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WaveGFD is a repository inspired by the development and analysis of meshless finite difference schemes for the wave equation in highly irregular domains, such as polygonal approximations of geographical regions. These methods' innovative approach allows to address the complexity of solving partial differential equations in highly irregular regions. They stand out for their precision and efficiency. The proposed methodology overcomes the limitations of conventional techniques, promising applicability in a broad spectrum of complex physical problems. The repository includes the methods necessary to find approximations to the solution of the wave equation, a set of test data consisting of clouds of points whose complexity varies from the unitary square (for comparison purposes) to regions that approximate actual geographic areas, examples of use, and results obtained with the proposed data and methods. WaveGFD considers the importance of having methods suitable for efficient implementations (i.e., that can be executed rapidly without the need for extensive and powerful computers) that can obtain satisfactory results when solving problems that may arise in different areas of engineering, such as civil and structural engineering (analysis of the vibrations in buildings and bridges), aerospace engineering (studies of the aeroelasticity of aircraft wings), electrical and telecommunications engineering (models of the propagation of electromagnetic waves), among others.

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In this paper, in order to establish the energy separation mechanism of the vortex tube, the hydrodynamic behavior of the compressible fluid in the asymmetric cavity space is investigated, and a numerical model of the trajectory deflection behavior is deduced and established; in order to form the optimal design method of the structural parameters of the vortex tube, the force situation of the fluid microelements entering different regions of the vortex chamber of the vortex tube is analyzed, and the trajectory deflection equations are corrected by combining with the expansion behavior of the fluid and the characterizing equations of vortex strength, transportability, and vortex initiation characteristics are given. The characterization equations of vortex strength, transportability and vortex initiation characteristics are given, and the numerical simulation of their influence parameters is carried out; in order to realize the prediction of the vortex tube performance of a given structure, the multifactor Pearson thermodynamic map is used to correlate and analyze the experimental data of vortex tubes reported publicly in the past years, and the polynomial regression equations are designed and established for the prediction of the vortex tube's energy separation effect and the confidence level and the degree of coincidence of the prediction results are examined. The confidence level and degree of agreement of the prediction results were examined. It is found that: the trajectory deflection motion of the compressible fluid in the asymmetric cavity space is the result of the combined effect of structural air pressure bias and the expansion behavior of the incident fluid; in order to improve the vortex strength in the vortex tube, the vortex initiation chamber space should be as small as possible; the increase of the diameters of the hot-end pipe and the cold-end pipe is conducive to the enhancement of vortex strength, but at the same time, it weakens the vortex transport in the heat pipe; the vortex initiation chamber size has a negative correlation with the hot-end temperature rise, and the inlet fluid pressure has a The negative correlation between the size of the vortex chamber and the temperature rise at the hot end, the positive correlation between the increase of inlet fluid pressure and the resulting temperature rise, and the strong correlation between the inlet fluid pressure and the friction coefficient on the effect of energy separation; the predictive equations for the effect of energy separation obtained by the fitting are in good agreement with the real situation.

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Ship noise emission has many environmental impacts. Recognizing noise-generating source and investigating noise reduction techniques is the first step in elimination or reduction of these harmful effects. Studies show that ship propeller is one of the main sources of ship noise emission. Ducted propeller is one of the well-known solutions for noise reduction. In this paper, results of numerical solution for governing mathematical equations of noise emission in far field is presented and sound pressure level is calculated using Ffowcs Williams and Hawkings (FWH) equations. Numerical solution is validated by valid research resources. Propeller noise emission is also calculated by experimental measurements and filtering ambient noise frequencies. Finally, a comparison has been made between numerical solution and experimental results and the effect of duct on noise reduction is calculated. The measured SPL emitted from the propeller in CFD approach (solving the FWH) shows 28% reduction for ducted propeller in comparison with the propeller without the duct. In experimental approach (after removing the ambient noise) shows 37% reduction for ducted propeller in comparison with the propeller without the duct.

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Current communication deals with the flow impact of blood inside cosine shape stenotic artery. The under consideration blood flow is treated as Newtonian fluid and flow is assumed to be two dimensional. The governing equation are modelled and solved by adopting similarity transformation under the stenosis assumptions. The important quantities like Prandtl number, flow parameter, blood flow rate and skin friction are attained to analyze the blood flow phenomena in stenosis. The variations of different parameters have been shown graphically. It is of interest to note that velocity increases due to change in flow parameter gamma and temperature of blood decreases by increasing nanoparticles volume fraction and Prandtl number. In the area of medicine, the most interesting nanotechnology approach is the nanoparticles applications in chemotherapy. This study provides further motivation to include more convincing consequences in the present model to represent the blood rheology.

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The world suffers from the acute respiratory syndrome COVID-19 pandemic, which will be scary if other co-existing illnesses exacerbate it. The co-occurrence of the COVID-19 virus with kidney disease has not been available in the literature. So, further research needs to be conducted to reveal the transmission dynamics of COVID-19 and kidney disease. This study aims to create mathematical models to understand how COVID-19 interacts with kidney diseases in specific populations. Therefore, the initial step was to formulate a deterministic Susceptible-Infected-Recovered (SIR) mathematical model to depict the co-infection dynamics of COVID-19 and kidney disease. A mathematical model with seven compartments has been developed using nonlinear ordinary differential equations. This model incorporates the invariant region, disease-free and endemic equilibrium, along with the positivity solution. The basic reproduction number, calculated via the next-generation matrix, allows us to assess the stability of the equilibrium. Sensitivity analysis is also utilised to understand the influence of each parameter on disease spread or containment. The results show that a surge in COVID-19 infection rates and the existence of kidney disease significantly enhances the co-infection risks. Numerical simulations further clarify the potential outcomes of treating COVID-19 alone, kidney disease alone, and co-infected cases. The study of the potential model can be utilised to maximise the benefits of simulation to minimise the global health complexity of COVID-19 and kidney disease.

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This paper investigates the impact of cubic autocatalysis on energy transport in Maxwell fluid flow induced into a rotating cylinder inspired by a solar radiative surface. The homogeneous-reaction is assumed to be furnished by the kinetics of isothermal cubic autocatalytic and the heterogeneous reaction by kinetics of first order. To prevent induced axial secondary flow, the cylinder's rotation is maintained at a constant rate. The characteristics of thermal radiation are also investigated to regulate the pace of heat transmission. A magnetic beam is projected in the upward radial direction to control the fluid momentum. A suitable flow ansatz is used to convert the entire physical problem of thermal energy transmission and fluid flow from partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). Results obtained numerically with the bvp4c approach are presented graphically and explained physically. It is observed that by flourishing the Reynolds parameter, the penetration depth decreases. Further, when the thermal relaxation period increases, the temperature field degrades. Moreover, when the homogeneous-heterogeneous reaction's strength is increased, a reduction in fluid concentration is shown.

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In this article, we investigate the bioconvection flow of Casson nanofluid by a rotating disk under the impacts of Joule heating, convective conditions, heat source/sink and gyrotactic microorganisms. When Brownian diffusion and thermophoretic effects exist, the Casson fluid is examined. The existing physical problem of Casson nanofluid flow with energy transports is demonstrated under the above considerations in the form of partial differential equations (PDEs). Using the appropriate transformations, the PDEs are converted into non-linear ordinary differential equations (ODEs). The mathematical results are calculated through MATLAB by using the function bvp4c. The problem's results are rigorously examined graphically and described with physical justifications. Velocity fields decrease as the bioconvection Rayleigh parameter rises. The thermal profile and soluteal field of species also magnify with an upsurge in thermophoresis number estimations. The microorganism's fields are decayed by larger microbes Biot number.

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The advancement of nanofluid innovation is a crucial area of research for physicists, mathematicians, manufacturers, and materials scientists. In engineering and industries, the fluid velocity caused by stretching sheets and nanofluids has a lot of applications such as refrigerators, chips, heat exchangers, hybrid mechanical motors, food development, and so on. The originality of the current study is the analysis of the thermal nanofluid in the existence of a porous matrix, and buoyancy force over the stretched sheet, so in limiting cases, the existing work is equated with the available effort, and excellent correspondence is originated. The governing equations in terms of PDEs are changed to the convection differential by utilizing the appropriate transformation and then solved by the ND-solved method along with bvph2. The thermal boundary layer thickness upsurges as the radiation and temperature factors are improved. It is observed that with the growing amount of volume fraction factor the velocity profile declines. When the velocity slip factors and permeability are enhanced the velocity profile augments. It is examined as the values of permeability factor, Biot number, and velocity slip factor are increased the inner temperature of the fluid improves. For the increasing values of θ_r, ϕ, and Nr, the temperature is increasing. In the future, the present model can be extended by using the hybrid nanofluid for the activation of thermal conductivity and heat enhancement analysis.

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The function of present work is to inspect heat transmission of radiative nanofluid in regard to boundary layer description. Carbon nanotubes (CNTs) dependent fluid is being evaluated and it flows overtop a curved stretching surface. Special features, like thermal radiation and internal heat generation, which corresponds to heat transmission along the flow have been incorporated. Dual nature of carbon nanotubes, that is, single walled carbon nanotubes (SWCNTs) as well as multiple walled carbon nanotubes (MWCNTs) together with blood (base fluid) have been utilized for the composition of nanofluid. The rheological properties of blood have been captured using Casson fluid model. Appropriate transformations have been applied to reduce the modeled system of nonlinear partial differential equations into a system of ordinary differential equations (ODEs). To achieve the desired numerical solution of obtained system of ODEs, NDSolve technique is employed using Mathematica. Numerous parameters appearing in governing equations, exert influence on focused physical quantities. Graphs have been engaged to capture these variations for both SWCNTs and MWCNTs. Likewise, numeric charts have been displayed to investigate impressions on skin friction coefficient and Nusselt number for distinct parameters.

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The present article describes the impact of variable thermal conductivity on the flow of ternary hybrid nanofluid with cylindrical shape nanoparticles over a stretching surface. Three nanoparticles combine in base fluid polymer. The assumption made will be used to model an equations. Modeled equations are in the form of a system of partial differential equations are difficult to solve can be converted to system of an ordinary differential equations, through resemblance substitutions, and will be solved numerically. Numerical scheme of Runge-Kutta order four is coupled with the shooting method to solve the resulting equations. The graphs in the study illustrate how physical quantities, such as magnetic field, injection/suction, nanoparticles volume fraction, and variable thermal conductivity, affected the velocity, skin friction, temperature, and local Nusselt number. The velocity profiles deflate as the volume fraction rises. While the temperature rises with an increase in the volume fraction of nanoparticles for both injection and suction, the velocity profiles also decline as the injection and suction parameter increases. Furthermore, as the magnetic field increases, the temperature profile rises while the velocity profile falls. The temperature curves increase as thermal conductivity increases. Finally, as the magnetic field is strengthened, the Nusselt number and skin friction decrease. The combination of mathematical modeling, numerical solution techniques, and the analysis of physical quantities contributes to the advancement of knowledge in this ternary hybrid nanofluid.

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The viscoelastic properties of food materials will change significantly while drying is in progress, which greatly influences the food deformation caused by drying. This study aims to predict the viscoelastic mechanical behavior of Hami melon during drying using the fractional derivative model. To characterize the relaxation characteristics, based on the finite difference method, an improved Grünwald-Letnikov fractional stress relaxation model is proposed to derive an approximate discrete numerical solution of the relaxation modulus by applying the time fractional calculus. The Laplace transform method is used to verify the obtained results, and the equivalence of the two methods is proved. In addition, the stress relaxation tests prove that the fractional derivative model has a better prediction effect on the stress relaxation behavior of viscoelastic food than classical Zener model. The significant correlations between the fractional order and the stiffness coefficient and the moisture content is also studied. Which is negative correlation and positive correlation respectively.

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An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.

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In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.

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Finite element analysis of complex bodies is frequently used in design to determine the size of deformations. Successive iterations, with progressive refinement of mesh densities, are most often required to obtain a sufficiently accurate convergent numerical solution. This process is costly, time consuming, and requires superior hardware and software. The paper presents a quick and effortless way to determine a sufficiently accurate value of the numerical solution. The mentioned solution is obtained by amending the numerical solution resulting for a certain value of the mesh density of the studied body with an adequate proportionality coefficient determined following the deformation study of simple bodies differently subject to external forces. It is assumed that the elastic displacement of the various bodies has a similar evolution as the mesh density increases and that the values of the proportionality coefficients considered are approximately equal for identical mesh densities. Examples presented are related to the reference body of the mechanical press PAI 25.

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The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, the Dynamical Survival Analysis (DSA) method has been shown to be an effective tool in analyzing complex non-Markovian epidemic processes that are otherwise difficult to handle using standard methods. One of the advantages of Dynamical Survival Analysis (DSA) is its representation of typical epidemic data in a simple although not explicit form that involves solutions of certain differential equations. In this work we describe how a complex non-Markovian Dynamical Survival Analysis (DSA) model may be applied to a specific data set with the help of appropriate numerical and statistical schemes. The ideas are illustrated with a data example of the COVID-19 epidemic in Ohio.

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The Caudrey-Dodd-Gibbon ( CDG ) model, a variation of the fifth-order KdV equation (fKdV) with significant practical consequences, is solved in this study using a precise and numerical technique. This model shows how gravity-capillary waves, shallow-water waves driven by surface tension, and magneto-acoustic waves move through a plasma medium. With a focus on accuracy, new computational and approximation methods have been made possible by recent improvements in analytical and numerical methods. Numeric information is represented visually in the tables. All simulation results are shown in two and three dimensions to show both the numerical and fundamental behavior of the single soliton. Recent research shows that this method is the best way to solve nonlinear equations that are common in mathematical physics.

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Increasing heat transfer is an important part of industrial, mechanical, electrical, thermal, and biological sciences. The aim of this study is to increase the thermal competency of a conventional fluid by using a ternary hybrid nanofluid. A magnetic field and thermal radiation are used to further improve the thermal conductivity of the base fluid. Irreversibility is analyzed under the influence of the embedded parameters. The basic equations for the ternary hybrid nanofluids are transformed from Partial Differential Equations (PDEs) to Ordinary Differential Equations (ODEs) using the similarity concept. The Marangoni convection idea is used in the mathematical model for the temperature difference between the two media: the surface and fluid. The achieved results are provided and discussed. The results show that ternary hybrid nanofluids are more suitable as heat-transmitted conductors than conventional fluids.

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When motor performance characteristic is unknown, non-linear differential equations of motion of nonideal gyroscopic rigid rotary system with nonlinear cubic damping and nonlinear stiffness of the elastic support turn out to be numerically unsolvable.•In this case, the method uses the motor performance characteristic expression found from the frequency equation of forced stationary oscillations based on assumption that the angular acceleration is many times less than the square of the angular speed of rotation, replacing the stationary rotation angular speed with the shaft rotation angle derivative.•The method correctness is evidenced by a good consistency between the rotor motion equation numerical solution results and the analytical solution results, and by the nonlinear cubic damping of the shaft angular coordinate oscillograms obtained by direct simulation, as well as by comparison with the results of numerical simulation for a straight-line DC motor performance characteristic.•The method limitations are that it is used for the first approximation and weak nonlinear oscillations in the resonance region, where the shaft rotation speed is of the order of the oscillating system natural frequency.

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As a result of the many real-world applications that may be derived from understanding stagnation point flow in designing, such as the coolant of nuclear reactors, there has been a great deal of interest in the topic. Consequently, the purpose of this research was to offer a numerical analysis of an unstable three-dimensional (3D) nodal stagnation point flow of polymer-based Al2O3-CuO-TiO2/polymer ternary nanofluid past a stretching surface with mass suction and heat source effects. In order to simplify the underlying partial differential equations, an appropriate similarity transformation is applied to them. This simplifies the ordinary differential equations. The shooting with the Runge-Kutta approach is used by the MATHEMATICA software to do the numerical calculation. Suction, stretching, unsteadiness, heat source, and nanoparticle volume fractions are other elements that play a role in regulating the flow and heat transfer as well as drag force profiles and how they affect the problem. The amount of heat transferred, and the friction coefficient increased in both directions when the suction parameter values were raised. In a ternary-hybrid nanofluid, the overall heat transfer rate decreases as the value of the heat source increases. Variations in the nanoparticles' volume fraction parameter cause an intensification in skin friction in both directions. Expanding the unstable and nanoparticles volume fraction parameters also reduces the Nusselt number. Furthermore, the heat transfer presentation of ternary-hybrid nanofluid has superior to the hybrid nanofluid and the normal nanofluid for the suction parameter. When the results of the current research were compared to those of a study that had already been done and published, they were found to be in good agreement.

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We consider a modified electrokinetic model to study the electrophoresis of a hydrophobic particle by considering the finite sized ions. The mathematical model adopted in this study incorporates the ion steric repulsion, ion-solvent interactions as well as Maxwell stress on the electrolyte. The dielectric permittivity and viscosity of the electrolyte is considered to vary with the local ionic volume fraction. Based on this modified model for the electrokinetics we have analyzed the electrophoresis in a single as well as mixture of electrolytes of monovalent and non- z : z $z:z$ electrolytes. The dependence of viscosity on local ionic volume fraction modifies the hydrodynamic drag as well as diffusivity of ions, which are ignored in existing studies on electrophoresis. A simplified model for electrophoresis of a hydrophobic particle incorporating the ion steric repulsion and ion-solvent interactions is developed based on the first-order perturbation on applied electric field. This simplified model is established to be efficient for a Debye layer thinner than the particle size and a smaller range of slip length. This model can be implemented for any number of ionic species as well as non- z : z $z:z$ electrolytes. It is established that the ion steric interactions and dielectric decrement creates a counterion saturation in the Debye layer leading to an enhanced mobility compared to the standard model. However, experimental data for non-dilute cases often under predicts the theoretically determined mobility. The present modified model fills this lacuna and demonstrate that the consideration of finite ion size modifies the medium viscosity and hence, ionic mobility, which in combination lowers the mobility value.

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