental equilibrium equations and the corresponding boundary conditions for the incompressible growing shells are summarized and afterward employed in order to analyze the behavior of spherical and cylindrical shells subjected to external pressure. The generalized differential quadrature method (GDQ) is utilized to solve the eigenvalue problem that results from a linear bifurcation analysis. It is shown that this numerical method can be efficiently utilized to solve the considered problem. The results are in full agreement with the previously obtained results. In the presence of external radial pressure, an elastic shell will buckle circumferentially to a noncircular cross-section. A change in thickness due to the growth can significantly affect buckling, both in terms of the critical pressure and the buckling pattern. Finally, the effects of the thickness ratio A1/A2, mode number n, and the growth parameter γ are studied on the shell’s stability.

On the flow of viscoplastic fluids in non-circular tubes

Steady flow of the viscoplastic Bingham and Herschel–Bulkley (H–B)​ fluids in tubes of non-circular cross-section is investigated analytically. The solution methodology is general in scope, does not put any restrictions on the Bingham number and thus allows the mapping of the flow field for high Bingham numbers in straight tubes with non-circular axially-symmetric but otherwise arbitrary cross-sectional contours. The circular tube contour is mapped onto an arbitrary non-circular contour on which the no-slip condition is satisfied via a one-to-one and continuous mapping. Governing equations are solved for the full spectrum of axially symmetrical cross-sectional shapes and a specific example is developed for the viscoplastic H–B fluid flow in a tube with an equilateral triangular cross-section. The shape and the extent of the plug zones centered on the tube axis and the stagnant zones in the corners are predicted for both Bingham and H–B fluids. The effect of the shear rate dependent viscosity of the H–B fluids, leading to either shear-thickening or shear-thinning behavior, on the formation of the plug and stagnation zones is examined.

The Influence of Fibre Cross Section Shape and Fibre Surface Roughness on Composite Micromechanics

Many of the carbon and natural fibres used in composite reinforcement have a non-circular cross section. Recently non-circular, or flat, cross section glass fibre products have become commercially available. This paper explores the potential effects that such non-circular fibre cross section shapes may have on the micromechanics of stress transfer at the composite fibre–matrix interface and the resulting changes in composite strength performance. Analytical modelling is used to show how the critical fibre length in composites with non-circular fibres is always less when compared to circular fibres with an equal cross-sectional area. This can result in significant changes to the strength performance of discontinuous fibre reinforced composites. Additionally, it is shown that the surface roughness found on natural and carbon fibres, many of which are also non-circular in cross section, can decrease the critical fibre length still further. These effects have important consequences for the use of single fibre micromechanical tests used for the characterisation of interfacial strength.

Flat glass fibres: The influence of fibre cross section shape on composite micromechanics and composite strength

Many of the fibres used in composite reinforcement have a non-circular cross section and recently non-circular glass fibre products have become commercially available. This paper explores the potential effects that such non-circular fibre shapes may have on the micro-mechanics of stress transfer at the fibre–matrix interface and the resulting changes in composite strength performance. Analytical modelling is used to show how the critical fibre length in composites with non-circular fibres is always less when compared to circular fibres with an equal cross sectional area. This can result in significant changes to the strength performance of discontinuous fibre reinforced composites. Additionally it is shown that non-circularity in fibre cross section can have important consequences for the use of single fibre micromechanical tests in the characterisation of interfacial strength.

The permanent magnet hypothesis: an intuitive approach to designing non-circular magnet arrays with high field homogeneity

Does the Halbach magnetization rotation rule that is used for designing circular magnet arrays for achieving the best homogeneity hold also for an elliptical or other non-circular cross-section? In this article, it is shown that a new numerically optimized magnetization rotation rule can provide more than three orders of magnitude improvement in field homogeneity as compared to a Halbach configuration for elliptical systems. Further it is demonstrated that such optimized magnetization rules can be easily derived in an intuitive way by studying virtual permanent magnets of a similar cross-section as the desired magnet array. This is coined as a permanent magnet hypothesis. Finally, it is shown that the applicability of this technique is not limited to circular or elliptical systems but can be applied to any arbitrarily shaped cross-section.

Torsional vibration of Timoshenko-Gere non-circular nano-bars

The displacement field and governing equation completely depend on the cross-section shape in the torsion of nano-bars. Due to the torsion of structure and warping of its cross-section, axial strain is created. A review of the literature demonstrates that the effect of the normal strain in the torsional analysis of nanostructures with non-circular cross-sections is ignored for the sake of simplicity and causes a computational error. While in the torsion of short nano-bars due to the great warping of the cross-section the normal strain appears and it shouldn’t be ignored. Therefore, for the first time, the effect of normal strain based on the torsion of Timoshenko-Gere theory is considered in this research. In this theory, the twist rate of non-circular sections in the axial direction is not considered constant, unlike studies in the literature. The governing equation of torsional vibration is extracted using the Hamilton principle, and the nonlocal strain gradient theory is used to show the size-dependent effects. The fundamental frequency is calculated for the arbitrary cross-section shape by using Galerkin’s method. The effect of parameters such as size effects, the thickness of nano-bar, mode number, and dimensions changes of cross-section versus natural frequency of nano-bar for both the Timoshenko-Gere and typical theories are investigated. Results indicate that neglecting normal strain due to warping the cross-section causes a significant error in the short nano-bars, especially at higher mode numbers. Also, a comparison is made between the obtained natural frequencies and those of the results reported in the literature.

Dependence of protein-induced lipid bilayer deformations on protein shape.

Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross sectionand yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.

Finite-Element Modeling of FRP-Confined Noncircular Concrete Columns Using the Evolutionary Potential-Surface Trace Plasticity Constitutive Model for Concrete

The compressive behavior of fiber-reinforced polymer (FRP)-confined concrete columns with a noncircular cross section has been investigated through extensive experimental, analytical, and numerical research, but a unified theoretical/numerical approach that can accurately predict both their section-average behavior and local concrete behavior is not yet available. In noncircular columns under axial compression, the concrete is typically under a nonuniform stress state of three-dimensional (3D) compression, with the lateral compressive stresses being the reactive stresses from the confining device (i.e., passive confinement). The authors of the present paper recently developed a plasticity constitutive model for concrete under general 3D compressive stresses, which possesses a potential surface with an evolutionary deviatoric trace that can accurately capture the results of existing compression tests of concrete cubes under nonuniform, passive confinement. This paper explores the application and capability of this evolutionary potential-surface trace (EPT) plasticity constitutive model in finite-element (FE) analysis of FRP-confined square, rectangular, and elliptical plain-concrete columns under concentric compression. The section-average behavior of all the selected noncircular columns predicted by these FE analyses was close to the existing experimental data. The numerical results obtained with the EPT plasticity constitutive model were then examined in detail to achieve an improved understanding of local concrete behavior in FRP-confined noncircular columns.

Eco-Friendly Fibers Embedded Yarn Structure in High-Performance Fabrics to Improve Moisture Absorption and Drying Properties.

This study examined the perspiration absorption and drying characteristics of eco-friendly fiber-embedded fabrics with different yarn structures. The wicking and drying rates of fifteen fabrics made from quadrilobal PET, Lyocell, and bamboo fibers were measured using two evaluation methods and compared with the pore diameter and hygroscopic characteristics of the constituent fibers in the yarns. The sheath/core yarn structure played a vital role in improving the moisture absorption and drying properties of the eco-friendly fibers embedded in high-performance fabrics, which was partly affected by the hygroscopicity and non-circular cross-section of constituent fibers in the yarns. Superior perspiration absorption and drying properties among the various eco-friendly high-performance fabrics were observed in the quadrilobal PET/Lyocell sheath/core and quadrilobal PET/bamboo spun yarn fabrics. By contrast, the PET/Lyocell Siro-fil, bamboo spun, and hi-multi PET yarn fabrics exhibited inferior moisture absorption and drying properties. In particular, the evaluated results between transverse and vertical wicking measuring methods in absorption property showed a similar trend. In contrast, the drying property measured between the drying rate (min) at a steady state and the drying rate (g) at a transient state showed a different trend. Multiple regression analysis showed that the wicking property of the eco-friendly fiber-embedded fabrics was mainly related to the pore diameter, cross-sectional shape, and absorption property of the fibers in the yarns, and it was also highly associated with the drying characteristics of the fabrics. The market application of the sheath/core yarn structure using Lyocell and bamboo fibers with quadrilobal PET is available for producing eco-friendly fabrics that can contribute to environmental improvement and wear comfort related to the moisture absorption and fast-drying properties of the woven fabrics.

The motion of long bubbles in microchannels using a meter-long, rectangular capillary on a chip

HypothesisThe dynamics of gas–liquid interfaces differs between aqueous surfactant and nanoparticle mixtures in rectangular cross-section capillaries. ExperimentsWe designed and fabricated a new microfluidic device with a meter-long channel and a noncircular cross section (35 μm by 100 μm by 1 m) to study the flow behavior of long bubbles in capillaries wetted by water as well as surfactant and nanoparticle solutions. Flow in the novel symmetric loop device maintains essentially straight and inertialess conditions over a wide range of flow rates. FindingsThe pressure-drop versus velocity relationship of long bubbles in capillaries with noncircular cross sections has been studied theoretically but not extensively validated. The measured pressure drop (normalized with respect to interfacial properties) experienced by bubbles varies as Ca2/3 over the range 10-7<Ca<10-4 where Ca=μUσ. Thus, the drag also scales as Ca2/3. The measurements from our new device thereby confirm previous theoretical relationships of the flow of long gas bubbles wetted by surfactant solutions in noncircular capillaries. Contrary to the hypothesis, the Ca2/3 drag–velocity relationship applies to gas bubbles in deionized water, nanoparticles in brine, surfactant in brine, and nanoparticle-surfactant mixtures in brine for the conditions studied.

A comprehensive geometric investigation of non-circular cross section spring-wire turbulator through the spiral-tube based heat exchangers

Non-circular cross section spring wire has not been investigated before as a turbulator through the spiral-tube based heat exchangers. Generally, spring diameter, springe pitch and wire diameter can impact the thermal performance of the spring wire employed as a turbulator through the heat exchangers. However, the impact level of these parameters becomes more severer and important when its cross section is non-circular shape such as triangular, rectangular, square, and hexagonal which are investigated in this research from thermal, exergetic and frictional viewpoints. According to the results, the general order of the highest to the lowest enhanced Nu number is triangular, rectangular, hexagonal, square, and circular. However, variation of the mentioned geometries significantly impacts the gap between the cases so that sometimes, the above order changes which are interesting. For instance, for smaller size of spring diameter there is no difference between the cross-section shapes so that all of them almost provides the same value of Nu number. However, by increasing spring diameter, different cross sections make completely different Nu number.

Comparative tests of the wall thickness effect of a glass-reinforced thermosetting plastic coating with a non-circular cross section in a soil-coating object for economic aspect

Comparative tests of the wall thickness effect of a glass-reinforced thermosetting plastic coating with a non-circular cross section in a soil-coating object for economic aspect

Many-body interactions between curvature-inducing membrane inclusions with arbitrary cross-sections.

By means of a multipolar expansion, we study analytically and numerically the interaction, in tensionless membranes, between multiple identical curvature-inducing membrane inclusions having arbitrary cross sections but uniform small detachment angles. In particular, for N circular inclusions forming regular polygons, we obtain analytical expressions for the total asymptotic interaction, up to N = 6, and we numerically compute the different multi-body contributions at arbitrary separations. We find that the latter are comparable to the sum of the two-body contributions. For N = 5 inclusions, the analytical asymptotic interaction scales as the inverse sixth power of the nearest neighbors distance d, weaker than the d-4 power for N ≠ 5. The analytical interactions are always repulsive and in good agreement with the numerical results. In the case of noncircular cross sections, we consider the case of two identical inclusions having a given number of equally shaped lobes. Depending on the number of lobes and their amplitude, we find that the interaction is asymptotically either repulsive as d-4 or attractive as d-2, and always repulsive at short distances. We also characterize how the interaction depends on the inclusion rotation angles in the membrane plane.