Difference Method Research Articles

Effects of new nonlinear curvature models and non-local elasticity on buckling investigation of FG tapered nano-beams locating on elastic foundations

New nonlinear curvature models are proposed to show their effects on the compressive critical buckling load on functionally graded (FG) tapered nano-beams locating on elastic foundations in the presence of non-local elasticity. Fourth and fifth orders finite difference methods (bvp4c and bvp5c) are applied on the governing differential equation which is a highly non-linear, due to curvature and has variable coefficients, due to properties. Dimensional analyses have been applied on the governing system together with the problem conditions to produce their dimensionless forms. For different considered parameters, the critical buckling load is computed using the eigenvalue theorem. The effects of nonlinear curvature, variable Young modulus, variable moment inertia and foundation parameters are studied and displayed in tables and figures. The stability and convergence of the present solution are tested using more than one strategy as: comparison with available results, comparison between bvp4c and bvp5c with different mesh intervals and tolerances of truncation errors. These comparisons show that, the new curvature model affects the critical buckling with different ratios depending on variability of properties and foundation parameters. The new results show that the nonlinear curvature model reduces the critical buckling load in comparison with the classical linear model, which, leads to decreasing in factor of safety in design of structures. The new results show that the design of structures will be influenced with the new reduction of the compressive critical buckling load, since it may affect the factor of safety in design of structures. The new results can lead, generally, to more reduction of critical buckling load for large or small input parameters and it will affect other critical values such that frequencies. The introduced Tables and Figures of the present problem with comparisons of previously exact, analytical and numerical works establish the higher accuracy and stability of current findings using bvp4c or bvp5c with preferable of the later. This study is related to some practical applications such as aeronautical and structural engineering.

Experimental study on flow and heat transfer characteristics of three types of finned tube bundle heat exchangers applied in aero-engines

This study outlines the design and manufacture of three types of finned tube bundle heat exchangers (HX) for advanced aero-engines followed by a series of experimental evaluations on flow and heat transfer characteristics. Considering the compactness and reliability, the finned tube bundle HX is more suitable for aero-engines when the heat transfer unit is small-diameter serpentine tubes with the enhanced heat transfer area provided by fins. In this paper, the Logarithmic Mean Temperature Difference method (LMTD) was utilized for the design of a small-diameter (OD: 3.6 mm with 0.3 mm thickness) finned tube bundle HX. Mass reduction was achieved by perforating the fins and removing the support devices, respectively. The flow and heat transfer characteristics of HXs and the impact of the mass reduction schemes were evaluated based on a series of comparative experiments. Among them, the connectionless scheme can significantly improve the power-to-mass ratio, providing it certain application value despite causing considerable flow resistance. Subsequently, empirical correlations for the flow and heat transfer outside the tubes suitable for small-diameter finned tube bundle HXs were proposed based on the experimental results, with over 95 % of the data falling within a 10 % error margin. These correlations have substantially modified the previous one for large-diameter straight tubes, providing an important reference for the future design of HXs in aero-engine.

Tangent hyperbolic MHD nanoliquids on non-isothermal stretched sheets: Analyzing the impact of transport parameters, variable fluid properties and convective boundary conditions

The key focus of this research is to look at how tangent hyperbolic magnetohydrodynamic (MHD) nano-liquids move in a non-isothermal coagulated stretched sheet. In this study, we intend to explore how fluid behavior responds to alternations in transport physical parameters. The coagulated sheet is subjected to two distinct boundary conditions to inspect the heat and mass transport rate of the nano liquid. The convective heat boundary condition (CBC) and mass-convective boundary condition (MCBC) are employed to specify the physical conditions at the boundaries of the problem domain. The boundary conditions, responsible for regulating heat flow and mass transfer rates, play a crucial role in shaping the liquid’s behavior. Using a similarity solution, the partial differential equation describing the flow of mass and heat within the system transforms into an interconnected network of non-linear ordinary differential equations. These mathematical equations are subsequently figured out using a numerical finite difference method. This study additionally examines the correlation between thermophoresis and Brownian motion, two fundamental concepts in the dynamics of colloidal suspensions. The study’s findings indicate that the temperature profile increases in all scenarios when the variable thermal conductivity and variable viscosity parameters are increased. In contrast, for the same parameters, the velocity profile is decreased. Further, increasing wall thickness reduces heat dissipation; consequently, the temperature profile similarly affects the velocity power index. The Biot number improves the rates of temperature transfer. These results underscore the significant influence of these parameters in predicting the behavior of MHD tangent hyperbolic nanofluids. This study elucidates the intricate interaction among different physical parameters in the dynamics of nano liquids, which holds significant implications for various industrial applications.

Analysis of Aerostatic Performance of a Flexure Pivot Tilting Pad Air Journal Bearing

Abstract Aerostatic performance of a flexure pivot tilting pad air journal bearing is examined with several numerical simulation under various working conditions. The air pressure distribution in the bearing clearance is obtained by solving the Reynolds equation with the finite difference method (FDM). The code consists of 3 main parts: mass flow rate equilibrium, moment equilibrium, and shaft equilibrium. They are used to study the gas pressure at the downstream of the nozzles, the motion of pads, and the position of the shaft in the bearing, respectively. Code accuracy is verified by comparing the results with those in other articles. This work lays the foundation for future research.

Partial abrasion modeling and variable load characteristics analysis for high-speed load sensing electro-hydrostatic actuator pump of aircraft

The load-sensing electro-hydrostatic actuator (LS-EHA) allows to reduce the thermal output and enhance the dynamic characteristics of the more electric aircraft (MEA). In addition, the forecasting of the LS-EHA is crucial for its efficient functioning. This study proposes a novel model for the analysis of overturning and wear characterization of the slipper, while focusing on the partial abrasion. The transient thermoelastic hydrodynamic (TEHD) lubricating analysis of the slipper pair is solved by an analytical model along with the finite difference method. In the proposed partial abrasion model, the non-uniformity of the oil film thickness and the partial abrasion contour for the slipper bottom surface are considered through the discrete friction area approach in order to reach a higher precision. Afterward, the overturning behavior characteristics of the slipper and the variation law in its overturning behavior under different rotation speeds, load delivery pressures, and swashplate angles are analyzed. The obtained results demonstrate that the lubricating oil film field is unevenly distributed, and the overturning behavior of the slipper has certain variable load characteristics. Finally, the effectiveness and precision of the proposed partial abrasion model are validated through comparative simulation experiments and analysis.

Numerical analysis of energy dissipation due to eddy currents in a vibrating beam

Vibration attenuation is a key aspect of mechanical engineering. One method to achieve this is through eddy currents, which can be generated in a vibrating system when a magnetic field is present, creating forces that oppose motion. This study examines a mechanical system consisting of a thin cantilever beam vibrating in a uniform and time-invariant magnetic field under steady-state conditions to understand the nature of energy dissipation and the relationship between motion, eddy currents, and damping forces. The calculation of eddy currents generally requires the use of complex numerical procedures. However, for systems with simple geometry, such as a cantilever beam, a recent numerical procedure based on the finite difference method, known for its simplicity in implementation, has been adapted and expanded to determine eddy currents under motional induction. A numerical application has been developed in which the vibration of a specific beam is characterised by its bending or torsional mode shapes, and the nature of the corresponding dissipative forces is analysed. Results indicate that the eddy currents are an effective means of dissipating energy at lower-order modes. Additionally, the direction of the applied magnetic field can induce coupling between bending and torsional vibrations.

Thermal recovery of heavy oil reservoirs: Modeling of flow and heat transfer characteristics of superheated steam in full-length concentric dual-tubing wells

Accurately predicting the flow and heat transfer characteristics of superheated steam (SHS) in the wellbore is essential for efficiently developing heavy oil reservoirs. However, few studies have examined SHS flow in full-length concentric dual-tubing wells (CDTWs). In this paper, firstly, based on fluid dynamics and thermodynamics theories, a mathematical model for SHS flow in vertical and horizontal wellbores is proposed. Then, this model is solved using a finite difference method for spatial discretization and an iterative technique. Finally, model verification, type curve analysis, and sensitivity analysis are conducted sequentially. The results indicate that SHS temperature and pressure are independent variables, and the effect of friction energy on temperature is greater than its impact on pressure. The injection rate has a critical value, and the critical injection rates of the main controlling factors affecting the pressure drop and temperature drop of SHS in the vertical tubing are different. When the injection rate is below the critical value, the gravitational force of the SHS helps maintain high enthalpy. The SHS should be transported to the well bottom as quickly as possible. To enhance the uniform heating effect of the reservoir and improve heat utilization efficiency, a relatively small injection rate, high injection pressure, and low injection temperature are recommended. The uniformity of SHS pressure and temperature distribution in the horizontal annulus positively correlates with the uniformity of the reservoir's heat absorption rate. Achieving more uniform SHS pressure and temperature profiles in the horizontal annulus benefits the uniform heating of the reservoir.

Systematic simulation of tumor cell invasion and migration in response to time-varying rotating magnetic field.

Cancer invasion and migration play a pivotal role in tumor malignancy, which is a major cause of most cancer deaths. Rotating magnetic field (RMF), one of the typical dynamic magnetic fields, can exert substantial mechanical influence on cells. However, studying the effects of RMF on cell is challenging due to its complex parameters, such as variation of magnetic field intensity and direction. Here, we developed a systematic simulation method to explore the influence of RMF on tumor invasion and migration, including a finite element method (FEM) model and a cell-based hybrid numerical model. Coupling with the data of magnetic field from FEM, the cell-based hybrid numerical model was established to simulate the tumor cell invasion and migration. This model employed partial differential equations (PDEs) and finite difference method to depict cellular activities and solve these equations in a discrete system. PDEs were used to depict cell activities, and finite difference method was used to solve the equations in discrete system. As a result, this study provides valuable insights into the potential applications of RMF in tumor treatment, and a series of in vitro experiments were performed to verify the simulation results, demonstrating the model's reliability and its capacity to predict experimental outcomes and identify pertinent factors. Furthermore, these findings shed new light on the mechanical and chemical interplay between cells and the ECM, offering new insights and providing a novel foundation for both experimental and theoretical advancements in tumor treatment by using RMF.

Hybrid multiscale computational approach for heat transfer in GaN semiconductors

Abstract With ongoing advancements in semiconductor technology, understanding thermal transport in semiconductor devices—where phonons are the primary charge carriers—is crucial. This involves a multiscale process in which phenomena at different scales are governed by distinct control equations, necessitating various numerical methods. In this context, this paper introduces a novel multiscale simulation method called the Second-Order Reconstruction Operator Finite Difference Lattice Boltzmann Method (ROsFDLBM). This method effectively combines the Lattice Boltzmann Method (LBM) with the Finite Difference Method (FDM). ROsFDLBM employs reconstruction operators to accurately map the relationship between distribution functions and macroscopic physical quantities, significantly reducing errors caused by the transmission of interface information. The efficacy of this coupling scheme has been confirmed through an interface-coupled thermal diffusion model. Comparative analyses have revealed that the relative error of ROsFDLBM does not exceed 1.2%, demonstrating its superior accuracy. Further simulations of GaN devices have confirmed that traditional macroscopic methods tend to underestimate the temperature in the heat source area at micro-nano scales, with discrepancies reaching up to 60.9 K. Overall, the ROsFDLBM aligns with current research findings and offers an accurate and efficient simulation strategy for addressing complex heat transfer problems.

On the numerical solution to space fractional differential equations using meshless finite differences

We derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and several examples over one dimensional irregular meshes are given.

Theoretical analysis for dynamic model of U-shaped electrothermal microactuator based on Chebyshev spectral method

Abstract This paper presents a largely and accurate analysis for dynamic model of U-shaped actuator that considers the material parameters dependent on temperature. The electro-thermal analysis for temperature distribution and thermo-mechanical analysis for deflection is carried out. The electro-thermal dynamic behaviour is described by piecewise one-dimensional (1D) heat transfer partial differential equations (PDE) for each beam of U-shaped actuator. A combination of Chebyshev spectral method for space domain and Euler forward difference method for time domain is used to solve these equations. The convergence test is first done to ensure the result convinced.

Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk

Environmental management and restoration should be designed such that the risk and uncertainty owing to nonlinear stochastic systems can be successfully addressed. We apply the robustified dynamic Orlicz risk to the modeling and analysis of environmental management and restoration to consider both the risk and uncertainty within a unified theory. We focus on the control of a jump-driven hybrid stochastic system that represents macrophyte dynamics. The dynamic programming equation based on the Orlicz risk is first obtained heuristically, from which the associated Hamilton–Jacobi–Bellman (HJB) equation is derived. In the proposed Orlicz risk, the risk aversion of the decision-maker is represented by a power coefficient that resembles a certainty equivalence, whereas the uncertainty aversion is represented by the Kullback–Leibler divergence, in which the risk and uncertainty are handled consistently and separately. The HJB equation includes a new state-dependent discount factor that arises from the uncertainty aversion, which leads to a unique, nonlinear, and nonlocal term. The link between the proposed and classical stochastic control problems is discussed with a focus on control-dependent discount rates. We propose a finite difference method for computing the HJB equation. Finally, the proposed model is applied to an optimal harvesting problem for macrophytes in a brackish lake that contains both growing and drifting populations.

Cilia-assisted flow of electrically conducting micropolar fluid in a heated curved channel under Soret and Dufour effects

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the influence of heat and mass transfer on the ciliary flow of electrical conducting micropolar fluid in a curved channel. The energy and concentration equations are modulated with viscous dissipation, Soret, and Dufour effects. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). Results for velocity, pumping phenomenon, concentration, thermal field, rate of heat transfer, streamlines, skin friction coefficient, Nusselt number, and Sherwood number are analyzed subject to pertinent parameters. The study reveals that velocity is enhanced via both the micropolar parameter and curvature parameter. Temperature enhances for larger values of Dufour and Brickman numbers. Furthermore, the radial magnetic field plays a resistive role in the trapped bolus. The findings presented in this study should prove beneficial for researchers in the domains of medicine, engineering, science, and fluid mechanics. Further, it is found that the micropolar fluid model is more suitable for biofluids like blood.

Numerical methods for scalar field dark energy in tabletop experiments and Lunar Laser Ranging

Numerous tabletop experiments have been dedicated to exploring the manifestations of screened scalar field dark energy, such as symmetron or chameleon fields. Precise theoretical predictions require simulating field configurations within the respective experiments. This paper focuses onto the less-explored environment-dependent dilaton field, which emerges in the strong coupling limit of string theory. Due to its exponential self-coupling, this field can exhibit significantly steeper slopes compared to symmetron and chameleon fields, and the equations of motion can be challenging to solve with standard machine precision. We present the first exact solution for the geometry of a vacuum region between two infinitely extended parallel plates. This solution serves as a benchmark for testing the accuracy of numerical solvers. By reparametrizing the model and transforming the equations of motion, we show how to make the model computable across the entire experimentally accessible parameter space. To simulate the dilaton field in one- and two-mirror geometries, as well as spherical configurations, we introduce a non-uniform finite difference method. Additionally, we provide an algorithm for solving the stationary Schrödinger equation for a fermion in one dimension in the presence of a dilaton field. The algorithms developed here are not limited to the dilaton field, but can be applied to similar scalar-tensor theories as well. We demonstrate such applications at hand of the chameleon and symmetron field. Our computational tools have practical applications in a variety of experimental contexts, including gravity resonance spectroscopy (q Bounce), Lunar Laser Ranging (LLR), and the upcoming Casimir and Non-Newtonian Force Experiment (cannex). A Mathematica implementation of all algorithms is provided.

Different built-in electric fields for transmission-mode GaAs photocathodes through doping engineering: Design and modeling

In order to enhance the emission performance of transmission-mode GaAs photocathodes used in optoelectronic field, different exponential doping structures are designed for the GaAs emission layer to generate different types of built-in electric fields. These built-in electric fields include the constant, increasing and decreasing types, which can help photoelectron transport toward the emission surface. By solving the one-dimensional continuity equation using the finite difference method, the electron concentration distribution and quantum efficiency of the three types of exponential doping GaAs photocathodes are derived. Meanwhile, the light absorption distributions in the emission layer are simulated by the finite difference time domain method. By comparing the optical absorption distribution and the electron concentration distribution, it is concluded that, among the three types of exponential doping structures, the exponential doping structure generating the increasing built-in electric field has the most sufficient long-wave light absorption capacity and the strongest photoelectron transport ability, thereby achieving the highest quantum efficiency. This theoretical work can help understand the mechanism of improving the photoemission performance of GaAs photocathodes through doping engineering.

Study on bearsing capacity and rigidity of surface throttling bearing

Abstract Based on the lubrication principle and Reynolds theory, the influence of the pressure field and structural parameters on the bearing characteristics of the surface throttle bearing is analyzed and studied by using the finite difference method. The results show that the surface throttling bearing has obvious static bearing characteristics when the shaft is not rotating; The dynamic pressure effect of oil wedge load can be seen obviously when the shaft rotates. With the increase of radius gap h0, the bearing capacity and rigidity will decrease significantly. The increase of oil supply pressure will reduce bearing capacity and rigidity. With the increase of length-diameter ratio L ¯ , the rigidity will be improved.

Brownian motion in a magneto Thermo-diffusion fluid flow over a semi-circular stretching surface

The current study explores the mass and heat transport analysis of a Casson liquid stream past a curved surface. The current model considers the effect of magnetic strength brought on by the strength of the applied uniform magnetic field. The significance of thermophoresis and Brownian motion are also taken into account using the Buongiorno nano-liquid model. The study of liquid flow over stretching sheets frequently addresses practical issues that have garnered significant attention from researchers due to their importance in various domains, including microfluidics, fibreglass production, manufacturing, transportation, metal extrusion, thermal insulation, glass production, paper manufacturing, and acoustic blasting. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity variables. These equations are numerically solved using the finite difference method (FDM). The concentration, temperature, and velocity graphs were produced by varying the different physical parameters. The upsurge in the magnetic parameter reduces the velocity profile. As the magnetic parameter increases, thermal and concentration profiles upsurge. The decrease in velocity profile can be seen as the Casson parameter rises. The intensification in values of thermophoretic parameter enhances the thermal and concentration profiles. The concentration and thermal profiles reduce as the curvature parameter upsurges.

Identification Source Term of the Distributed Order Time-Space Fractional Diffusion Equation

Abstract The inverse source problem for time-distributed order spatial fractional diffusion equations is examined in this study. The forward problem is solved by combining finite difference methods with matrix transformation techniques. The Tikhonov regularization approach is then applied to convert the inverse problem into a variational problem. The optimal perturbation approach is used to find the minimizer of the variational problem, leading to an approximation solution that depends solely on the time-dependent source term. The algorithm’s effectiveness and stability are demonstrated using numerical examples in one-dimensional domains.

A novel binary data classification algorithm based on the modified reaction-diffusion predator-prey system with Holling-II function.

In this study, we propose a modified reaction-diffusion prey-predator model with a Holling-II function for binary data classification. In the model, we use u and v to represent the densities of prey and predators, respectively. We modify the original equation by substituting the term v with f-v to obtain a stable and clear nonlinear decision surface. By employing a finite difference method for numerical solution of the original model, we conduct various experiments in two-dimensional and three-dimensional spaces to validate the feasibility of the classifier. Additionally, with consideration for wide real applications, we perform classification experiments on electroencephalogram signals, demonstrating the effectiveness and robustness of the classifier in binary data classification.

CONTACT INTERACTION OF AN UNDERGROUND PIPELINE WITH SOIL UNDER DYNAMIC IMPACTS

The interaction between a semi-infinite underground pipeline and the surrounding soil during longitudinal seismic wave propagation is examined in the article. The wave travels through the soil with its front perpendicular to the pipeline's axis, and the nonlinear laws of interaction (friction) on the surface of their contact, including the Amonton-Coulomb law, are used to solve related wave problems for the pipeline and soil. The method of characteristics and the finite difference method are sequentially used to solve these problems numerically. The implementation of the law of interaction (friction) processes is shown, depending on the parameters of the wave in soil and the mechanical characteristics of soil. It was determined that a wave in soil that involves the pipeline generates a powerful wave in the pipeline. The amplitude of this wave is many times greater than the amplitude of the wave in soil, and it propagates through the pipeline without attenuation. The dependences of the amplitude of this wave on the parameters of the law of friction, waves in soil, and the mechanical characteristics of soil are determined.