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The objective of current investigation is to examine Maxwell fluid flow generated by cylindrical stretching pipe. Thermophoresis and Brownian moment phenomena will also incorporate on the said fluid. Melting heat shifting phenomenon incorporated at the surface of the elongating cylinder. Mathematical formulation is supported by boundary layer assumption. Suitable similarity transformations diminishes model of nonlinear partial differential equations into a model of nonlinear ordinary differential equations that ultimately solved via numerical technique named Finite Element Technique. The properties of numerous effective variables are graphically displayed and examined. Further the physical quantities like velocity gradient, heat and mass fluxes are tabulated numerically and analyzed. The dimensionless temperature distribution rises for rising values of curvature parameter and Brownian motion parameter however an opposite behavior is observed for melting parameter and Prandtl number. Moreover, a reduction occurs in heat and mass fluxes for sufficiently high values of curvature parameter. [ABSTRACT FROM AUTHOR]

This study investigates the flow and heat transfer characteristics of a second grade fluid over a flat surface with variable heat flux. Utilizing a mathematical model based on distributed order fractional derivatives, we offer a more precise representation of non-Newtonian fluid behavior. The associated highly nonlinear equations are tackled numerically through an innovative amalgamation of the finite difference scheme and the L1 technique. Our investigation thoroughly evaluates the influence of several critical parameters on the fluid’s motion and thermal characteristics. Notably, the magnetic parameter significantly inhibits the fluid’s velocity, illustrating the impact of magnetic forces. Additionally, the power law parameter leads to a decrease in both velocity and temperature profiles, highlighting its influence on fluid dynamics. Furthermore, changes in the Reynold number and the second-grade fluid parameter are observed to cause a substantial increase in skin friction, by approximately 40% to 50%. These simulation results provide valuable insights into the complex interaction between fluid flow and heat transfer characteristics, enhancing our understanding of such systems in industrial applications. [ABSTRACT FROM AUTHOR]

After applying a magnetic field, the behavior of the partly ionized liquids is completely different from that of the ordinary fluids. In this study, we concentrated on the Cattaneo–Christov heat flux model-based three-dimensional partly ionized bio-convective flow of a second-order fluid on a bidirectional permeable stretching surface. The development of the thermal and solutal flow models takes into account the impacts of non-uniform sources and sinks, Ohmic viscous dissipation, and chemical reactions. In addition, the surface boundary effects of electron and ion collisions with convective boundary conditions are seen. The mathematical flow model is transformed appropriately to create an ordinary differential equations, which is then numerically solved with MATLAB's BVP4C approach. To demonstrate the physical relevance of the flow field along various developing parameters, graphical and tabular results are created. It is noteworthy to note that while fluid temperature decreases with stronger values of the second-order fluid parameter, fluid velocity improves in both directions. In addition, it is shown that raising the thermal and concentration relaxation parameters, respectively, causes a drop in the fluid temperature and nanoparticle concentration. [ABSTRACT FROM AUTHOR]

Particle dissolution is an important process that occurs during heat treatment in the transportation process. We present a one-dimensional model of spherical wax particle dissolution in a fluid. The model includes a nonlinear equation at the free boundary, which was established to describe the dissolution rate of a wax particle assuming a diffusion process. At the moving boundary, we compute the concentration distributions of partial solutions. To estimate wax dissolution in solution and related expressions for the dissolved radius, an analytical solution of a mathematical model for spherical particle dissolution in flow is used. [ABSTRACT FROM AUTHOR]

This article presents an analysis of the radiative flow of nanofluid past a convected vertical Riga plate with activation energy and nonlinear heat generation. A Riga plate is a surface-mounted electromagnetic actuator with a spanwise aligned array of alternating electrodes and permanent magnets. The aforementioned rheological model is formulated in the way of the nonlinear partial differential equations (PDEs). The system of nonlinear coupled ordinary differential equations (ODEs) is obtained from the modeled nonlinear PDEs by incorporating valid similarity transformations. The system of ODEs is then figured out by the reliable shooting method. The effects of mixed convection, modified Hartmann number, Biot number, thermophoresis, Eckert number, reaction rate, the width of magnets and electrodes, and Lewis and Prandtl numbers on the velocity, temperature, and concentration profiles are investigated graphically and numerically. It is found that the speed of the fluid can be managed with the separation of magnets and electrodes. Further, the concentration of nanofluid is significantly enhanced in the presence of activation energy. Also, the nonlinear exponential index parameter of heat generation declines the temperature of the fluid. Further, it is found that in the presence of thermal radiation, viscous dissipation, and nonlinear heat generation, the Nusselt number increases averagely by about 11.3%. [ABSTRACT FROM AUTHOR]

In this paper, a universal computational algorithm is constructed by using F and G series, which can be applied for any of conic orbit. In particular, to find the solution of the two–body problem. In this context, the solution of geocentric system motion of the Mercury planet in the solar system is found using the obtained computational algorithm. [ABSTRACT FROM AUTHOR]

Currently, owning a car is a necessity, as it plays a significant role in human transportation for different purposes such as going to work and to the hospital. However, with the current economic challenges, buying expensive cars can be a burden. The car market has shifted toward more affordable used cars. Due to the increasing number of used cars being sold, the price of used cars has become a major issue that could affect our sustainable way of living. The objective of this research is to understand the impact of the problem and to find empirical solutions by implementing a variety of machine learning techniques and big data tools on the prices of used cars. Thus, we develop a linear regression model that can estimate used car prices based on various features to answer the following research questions: (R.Q.1) How significantly does an independent feature in the dataset affect the dependent variable (car price)? (R.Q.2) Is a linear regression model effective for prediction of used car prices? (R.Q.3) How does prediction of used car prices support sustainability? Finally, we present our results in the form of answers to these questions, including some limitations and future research. [ABSTRACT FROM AUTHOR]

Human survival is purely based on the environment. Through natural calamities or man-made depredation, the pleasant existence is disturbed. Trees provide not just foliage for the environment but also a pleasant atmosphere for the human population. One of the most serious threats to the forest and ecology is the pine wilt disease (PWD). It is a devastating disease that kills pine trees in a matter of weeks. The pine-wood nematode Bursaphelenchus Xylophilus causes PWD. This study emphasises on the infectious model of PWD engaging the q -homotopy analysis transform method (q -HATM) to a leading fractional operator Caputo–Fabrizio fractional time derivative to arrive for superior understanding. The denouements are presented in the forms of plots and tables. At last the paper supports to examine the real-world models and helps to forecast their behavior that communicate the instructions considered in the models. [ABSTRACT FROM AUTHOR]

The heat and mass transfer in normal impingement of the Hiemenz stagnation-point flow of a viscous nanofluid on a bidirectional stretching sheet under the influence of the magnetic field is investigated. In a recent study, Weidman (Meccanica, vol. 53, p.833, 2018) has analyzed the phenomenon of the Hiemenz stagnation-point flow over the biaxially stretching sheet. Dual solutions have been found in this study for the various values of α (streamwise stretching rate) and β (cross-stream stretching rate). In the present work, the mechanism of thermal and solutal energy transport in the Hiemenz stagnation-point flow of nanoliquid is studied in the view of thermophoretic and Brownian forces. The solutions of similar ordinary differential equations (ODEs) for flow and energy transport in viscous nanofluid are computed with help of bvp4c numerical technique. The impact of dimensionless parameters on flow field and energy transport is presented graphically and discussed with physical reasoning. The outcomes reveal that the higher magnitude of Lorentz force declines the flow field in cross-stream and vertical directions, but conflicting behavior is noted for streamwise velocity component in the case of α < 1 and α > 1. Both thermophoresis and Brownian motion of nanoparticles enhance the energy transport in Hiemenz flow of viscous fluid. The results of the present study are validated through the shear stress parameters with a previously published study. [ABSTRACT FROM AUTHOR]

The energy and mass dissemination rate have been studied through Williamson hybrid nanofluid (NF) flow comprised of silver (Ag) and magnesium oxide (MgO) nanoparticles (NPs) past over an extending porous surface. The hybrid nanofluid has synthesized by dispersion of Ag and MgO nanoparticles in the base fluid (engine oil). The effects of the constant magnetic field, thermal dissipation, and heat source are also studied in the present analysis. The above scenario has been designed in the form of a nonlinear system of partial differential equations, which are processed through a similarity framework to the system of dimensionless ordinary differential equations. The results are obtained by the numerical computational approach parametric continuation method. It has been perceived that the velocity contour decreases with rising upshots of porosity parameter Kp and magnetic force M, while enhances with the variation of volume friction coefficient. The increment of Biot number Bi, heat source Q, and Eckert number Ec enhances the energy profile, respectively. Furthermore, the mass conversion rate decreases with the variation of thermophoretic parameters and Schmidt number. [ABSTRACT FROM AUTHOR]

The current paper focused on an unsteady bio-convective Maxwell nanofluid flow subject to convective boundary conditions through an exponentially stretching curved surface. The transportation of heat and mass are observed with thermophoresis and Brownian effect along with chemical reaction. The mathematical flow model is converted into a system of nonlinear system of ODEs via suitable transformation. The numerical solution of a nonlinear system of equations is established with the help of bvp4c MATLAB technique. It is deeply studied that in the curved surface, the pressure is never ignored. The graphical representation of several parameters along the temperature, concentration, microorganism density and velocity distribution is presented. It is examined that the greater estimation of curvature parameter boosts the temperature of fluid and concentration of nanoparticles, although a reverse trend is seen for the velocity profile. Further, it is examined from the numerical values that the heat and mass transfer rate reduce consequently with the enlargement of the curvature parameter. [ABSTRACT FROM AUTHOR]

The modeling of nonlinear dynamical models and their solutions have imperative values, whereas the soliton mathematical methods are favorable tools for analyzing such highly nonlinear practical problems. Herein, time-fractional coupled Burger's model is analyzed. Some solitary wave solutions, containing one-soliton, two-soliton, three-soliton and N -soliton, have been fetched using a modified sort of the well-known exp-function approach. Dominant effects of the fractional parameters have been illustrated and it is noted that the higher values of the fractional number cause a significant impact on the wave propagation. The one wave pattern for the u -component is quite identical, while an increase in the fractional parameter is producing an increment in the wave structure while a similar but opposite pattern is noted for the v -component. An increment in the wave structure is noted for higher values of the time-fractional parameter for both u - and v -components in the case of a two-wave solution. The benefits of the proposed computational code of the exp-function scheme are consistent, a general form of exact solutions, reduced computational complexity and stable and efficiently useful. The obtained solitary waves solutions will be a useful extension to the preceding results and greatly assist in clarifying the features of nonlinear waves in viscous flow. [ABSTRACT FROM AUTHOR]

Nowadays, the heat transfer potential of the base fluids can also be improved by adding nanoparticles to them. These nanotechnology-based fluids, called nanofluid, have superior properties such as high thermal conductivity, large critical heat flux (CHF) and improved heat transfer coefficient. The purpose of this paper is to study the thermal effectiveness of nanoparticles in transient flow of Maxwell fluid together the properties of mixed convection and magnetic field. Thermal field is controlled with the novel aspects of variable conductivity and nonuniform heat sink/source. Additionally, the impact of Brownian and thermophoretic diffusions is considered caused by nanoparticles dispersion in the fluid. The appropriate conversions yield the governing nonlinear ordinary differential system. Homotopic approach has been utilized to attain the solution of differential system and results are envisioned graphically. This study explores that the buoyancy ratio and mixed convection parameters enhance the velocity field. Further, the heat transfer rate rises significantly as the thermophoretic and Brownian diffusion parameters increase. Moreover, the effect of nonuniform heat source/sink on temperature field is noticed to be an increasing trend of temperature profile. [ABSTRACT FROM AUTHOR]

Using a thermally stratified water-based nanofluid and a permeable stretching sheet as a simulation environment, this research examines the impact of nanoparticle aggregation on MHD mixed convective stagnation point flow. Nanoparticle aggregation is studied using two modified models: the Krieger–Dougherty and the Maxwell–Bruggeman. The present problem's governing equations were transformed into a solvable mathematical model utilizing legitimate similarity transformations, and numerical solutions were then achieved using shooting with Runge–Kutta Fehlberg (RKF) technique in Mathematica. Equilibrium point flow toward permeable stretching surface is important for the extrusion process because it produces required heat and mass transfer patterns and identifies and clarifies fragmented flow phenomena using diagrams. Nanoparticle volume fraction was shown to have an impact on the solutions' existence range, as well. Alumina and copper nanofluids have better heat transfer properties than regular fluids. The skin friction coefficients and Nusselt number, velocity, temperature profiles for many values of the different parameters were obtained. In addition, the solutions were shown in graphs and tables, and they were explained in detail. A comparison of the current study's results with previous results for a specific instance is undertaken to verify the findings, and excellent agreement between them is observed. [ABSTRACT FROM AUTHOR]

The analysis of nanofluids under various physical scenarios convinced the researchers and scientists because of their broad range of applications in potential area of the current time like chemical engineering, biomedical engineering and applied thermal engineering etc. To give the final shape of many industrial and engineering processes, enhanced heat transfer desired, therefore, the study of Al2O3-H2O, γAl2O3-H2O, Al2O3-C2H6O2, and γAl2O3- C2H6O2 nanofluids is reported. The model successfully achieved after mathematical operations and by appealing similarity transforms. To examine the behavior of heat transfer, numerical tools utilized and performed the results. It is observed that enhanced heat transfer in Al2O3-H2O, γAl2O3-H2O, Al2O3-C2H6O2, and γAl2O3-C2H6O2 could be attained by setting nanoparticles concentration up to 20%. For Al2O3-H2O, γAl2O3-H2O, optimum heat transfer trends noticed due to their prominent thermophysical values. Also, fewer effects of combined convection on θ (η) examined. [ABSTRACT FROM AUTHOR]

A magneto couple stress nanofluid flow along with double diffusive convection is presented for peristaltic induce flow through symmetric nonuniform channel. A comprehensive mathematical model is scrutinized for couple stress nanofluid magneto nanofluids and corresponding equations of motions are tackled by applying small Reynolds and long wavelength approximation in viewing the scenario of the biological flow. Computational solution is exhibited with the help of graphical illustration for nanoparticle volume fraction, solutal concentration and temperature profiles in MATHEMTICA software. Stream function is also computed numerically by utilizing the analytical expression for nanoparticle volume fraction, solutal concentration and temperature profiles. Whereas pressure gradient profiles are investigated analytically. Impact of various crucial flow parameter on the pressure gradient, pressure rise per wavelength, nanoparticle volume fraction, solutal concentration, temperature and the velocity distribution are exhibited graphically. It has been deduced that temperature profile is significantly rise with Brownian motion, thermophoresis, Dufour effect, also it is revealed that velocity distribution really effected with strong magnetic field and with increasing non-uniformity of the micro channel. The information of current investigation will be instrumental in the development of smart magneto-peristaltic pumps in certain thermal and drug delivery phenomenon. [ABSTRACT FROM AUTHOR]

In this work, the quantized Hill problem is considered in order for us to study the existence and stability of equilibrium points. In particular, we have studied three different cases which give all whole possible locations in which two points are emerging from the first case and four points from the second case, while the third case does not provide a realistic locations. Hence, we have obtained four new equilibrium points related to the quantum perturbations. Furthermore, the allowed and forbidden regions of motion of the first case are investigated numerically. We demonstrate that the obtained result in the first case is a generalization to the classical one and it can be reduced to the classical result in the absence of quantum perturbation, while the four new points will disappear. The regions of allowed motions decrease as the value of the Jacobian constant increases, and these regions will form three separate areas. Thus, the infinitesimal body can never move from one allowed region to another, and it will be trapped inside one of the possible regions of motion with the relative large values of the Jacobian constant. [ABSTRACT FROM AUTHOR]

Ethylene glycol is commonly used as a cooling agent in the engine, therefore the study associated with EG has great importance in engineering and mechanical fields. The hybrid nanofluid has been synthesized by adding copper and graphene nanoparticles into the Ethylene glycol, which obeys the power-law rheological model and exhibits shear rate-dependent viscosity. As a result of these features, the power-law model is utilized in conjunction with thermophysical characteristics and basic rules of heat transport in the fluid to simulate the physical situations under consideration. The Darcy Forchhemier hybrid nanofluid flow has been studied under the influence of heat source and magnetic field over a two-dimensionally stretchable moving permeable surface. The phenomena are characterized as a nonlinear system of PDEs. Using resemblance replacement, the modeled equations are simplified to a nondimensional set of ODEs. The Parametric Continuation Method has been used to simulate the resulting sets of nonlinear differential equations. Figures and tables depict the effects of physical constraints on energy, velocity and concentration profiles. It has been noted that the dispersion of copper and graphene nanoparticulate to the base fluid ethylene glycol significantly improves velocity and heat conduction rate over a stretching surface. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of collinear and noncollinear equilibrium points within the frame of the perturbed restricted problem of 2 + 2 bodies by a planetesimal belt. We compare and investigate the corresponding results of the perturbed and unperturbed models. The impact of the planetesimal belt is observed on collinear and noncollinear equilibrium points. We demonstrate that all equilibrium points are unstable, and we numerically investigate the noncollinear equilibrium points. Finally, we emphasize that the proposed problem is a credible model for describing the capture of small bodies by a planet. [ABSTRACT FROM AUTHOR]

The analysis of nanofluids under various physical scenarios convinced the researchers and scientists because of their broad range of applications in potential area of the current time like chemical engineering, biomedical engineering and applied thermal engineering etc. To give the final shape of many industrial and engineering processes, enhanced heat transfer desired, therefore, the study of Al2O3-H2O, Al2O3-H2O, Al2O3-C2H6O2, and Al2O3- C2H6O2 nanofluids is reported. The model successfully achieved after mathematical operations and by appealing similarity transforms. To examine the behavior of heat transfer, numerical tools utilized and performed the results. It is observed that enhanced heat transfer in Al2O3-H2O, Al2O3-H2O, Al2O3-C2H6O2, and γAl2O3-C2H6O2 could be attained by setting nanoparticles concentration up to 20%. For Al2O3-H2O, Al2O3-H2O, optimum heat transfer trends noticed due to their prominent thermophysical values. Also, fewer effects of combined convection on θ(η) examined. [ABSTRACT FROM AUTHOR]

We study the motion of the negative curved symmetric two and three center problem on the Poincaré upper semi plane model for a surface of constant negative curvature κ, which without loss of generality we assume κ = −1. Using this model, we first derive the equations of motion for the 2-and 3-center problems. We prove that for 2–center problem, there exists a unique equilibrium point and we study the dynamics around it. For the motion restricted to the invariant y–axis, we prove that it is a center, but for the general two center problem it is unstable. For the 3–center problem, we show the non-existence of equilibrium points. We study two particular integrable cases, first when the motion of the free particle is restricted to the y–axis, and second when all particles are along the same geodesic. We classify the singularities of the problem and introduce a local and a global regularization of all them. We show some numerical simulations for each situation. [ABSTRACT FROM AUTHOR]

The original article can be found online at https://doi.org/10.1038/s41598-022-20074-1. Correction to: I Scientific Reports i https://doi.org/10.1038/s41598-022-20074-1, published online 26 September 2022 The Acknowledgments section in the original version of this Article was omitted. [Extracted from the article]

In this work, we investigated the differences and similarities among some perturbation approaches, such as the classical perturbation theory, Poincaré–Lindstedt technique, multiple scales method, the KB averaging method, and averaging theory. The necessary conditions to construct the periodic solutions for the spatial quantized Hill problem—in this context, the periodic solutions emerging from the equilibrium points for the spatial Hill problem—were evaluated by using the averaging theory, under the perturbation effect of quantum corrections. This model can be used to develop a Lunar theory and the families of periodic orbits in the frame work for the spatial quantized Hill problem. Thereby, these applications serve to reinforce the obtained results on these periodic solutions and gain its own significance. [ABSTRACT FROM AUTHOR]

In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated solutions patterns, the initial conditions are important. In the sense of a numerical solution, the motion is periodic in a certain interval, but beyond this interval, the motion is not periodic. But, the Lindstedt–Poincaré method constantly gives regular and periodic motion all time. Finally, we observed that the solution obtained by the Lindstedt–Poincaré method gives the true motion of the circular Sitnikov RFBP and the fourth approximate solution has more accuracy than the first, second, and third approximate solutions. [ABSTRACT FROM AUTHOR]