Semi-analytical Investigation Research Articles

Thermally developing streaming potential-mediated pressure-driven flow of Phan–Thien–Tanner fluid in a microchannel

In this study, we have conducted a semi-analytical investigation into the streaming potential-mediated pressure-driven flow of hydrodynamically fully developed and thermally developing viscoelastic fluid in a parallel plate microchannel. We have utilized a simplified Phan–Thien–Tanner model to describe the rheology of the viscoelastic fluid. Our approach delved into the full Poisson–Boltzmann equation, deriving exact analytical solutions for the electrostatic potential distribution and velocity profile. Furthermore, we concurrently derived semi-analytical solutions for the temperature distribution and Nusselt number, accounting for the effects of heat generation from viscous dissipation and Joule heating in thermally developing flows. We have demonstrated that an increase in the degree of surface charge triggers the streaming potential field, while the volumetric flow rate escalates with the viscoelastic parameter εWik¯2. Moreover, we have observed that the magnitude of the dimensionless temperature decreases with increasing values of the effective Joule heating parameter Speff. Our analysis reveals that the streaming potential effect hampers fluid flow, resulting in an increase in the bulk fluid temperature and consequently reducing the heat transfer rate. We observe that the magnitude of the Nusselt number decreases with increasing Speff. The entropy generation analysis reveals that increasing the Peclet number amplifies flow and temperature gradients, leading to higher fluid irreversibility in microchannels. The Bejan number experiences a significant decrease across the channel, reaching its minimum at a specific axial location before stabilizing further downstream. We find that heat transfer irreversibility predominantly influences system irreversibility, except for the Brinkmann number Br = 0.01, where convective heat transfer dominates at the entrance region, transitioning to friction losses beyond the thermal entry zone.

Secular evolution of co-orbital motion of two exoplanets: semi-analytical investigation

Secular evolution of co-orbital motion of two exoplanets: semi-analytical investigation

Efficient semianalytical investigation of a fractional model describing human cornea shape

Purpose: This study presents a novel application of the semianalytical residual power series method to investigate a one-dimensional fractional anisotropic curvature equation describing the human cornea, the outermost layer of the eye. The fractional boundary value problem, involving the fractional derivative of curvature, poses challenges that conventional methods struggle to address. Methods: The analytical results are obtained by utilizing the simple and efficient residual power series method. The proposed method is accessible to researchers in all medical fields and is extendable to various models in disease spread and control. Results: The derived solution is a crucial outcome of this study. Through the application of the proposed method to the corneal shape model, an explicit formula for the curvature profile is obtained. To validate the solution, direct comparisons are made with numerical solutions for the integer case and other analytical solutions available in the literature for the fractional case. Conclusion: Our findings highlight the potential of the proposed method to significantly contribute to the diagnosis and treatment of various ophthalmological conditions.

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

Semianalytical investigation on heat transfer in porous fins with temperature‐dependent thermal conductivity via the homotopy perturbation Sumudu transform approach

AbstractA unique investigation has been undertaken to analyze the heat transmission by convective and radiative mechanisms in a fully saturated penetrable fin of a longitudinal structure positioned on a leaning surface. This study introduces the fusion of the realms of Homotopy perturbation and Sumudu transform techniques to address a previously unexplored problem involving a moving fin with temperature‐dependent thermal conductivity. In prior research papers, the Homotopy Perturbation Sumudu Transform Method (HPSTM) was utilized to obtain analytical solutions for fins featuring temperature‐dependent thermal conductivity. However, in our current study, we employ the HPSTM to tackle a novel problem involving a moving porous fin. This fin exhibits temperature‐dependent thermal conductivity and is subjected to convection and radiation effects. Through a comparison with numerical results, the present study has validated the dependability of its findings. The dimensionless temperature profile has been investigated by studying its relationship with several parameters. Here we observed that when the Peclet number is augmented by 400%, there is a corresponding 1.11% increase in thermal outline at the fin's extremity. Enhancing the value of radiation parameter by 400% declines the temperature of the fin tip by 14.079%. This study encourages the application of the Homotopy perturbation Sumudu transform technique in more complex fin problems.

A stratified flow of a non-Newtonian Casson fluid comprising microorganisms on a stretching sheet with activation energy

A stratified flow may be seen regularly in a number of significant industrial operations. For instance, the stratified flow regime is typically used by gas-condensate pipelines. Clearly, only a limited set of working situations for which this flow arrangement is stable allow for the achievement of the stratified two-phase flow zone. In this paper, the authors are considered the laminar, steady and incompressible magnetohydrodynamic flow of a non-Newtonian Casson fluid flow past a stratified extending sheet. The features of bio-convection, Brownian motion, thermal radiation thermophoresis, heat source, and chemically reactive activation energy have been employed. The set of equations administered flow of fluid is converted into ordinary differential equation by suitable variables. A semi-analytical investigation of the present analysis is performed with homotopy analysis method. Endorsement of the current results with previous results is also investigated. The outcomes showed that the velocity distribution of the fluid flow lessens with higher Casson and magnetic factors. The temperature profiles of fluid flow shrinkage as the Prandtl number and Casson factor increase and enlarges with higher values of thermal radiation, magnetic, and Brownian motion factors. It is found that the growing thermophoretic and Brownian motion factors reduce the rate of thermal flow of the Casson fluid flow. In contrast, the increasing thermal stratification parameter increases the thermal flow rate of fluid.

Hydrodynamic Performance of a Very Large Floating Structure with Oscillating Water Columns: Semi-analytical Investigation

Hydrodynamic Performance of a Very Large Floating Structure with Oscillating Water Columns: Semi-analytical Investigation

Evolution of equal mass binary bare quark stars in full general relativity: Could a supramassive merger remnant experience prompt collapse?

We have evolved mergers of equal-mass binary quark stars, the total mass of which is close to the mass shedding limit of uniformly rotating configurations, in fully general relativistic hydrodynamic simulations, aimed at investigating the post-merger outcomes. In particular, we have identified the threshold mass for prompt black hole formation after the merger, by tracing the minimum lapse function as well as the amount of ejected material during the merger simulation. A semi-analytical investigation based on the angular momentum contained in the merger remnant is also performed to verify the results. For the equation of state considered in this work, the maximum mass of TOV solutions for which is 2.10 $M_\odot$, the threshold mass is found between 3.05 and 3.10 $M_\odot$. This result is consistent (with a quantitative error smaller than 1%) with the universal relation derived from the numerical results of symmetric binary neutron star mergers. Contrary to the neutron star case, the threshold mass is close to the mass shedding limit of uniformly rotating quark star. Consequently, we have found that binary quark stars with total mass corresponding to the long-lived supramassive remnant for neutron star case, could experience collapse to black hole within several times dynamical timescale, making quark stars as exceptions of the commonly accepted post-merger scenarios for binary neutron star mergers. We have suggested explanation for both the similarity and the difference, between quark stars and neutron stars.

Elastoplastic semi-analytical investigation on a deep circular tunnel incorporating generalized Zhang–Zhu rock mass strength

The semi-analytical method based on finite difference method is widely used in the study of the mechanical response of surrounding rocks in a circular tunnel. The core of the three-dimensional (3D) mechanical analysis of the plastic zone is to solve nonlinear equations with a complex yield criterion, which leads to a long iterative solution time and low accuracy. In this study, a new 3D semi-analytical method is proposed for a circular tunnel excavation. The method is based on the finite difference method, wherein a linear equation is used to replace the complex yield surface equation. This significantly reduces the iterative solution process and effectively improves the calculation rate. The accuracy of the proposed method is verified using conventional and 3D numerical methods. The two-dimensional (2D) generalized Hoek–Brown criterion (GHB), 3D generalized Pan–Hudson criterion (GPH), and 3D generalized Zhang–Zhu criterion (GZZ) are used to analyze the applicability of the proposed method. The mechanical properties of a circular tunnel excavation are studied using these criteria. Our results show that the calculation rate of the plastic zone response of the proposed method (based on the GZZ criterion) is 12,000 times higher than that of the conventional iterative method. The overall calculation rate is increased by a factor of 65, and the calculation error is smaller than that of the conventional method. The GHB does not consider the intermediate principal stress, and the GPH cannot reflect the mechanical properties of rock masses with different tensile and compressive strengths, although it considers the intermediate principal stress. The convergence–constraint characteristics of the surrounding rock of the GHB and GPH are significantly different from those of the GZZ. There is an optimal initial axial stress value qopt that yields the smallest deformation of the surrounding rock and the best stability. The internal support pressure and residual strength of the rock mass have a significant effect on the mechanical response of the surrounding rock. The proposed method has acceptable applicability to elastic–brittle and elastic–perfectly plastic rock masses. Additionally, it can be used in the study of deep-buried tunnel excavation at high geo-stresses.

Semi-analytical investigations on the dynamics of BeiDou inclined geosynchronous satellite orbit

A semi-analytical investigation on the dynamics of BeiDou IGSO is conducted in this paper. First, a semi-analytical propagator is constructed based on the mean element method. The comparison of results of semi-analytical propagation with reference orbits shows that all orbital elements except the semi-major axis agree well within six centuries. For some example orbits, the semi-analytical propagation of the semi-major axis is accurate only within several decades, which is related to the chaotic motion of the one-to-one tesseral resonance. Compared with the numerical ephemeris of Moon, an improvement of accuracy in the semi-analytical propagation is observed when a simple analytical ephemeris of Moon is adopted. This phenomenon agrees with the doubly averaging process of the third-body perturbation. Second, the dynamics of BeiDou IGSO are investigated using the Hamiltonian approach with simplified models. The transition between different resonance regions of one-to-one tesseral resonance is investigated by the computation of one-dimensional maximal Lyapunov characteristic exponent (1-mLCE). The secular resonance from the lunisolar perturbation modeled by a 2-DOF system is systematically investigated using the surface of section. The secondary resonance related to the precession of lunar node is identified by the computation of 1-mLCE. In the end, the reentry disposal for BeiDou IGSO is investigated as an optimization problem. With IGSO3 as an example of reentry orbit, the sensitivity analysis is conducted to study its stability and predictability.

Interaction between a non-concentric rigid sphere immersed in a micropolar fluid and a spherical envelope with slip regime

A semi-analytical investigation of a quiescent micropolar fluid between a rigid sphere and a non-concentric spherical envelope with a slip regime is obtained. Two different cases have been considered one is the hydrodynamic drag strength and the translational wall correction factor (TWCF) exerted by the fluid on the inner sphere are proportional to the translational velocities and the second is the hydrodynamic torque and the rotational wall correction factor (RWCF) are applied to the inner sphere which is proportional to the angular velocities. The numerical solution is composed of the superposition of the fundamental solutions in the two spherical coordinate systems setups on the poles of the rigid sphere and the spherical envelope by using a collocation scheme. The boundary conditions, slip, and spin-slip are presented on the sphere’s surfaces. The results were achieved numerically with excellent convergence for the parameters, size ratio, separation distance, micropolarity parameter, slip, slip-spin parameters. Limiting cases are agreeable with the obtainable results in the literature.

Semi-analytical investigations on bistable cross-ply laminates with MFC actuators

Most existing semi-analytical models to analyse multistable structures are based on the principle of minimum potential energy, which inherently does not satisfy the in-plane equilibrium equations in a strong sense. Although such models predict the multistable shapes with reasonable accuracy, there is a significant discrepancy in predicting the snap-through behaviour when compared to the finite element (FE) or experimental results. In this work, a refined analytical model is derived to analyse a bistable cross-ply elliptical disc using Föppl von Kármán kinematics. The Rayleigh–Ritz approach with a decoupled energy formulation is used, where the stretching and bending energies are separated using the semi-inverse constitutive equation. The in-plane stress resultants are expressed in terms of curvatures using the compatibility and the in-plane equilibrium equations. A closed-form solution for the curvatures is derived to predict the cured bistable shapes of elliptical laminates. A layer of macro fibre composite actuator is added to trigger the snap-through between the stable shapes. Consequently, the critical voltage at which the snap-through occurs is predicted using the analytical model. The model is further extended to square plates, where the solutions of the differential equations emanating from the compatibility and in-plane equilibrium equations are obtained by converting the resulting differential equations into the form of standard FE elasticity problem. The in-plane stress resultants for the square plates are calculated by numerically solving the resulting elasticity problem using a standard FE discretization approach. The solutions are further compared with previous experimental studies and the results from a fully geometrically non-linear FE model.

Abundant breather and semi-analytical investigation: On high-frequency waves’ dynamics in the relaxation medium

This paper investigates the high-frequency waves’ dynamical behavior in the relaxation medium through two recent analytical schemes. This study depends on the Vakhnenko–Parkes (VP) equation that has been reduced from the well-known Ostrovsky equation. The modified Khater (MKhat) and the extended simplest equation (ESE) methods are used to handle the considered model. As a result, many novel solitary wave solutions have been obtained to construct the initial and boundary conditions. These conditions allow employing the variational iteration (VI) method to study the semi-analytical solutions of the considered model. The accuracy of solutions is explained along with showing the matching between analytical and semi-analytical solutions and comparing our obtained solutions with the previous results that have been obtained in published research papers. Moreover, the high-frequency waves’ behavior relaxation medium is illustrated through some distinct sketches. The methods’ performance shows their effectiveness, direct, easy, and consequential for studying many nonlinear evolution equations.

Nonlinear Response and Buckling of Imperfect Plates Under In-Plane Pulse Forces: A Semi-analytical Investigation

This study presents a semi-analytical solution of the nonlinear dynamic response, shock spectrum, and dynamic buckling of a simply supported imperfect plate under various types of in-plane pulse forces. Here, the plate is modelled based on higher-order shear deformation theory (HSDT) considering the von-Karman geometric nonlinearity. The governing nonlinear partial differential equations (NLPDEs) of the imperfect plates are developed via Hamilton’s principle. Using Galerkin’s method, the NLPDEs are converted into sets of nonlinear algebraic equations (NLAEs) for static stability problems and nonlinear ordinary differential equations (NLODEs) for dynamic problems. The critical buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the plate is evaluated using nonlinear static stability analysis based on the yield stress failure criterion. The dynamic response and shock spectrum of the plates are plotted via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the yield stress failure criterion. Dynamic load factor (DLF) is the ratio of dynamic failure load to static failure load. Based on the pulse duration time, the pulse forces are divided into three categories known as impulsive, dynamic, and quasi-static. In the case of impulsive, dynamic, and quasi-static loading regimes, DLF > 1, DLF < 1, and DLF $$\approx$$ 1, respectively. The results obtained from the current works will help in the appropriate design of the imperfect plates against dynamic buckling.

Semi-analytical investigation on plasma density and reduced electric field of glow discharge in a turnery gas cw-CO2 laser

The plasma density and the reduced-electric-field (REF) parameters of CO2 gas laser have been measured and calculated at the maximum and minimum discharge current in terms of the similarity variable in order to investigate the discharge regimes. These parameters have been obtained with various combinations of ratios of CO2: N2: He gases. The obtained results were based on a new definition of the reduced-mobility variable for each gas species. The REF values had reducing behavior and did not much differed at both maximum and minimum discharge currents. The electron density had ascending behavior at the maximum discharge current, while it remained almost constant at the minimum discharge current. These results show that the regime of normal glow predominates at the minimum current, while a sub-normal glow regime governs at the maximum discharge current

Non-linear vibration and instability of multi-phase composite plate subjected to non-uniform in-plane parametric excitation: Semi-analytical investigation

Non-linear vibration and instability of a randomly distributed carbon nanotube fiber-reinforced composite (CNTFRC) plate under the action of different types of non-uniform in-plane periodic loadings are presented in this study. The composite plates are modeled considering von Kàrmàn non-linearity and Higher-order shear deformation theory (HSDT). The analytical expression for stresses (σxx,σyy,andτxy) distribution within the CNTFRC plate due to non-uniform loads is developed by solving the in-plane elasticity problem using Airy’s stress approach. Using these stresses, Hamilton’s principle is applied to derive the non-linear partial differential equations for dynamic instability and non-linear vibration of CNTFRC plates. Employing the Galerkin method, the non-linear partial differential equations are transformed into a set of non-linear ordinary differential (Mathieu type) equations. After dropping the nonlinearity terms, the linear ordinary differential equations are solved by using Bolotin’s method to trace the boundaries of the dynamic instability region corresponding to periods 2T and T. In the end, the non-linear ordinary differential equations are solved by using the Incremental Harmonic Balance method (IHB) for analyzing the non-linear vibration behavior of the CNTFRC plate. The result obtained from the current work will help in the appropriate design of the CNTFRC plate against stability and vibration in presence of non-uniform in-plane loadings.

Semi Analytical and Numerical Investigation of Vibration of Beams Partially Supported by Elastic Foundation

Bu çalışmada kısmen elastik zemin üzerindeki bir kirişin serbest titreşim problemi incelenmiştir. Kiriş modeli olarak Euler kirişi modeli, zemin modeli olarak da en yaygın kullanılan zemin modeli olan Winkler modeli kullanılmıştır. Elastik zemin üzerindeki kirişlerin titreşim problemi ile ilgili çeşitli araştırmalar literatürde mevcut olmakla birlikte, kısmen elastik zemin problemi için analitik çözümler mevcut olmayıp ve diğer yöntemlerle yapılan çalışmalarda oldukça sınırlıdır. Bu amaçla problemin varyasyonel iterasyon metodu ile önce yarı analitik çözümü yapılmış daha sonra da SAP 2000 yazılımı ile sonlu eleman analizleri gerçekleştirilmiştir. Farklı sınır koşulları altında kısmen elastik zemin üzerindeki kirişlerin analizi gerçekleştirilmiş, elastik zeminle desteklenen bölgenin değişimine bağlı olarak ilk dört serbest titreşim frekansı elde edilmiştir.

On the mechanism responsible for unconventional thermal behaviour during freezing

Abstract

Detection of cell-free DNA nanoparticles in insulator based dielectrophoresis systems.

In this paper, a semi-analytical investigation was performed to study the effect of the geometrical parameters of insulator-based dielectrophoresis (iDEP) systems for cell free DNA (cfDNA) trapping. For this purpose, first electrical potential and fluid flow fields were calculated by solving the governing equations including Poisson and Navier-stokes equations with appropriate boundary conditions (BCs) and then a Lagrangian approach was utilized to analyze the motion of cfDNA under the most important forces affected on it including Brownian, Drag, electrophoresis and dielectrophoresis (DEP) forces. The effect of the different parameters such as the electrical conductivity of the medium, shape and geometrical parameters of the insulators on the dielectrophoretic behavior of cfDNA was studied and the optimal value of these parameters was presented. Finally, in order to predict the minimum voltage required for cfDNA trapping, artificial neural network (ANN) was utilized and a relation between input and output parameters was introduced.

Semi-analytical investigation of electronic transport properties of a deformed simple cubic nanocrystal

We investigate semi-analytically the coherent electronic transport properties of a bent, twisted, compacted or stretched simple cubic nanocrystal within the nearest neighbor tight-binding approach and Green’s function technique. We take the bent, twisted, compacted and stretched part of the nanocrystal as a center wire and the other ideal parts as two semi-infinite similar left and right leads. Also, the cross-section of the wire is assumed to have square shape consisting of a finite number of atoms. We use a unitary transformation to separate the conductance modes in the ideal parts in order to calculate fully analytically center wire self-energies due to the existence of ideal leads. Then, we compute numerically the transport properties of the system by using the transformed Green’s function of the center wire which includes these self-energies. The results show that for bent and twisted configuration, some localized states form in perturbed part. The compacting has more influence on the electronic transport with respect to stretching. Also, the value of conductance at zero (Fermi) energy depends on the deformation strength in compacted and twisted nanocrystals.