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Abstract This study aims to formulate a mathematical framework to examine how the Lassa virus spreads in humans of opposite genders. The stability of the model is analyzed at an equilibrium point in the absence of the Lassa fever. The model’s effectiveness is evaluated using real-life data, and all the parameters needed to determine the basic reproduction number are estimated. Sensitivity analysis is performed to pinpoint the crucial parameters significantly influencing the spread of the infection. The interaction between threshold parameters and the basic reproduction number is simulated. Control theory is employed to devise and evaluate strategies, such as awareness campaigns, advocating condom usage, and deploying rodenticides to reduce the possibility of virus transmission efficiently.

Comprehending the temperature-dependent variable viscosity Phan Thien Tanner fluid film flow over a horizontal heated plate with surface tension is essential to enhancing coating and lubrication process prediction models. This paper accords with the flow analysis of a temperature-dependent variable viscosity Phan Thien Tanner fluid film over a horizontal heated plate. The flow over a heated plate occurs as a result of the plate’s motion and the surface tension gradient. The Adomian decomposition method is utilized to solve a system of linear and nonlinear ordinary differential equations, resulting in series-form solutions. The series-form expressions for flow variables such as velocity, temperature, volume flow rate, and surface tension are derived. Moreover, the positions of stationary points are computed using MATHEMATICA. The analysis delineated that when the inverse capillary number, variable viscosity parameter, Deborah number, elongation parameter, and Brinkman number increase, the stationary points move closer to the heated plate. The temperature also rises with an increase in these parameters. The temperature rises with increasing viscous dissipation while it lowers with increasing thermal diffusion. When the Deborah number is high, the Phan Thien Tanner fluid behaves like a solid and the flow is only driven by the motion of the plate. A comparison between Newtonian and Phan Thien Tanner fluids is made for velocity, temperature, and stationary points as a special case.

Abstract Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique ( $$W_e^2$$ W e 2 as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

In this study, we have considered the peristaltic flow of Eyring–Powell hybrid nanofluid flow across a conduit having an elliptical cross-section. The polystyrene and graphene oxide nanoparticles are considered. The mathematical model of the problem is solved analytically in the dimensionless form with the application of long wavelength approximation. The perturbation technique is adopted with polynomial solutions to solve it. The analytically acquired results are assessed and discussed comprehensively by graphical examination for various physical parameters. The disorder of the system is also studied by entropy production analysis. The pressure gradient is noted to reduce when the elliptical nature of the conduit’s cross-section reduces towards a circular shape. The percentage (volume fraction) of nanoparticles is found to have a strong impact on temperature distribution among all physical constraints.

In this study, we examine soliton solutions of extended (2+1)-dimensional Kadomtsev–Petviashvili equation arising in fluid mechanics and plasma physics. The research utilizes an improved modified extended tanh-function method to derive new soliton solutions. The diverse set of soliton solutions obtained in this study, featuring a combination of rational, trigonometric, and hyperbolic functions, enhances the model’s applicability for real-world fluid mechanics and plasma physics scenarios. The visual representations of the obtained solutions through contour, three-dimensional, and two-dimensional depictions in various simulations are shown in the figures. The results propose that the employed method is an efficient and powerful tool to be implemented for different differential equations in applied sciences and engineering.

This study aims to develop a mathematical model for analyzing Lassa fever transmission dynamics and proposing effective control measures. The stability of the Lassa fever-free equilibrium point is examined and the model's accuracy is assessed using real-world data. Additionally, the parameter values and the basic reproduction number are estimated. A sensitivity analysis is also conducted, which identifies the key drivers influencing transmission dynamics. Moreover, the impact of model parameters on basic reproduction numbers is investigated. Multiple control methodologies including use of Ribavirin, implementing mobile health technology and incorporating natural predators are devised and analyzed using optimal control theory to curtail virus transmission.

In many nonlinear partial differential equations, noise or random fluctuation is an inherent part of the system being modeled and have vast applications in different areas of engineering and sciences. This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Itô calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. By using Mathematica 11, some 3D and 2D plots are illustrated to check the influence of multiplicative noise on solutions. The presence of multiplicative noise leads the fluctuations and have significant effects on the long-term behavior of the system. So, it is observed that multiplicative noise stabilizes the solutions of BAE around zero.

The study of blood flow through stenotic arteries is more important as the existence and progression of stenosis may lead to severe damage. The current study aims to analyze and understand the non-Newtonian nature of blood flow through the multi-stenosed artery of an elliptical cross-section. The Carreau fluid model accounts for the non-Newtonian nature of blood. The mathematical equations are transformed to dimensionless form, and assumptions of mild stenosis are employed to reduce the non-linearity of the mathematical model. The perturbation method via polynomial technique is utilized to solve the resulting equations by considering We2 as the perturbation parameter. The results of the velocity and wall shear stress are examined graphically. It is found that stenosis severity substantially impacts flow velocity in the narrower portion of the artery. The stenosis growth strongly affects the flow velocity and wall shear stress in the stenotic region. The non-Newtonian effects are found to dominate along the minor axis. This fact assures that the conduit’s narrower cross-section strengthens the fluid’s non-Newtonian behavior. It is observed that the non-Newtonian fluid has a smaller velocity than the Newtonian fluid. Moreover, non-Newtonian fluid has a different nature along the minor and major axes, but Newtonian fluid has the same behavior.

The effect of body acceleration on the pulsatile flow of blood through the elliptical artery having stenosis at the multiple positions of its wall is investigated in the current study. The artery is inclined at angle θ with horizontal, and blood is considered as Casson fluid. The mathematical model is processed into non-dimensional form and simplified using assumptions of mild stenosis. The analytical solution of mathematical equations is obtained in the elliptic bounded domain by employing the perturbation technique with Womersley frequency as a perturbation parameter and validated through case comparison with the previous study. The impacts of external acceleration, stenosis height, shape, gravitational acceleration, yield stress, and inclination angle on the flow velocity, flow rate, wall shear stress, and flow resistance are analyzed. It is found that body acceleration, gravitational acceleration, and inclination angle increase the flow rate and diminish the frictional resistance. The more significant yield stress and stenosis height enhance the flow resistance and reduce the flow rate. Moreover, fluid has higher velocity in the case of the non-symmetric shape of stenosis compared with the symmetric form.

The coupled Drinfeld–Sokolov–Wilson (DSW) equation is a system of nonlinear partial differential equations (NLPDEs) in (1+1)-dimensions that play a fundamental role in soliton theory and integrable systems. Due to its ability to accurately describe wave phenomena in dispersive water waves, coupled DSW equation has wide-ranging applications in fluid dynamics, plasma physics, and mathematical physics. This study investigates the solitary wave solution of coupled DSW equation by using ϕ6-model expansion. This technique reveals the diverse types of solutions, including bright, dark, singular, and periodic singular solitons. The 3D, contour, and 2D plots are also illustrated to demonstrate the physical behavior of the obtained solutions. The findings of this study can contribute to the development of new analytical and numerical tools for solving other nonlinear equations in the future. The inclusion of constraint conditions in the ϕ6-model expansion technique enhances its applicability and reliability, rendering it a valuable approach for investigating nonlinear systems in various scientific domains.

In this research paper, the improved generalized Riccati equation mapping (IGREM) method is employed to get analytical soliton solutions of (3+1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV-ZK) equation. By giving appropriate parametric values, we obtain soliton solutions of various types, such as kink soliton, singular soliton, and periodic-singular soliton. The description provided in physical variables allows for the study of genuine multispecies plasmas, plasma models, and frequency regimes. These solutions are essential in illuminating several physical phenomena in engineering and other applied sciences. In addition, 3D and 2D graphs of some selected solutions are sketched for the best physical characterization of the obtained results. This method can also be implemented in many non-linear equations in contemporary research areas. Comparison with previous studies shows that the discovery of singular soliton is novel. Therefore, our research represents a significant advancement in the field and contributes to expanding the knowledge regarding soliton behavior. The applications of this study include electron and ion-acoustic modes in regular plasmas with hot Boltzmann electron species, as well as ion and dust-acoustic modes, depending on the specific modeling of the heavier components.

This work covers the theoretical and computational examination of the Ellis hybrid nanofluid flow model with magnetic, Darcy-Forchheimer, and non-linear thermal radiation effects across the stretching cylinder. The convective slip boundary condition is imposed on the surface of the cylinder. Hybrid nanoparticles (AA7072 and AA7075) are scattered in base fluid (water) to create a hybrid nanofluid. The phenomenon of fluid flow has been analytically developed for energy and fluid velocity as a non-linear partial differential equation (PDE)-based system. Through appropriate similarity replacements, the design of PDEs is further streamlined to the set of ordinary differential equations (ODEs). Utilizing a built-in MATLAB (R2020b) algorithm called bvp4c, numerical solutions are found for the obtained dimensionless equations. Graphical discussions are used to illustrate the outcomes of velocity and temperature profiles. The velocity profile of mono and hybrid nanofluids declined for higher inputs of Darcy–Forchheimer and magnetic parameters. Additionally, it has been observed that the energy contour is improved caused of thermal radiation and thermal Biot number. Moreover, our results are consistent with the existing literature.

Abstract Due to their unique microstructures, micropolar fluids have attracted enormous attention for their industrial applications, including convective heat and mass transfer polymer production and rigid and random cooling particles of metallic sheets. The thermodynamical demonstration is an integral asset for anticipating the ideal softening of heat transfer. This is because there is a decent connection between mathematical and scientific heat transfers through thermodynamic anticipated outcomes. A model is developed under the micropolar stream of a non-Newtonian (3rd grade) liquid in light of specific presumptions. Such a model is dealt with by summoning likeness answers for administering conditions. The acquired arrangement of nonlinear conditions is mathematically settled using the fourth-fifth order Runge-Kutta-Fehlberg strategy. The outcomes of recognized boundaries on liquid streams are investigated in subtleties through the sketched realistic images. Actual amounts like Nusselt number, Sherwood number, and skin-part coefficient are explored mathematically by tables. It is observed that the velocity distribution boosts for larger values of any of $$\alpha _1$$ α 1 , $$\beta$$ β , and declines for larger $$\alpha _2$$ α 2 and Hartmann numbers. Furthermore, the temperature distribution $$\theta (\eta )$$ θ ( η ) shows direct behavior with the radiation parameter and Eckert number, while, opposite behavior with Pr, and K. Moreover, the concentration distribution shows diminishing behavior as we put the higher value of the Brownian motion number.

Abstract In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for $$\sigma > 0$$ σ > 0 and Dilatant fluid behaviour for $$\sigma < 0.$$ σ < 0 . The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.

This paper discusses optical soliton solutions for the paraxial wave model (PWM) in Kerr law media. Mathematically, the PWM for a monochromatic beam is equivalent to the Schrödinger equation of free quantum particle. The ϕ6 model expansion technique is used to obtain dark, bright, singular, bright-dark combined and periodic solitons. The solutions obtained by this method are in the form of trigonometric, hyperbolic, and exponential functions. To prompt the important propagated structures, some scrutinized solutions are demonstrated in the form of 3D, contour, and 2D plots using specific values to the parameters with constrained conditions. It is observed that this method is an efficient, secure, and stable tool for new precise solitons for various NLPDEs in engineering and applied sciences.

By employing the extended hyperbolic function method (EHFM), we extract the exact solutions of the (2+1)-dimensional nonlinear soliton equation (SE). A soliton equation is used for investigation of the dynamics of nonlinear waves in plasma physics and fluid dynamics. A various new techniques for finding exact solutions of the (2+1)-dimensional nonlinear SE are satisfactorily acquired with the help of EHFM. The EHFM presents various types of new solutions in the form of dark, singular, periodic, bright solitons and some rational function solutions. In addition, for the physical characterization of the acquired solutions of (2+1)-dimensional SE, some 2-dim and 3-dim plots are drawn. The attained results are novel for the considered equation, and results reveal that the method is concise, direct and competent which can be assembled in other complex phenomena.

The heat transmission process is a prominent issue in current technology. It occurs when there is a temperature variation between physical processes. It has several uses in advanced industry and engineering, including power generation and nuclear reactor cooling. This study addresses Maxwell fluid’s steady, two-dimensional boundary layer stream across a linearly stretched sheet. The primary objective of this research is to investigate the impact of the non-Newtonian fluid parameter (Deborah number) on flow behavior. The secondary objective is to investigate the effect of linear and quadratic convection to check which model gives higher heat transfer. The flow is caused by the surface stretching. The mathematical model containing the underlying partial differential equations (PDEs) is built using the boundary layer estimations. The governing boundary layer equations are modified to a set of nonlinear ordinary differential equations (ODEs) using similarity variables. The bvp4c approach is employed to tackle the transformed system mathematically. The impacts of numerous physical parameters like stretching coefficient, mixed convective parameter, heat source/sink coefficient, magnetic coefficient, variable thermal conductance, Prandtl number, and Deborah number over the dimensionless velocity and temperature curves are analyzed via graphs and calculated via tables. After confirming the similarity of the present findings with several earlier studies, a great symmetry is shown. The findings show that the linear convection model gains more heat transport rate than the quadratic convection model, ultimately giving a larger thermal boundary layer thickness. Some numeric impacts illustrate that boosting the magnetic coefficient elevates the fluid’s boundary layer motion, causing an opposite phenomenon of Lorentz force because the free stream velocity exceeds the stretched surface velocity.

In this article, a strain wave equation (SWE) is studied, which is used to model wave propagation in microstructured materials that earn a noteworthy place in solid-state physics. This equation also signifies the dynamics of various physical phenomena. The Sardar-subequation method (SSM) is utilized for this model. Granting appropriate values to parameters, we obtain various types of soliton solutions such as periodic singular solitons, bright solitons, dark solitons, singular soliton, combined dark-bright solitons, and some other wave solutions. These novel solitons and other wave results have significant applications in engineering and applied sciences. The graphical sketchings of the results are illustrated to purify the impact of the SSM. Furthermore, the executed technique can be utilized for further studies to discuss the realistic phenomena developing in physical and engineering problems.

Nonlinear science is a fundamental science frontier that include studies and the common properties of nonlinear phenomena. This article is devoted to the study of sub-pico second optical pluses in birefringent fibers for Kaup-Newell equation (KNE) without four-wave mixing. Three prominent integrations techniques are successfully implemented on KNE in coupled vector form. Variety of soliton solutions namely dark, bright, periodic singular, singular and bright-singular combo solitons are constructed for the KNE in birefringent fibers. The obtained solutions are reckoned with their respective existence criterion. In addition, two-dimensional and three-dimensional graphs are drawn to exhibit the physical behavior of the obtained solutions.

The current research article discusses the two-dimensional, laminar, steady, and incompressible third-grade viscoelastic micropolar fluid flow along with thermal radiation caused by an exponentially stretched sheet. The primary goal of this extensive study is to improve thermal transportation. Thermophoresis and Brownian motion are two key causes of nanoparticle migration in nanofluids, and their impacts on the thermophysical properties of nanofluids are significant. Micropolar fluids are investigated due to their micro-motions that are significant in convective thermal and mass transport polymer formation, nanotechnology, and electronics. The consequences of third-grade fluid parameters, thermophoresis and Brownian motion, induced magnetic field, micro-polarity, and micro-inertia density on the stream of an electrically conductive fluid are analyzed. A homogeneous magnetic field is supplied perpendicularly to the surface, and the liquid is believed to be electrically conducting. As the flow has a significant magnetic Reynolds number, the contribution of the evoked magnetic field is properly accounted in the governing equations. A mathematical model in the form of partial differential equations (PDEs) is built under certain assumptions. By invoking the suitable similarity transformation, the non-linear PDEs are modified into dimensionless coupled ordinary differential equations (ODEs). The MATLAB numerical technique bvp4c is employed to settle the subsequent ODEs together with the boundary constraints. The consequences of numerous physical parameters on the non-dimensional concentration, temperature, micropolar, velocity, and induced magnetic field profiles are portrayed in graphs. It is found that the concentration boundary layer, thermal boundary layer, and micropolar boundary layer thickness decelerate with the increment in the micro-polarity of the fluid.

Abstract Transmission dynamics of swine influenza pandemic is analysed through a deterministic model. Qualitative analysis of the model includes global asymptotic stability of disease-free and endemic equilibria under a certain condition based on the reproduction number. Sensitivity analysis to ponder the effect of model parameters on the reproduction number is performed and control strategies are designed. It is also verified that the obtained numerical results are in good agreement with the analytical ones.

In this paper, the extended simple equation method (ESEM) and the generalized Riccati equation mapping (GREM) method are applied to the nonlinear third-order Gilson–Pickering (GP) model to obtain a variety of new exact wave solutions. With the suitable selection of parameters involved in the model, some familiar physical governing models such as the Camassa–Holm (CH) equation, the Fornberg–Whitham (FW) equation, and the Rosenau–Hyman (RH) equation are obtained. The graphical representation of solutions under different constraints shows the dark, bright, combined dark–bright, periodic, singular, and kink soliton. For the graphical representation, 3D plots, contour plots, and 2D plots of some acquired solutions are illustrated. The obtained wave solutions motivate researchers to enhance their theories to the best of their capacities and to utilize the outcomes in other nonlinear cases. The executed methods are shown to be practical and straightforward for approaching the considered equation and may be utilized to study abundant types of NLEEs arising in physics, engineering, and applied sciences.

The purpose of this article is to achieve new soliton solutions of the Gilson–Pickering equation (GPE) with the assistance of Sardar’s subequation method (SSM) and Jacobi elliptic function method (JEFM). The applications of the GPE is wider because we study some valuable and vital equations such as Fornberg–Whitham equation (FWE), Rosenau–Hyman equation (RHE) and Fuchssteiner–Fokas–Camassa–Holm equation (FFCHE) obtained by particular choices of parameters involved in the GPE. Many techniques are available to convert PDEs into ODEs for extracting wave solutions. Most of these techniques are a case of symmetry reduction, known as nonclassical symmetry. In our work, this approach is used to convert a PDE to an ODE and obtain the exact solutions of the NLPDE. The solutions obtained are unique, remarkable, and significant for readers. Mathematica 11 software is used to derive the solutions of the presented model. Moreover, the diagrams of the acquired solutions for distinct values of parameters were demonstrated in two and three dimensions along with contour plots.

In this paper, the geodesic motion of neutral and test particles around the time conformal (TC) Dilaton black hole (BH) is investigated using the eϵg(t) as the time conformal factor in which g(t) is an arbitrary function of time and ϵ is a perturbation parameter. The function g(t) leads to (ta) by utilizing the well-known approximate Noether symmetry (ANS). Furthermore, we discuss the effect of magnetic fields and find the location of stable and unstable orbits w. r. t time, graphically. After that, in the presence and absence of a magnetic field, we interrogate the crucial physical parameters such as effective potential (Ueff), effective force (Feff) and escape velocity (ν⊥). We find the unstable and stable regions of particles for different values of angular momentum (Lz) and magnetic field (B) near the TC Dilaton BH. Moreover, the effects of the Dilaton parameter (μ) on neutral and charged particles are also discussed, which provide some new features. The important results in this study could estimate the powerful relativistic jets originating from the BH.

This article analyzes the significance of linear and quadratic convection on the dynamics of micropolar fluid due to a stretching surface in the presence of magnetic force and a rotational frame. Modern technological implementations have attracted researchers to inquire about non-Newtonian fluids, so the effect of linear and nonlinear convection conditions is accounted for in the dynamics of non-Newtonian fluid. The highly nonlinear governing equations are converted into a system of dimensionless ODEs by using suitable similarity transformations. The bvp4c technique is applied in MATLAB software to obtain a numerical solution. This investigation examines the behavior of various parameters with and without quadratic convection on the micro-rotation, velocity, and temperature profiles via graphical consequences. The velocity profile decreases with a higher input by magnetic and rotating parameters, and fluid velocity is more elevated in the nonlinear convection case. However, the temperature profile shows increasing behavior for these parameters and quadratic convection increases the velocity profile but has an opposite tendency for the temperature distribution. The micro-rotation distribution is augmented for higher magnetic inputs in linear convection but reduces against thermal buoyancy.

In this work, a deterministic model is dedicatedly studied for the infection mechanism of pine wilt disease subject to varying sensitivity and optimality. We include time dependent controls into the pine wilt disease model and then analysed optimal conditions for the control of infection. Explicit form for the reproduction number has been obtained. Ultimate constant levels of infectious vectors and hosts have been discussed by employing the threshold condition. Two most effective techniques namely Lyapunov functional and graph theoretic have been used to find the final endemic level of population. The concept of full eradication of disease and reduction of constant level has been investigated through the utilization of two effective techniques. Using the concept of sensitivity analysis, control policies have been designed to control the disease. Additionally, the robustness of control plans has been shown graphically on the basis of data collected from open literature.

The shear stress and velocity field related to the oscillatory motion of a fractional Burgers’ fluid model in an infinitely circular cylinder are examined using modified Bessel equation and Laplace transformation. The fluid is at rest initially and after t=0+, because of shear, it instantly starts to move along the axis of cylinder. The procured results are expressed in modified Bessel fields I0(·) and I1(·) and fulfill both initial and boundary conditions. Inverse Laplace transformation has been found numerically using Matlab software. In the end, numerical simulations have been performed to analyze the behavior of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R and material parameter λ2 on our obtained solutions of velocity field and shear stress. The comparison between numerical and exact results are also presented in graphical and tabular form. Keywords: Laplace transformation, Velocity field, Burgers’ fluid, Stehfest’s algorithm, Shear stress

This article addresses the dynamic of three-dimensional rotating flow of Maxwell nanofluid across a linearly stretched sheet subject to a water-based fluid containing copper nanoparticles. Nanoparticles are used due to their fascinating features, such as exceptional thermal conductivity, which is crucial in modern nanotechnology and electronics. The primary goal of this comprehensive study is to examine the nanoparticles size and shape factors effect on the base fluid temperature. The mathematical model contains the governing equations in three dimensional partial differential equations form, and these equations transformed into dimensionless ordinary dimensional equations via suitable similarity transformation. The bvp4c technique is harnessed and coded in Matlab script to obtain a numerical solution of the coupled non-linear ordinary differential problem. It is observed that the greater input of rotating, Deborah number, and magnetic parameters caused a decline in the fluid primary and secondary velocities, but the nanoparticles concentration enhanced the fluid temperature. Further, a substantial increment in the nanofluid temperature is achieved for the higher nanoparticle’s diameter and shape factors.

This study aims to determine the heat transfer properties of a magnetohydrodynamic Prandtl hybrid nanofluid over a stretched surface in the presence of bioconvection and chemical reaction effects. This article investigates the bio-convection, inclined magnetohydrodynamic, thermal linear radiations, and chemical reaction of hybrid nanofluid across stretching sheets. Also, the results are compared with the nanofluid flow. Moreover, the non-Newtonian fluid named Prandtl fluid is considered. Microfluidics, industry, transportation, the military, and medicine are just a few of the real-world applications of hybrid nanofluids. Due to the nonlinear and convoluted nature of the governing equations for the problem, similarity transformations are used to develop a simplified mathematical model with all differential equations being ordinary and asymmetric. The reduced mathematical model is computationally analyzed using the MATLAB software package’s boundary value problem solver, Runge-Kutta-fourth-fifth Fehlberg’s order method. When compared to previously published studies, it is observed that the acquired results exhibited a high degree of symmetry and accuracy. The velocity profiles of basic nanofluid and hybrid nanofluid are increased by increasing the Prandtl parameters’ values, which is consistent with prior observations. Additionally, the concentration and temperature of simple and hybrid nanofluids increase with the magnetic parameter values.

In this paper, the velocity field and the time dependent shear stress of Maxwell fluid with Caputo fractional derivatives in an infinite long circular cylinder of radius R is discussed. The motion in the fluid is produced by the circular cylinder. The fluid is initially at rest and at time t=0+, cylinder begins to oscillate with the velocity fsinωt, due to time dependent shear stress acting on the cylinder tangentially. The hybrid technique used in this paper for the solution of the problem has less computational efforts and time cost as compared to other commonly used methods. The obtained solutions are in transformed domain, which are expressed in terms of modified Bessel functions I0(·) and I1(·). The inverse Laplace transformation has been calculated numerically by using MATLAB package. The semi analytical solutions for Maxwell fluid with fractional derivatives are reduced to the similar solutions for Newtonian and ordinary Maxwell fluids as limiting cases. In the end, numerical simulations have been performed to analyze the behavior of fractional parameter α, kinematic viscosity ν, relaxation time λ, radius of the circular cylinder R and dynamic viscosity μ on our obtained solutions of velocity field and shear stress. Keywords: Shear stress, Maxwell fluid, Laplace transformation, Velocity field, Modified Bessel function

Optimality for operating temperature can improve the reliability of thermodynamics of convection flow of Jeffrey fluid through mathematical techniques; this is because thermal convection is invoked in several engineering problems for knowingan accurate assessment and stable or unstable heat transference characteristics. In this context, the free convection flow of Jeffrey fluid among two vertical plates is characterized by stable or unstable heat transfer. The heat transference mechanism is designed by employing a generalized and a fractional form of Fourier's law that delivers damping for thermal flux. In this process, we make use of the Caputo time-fractional derivative (CTFD) having a power-law singular kernel. The free convection is induced by the temperature gradient. The analytical solutions have been obtained through a method of Laplace coupled with finite sine-Fourier transform and have been embedded with regards to the Mittag-Leffler function. The behavior of velocity and temperature profiles is analyzed through numerical computations and graphical representations for different embedded parameters with Mathcad. Certainly, this article presents a comprehensive discussion as well as a graphical interpretation of the achieved results.

A numerical investigation of three-dimensional hybrid nanomaterial micropolar fluid flow across an exponentially stretched sheet is performed. Recognized similarity transformations are adopted to convert governing equations from PDEs into the set ODEs. The dimensionless system is settled by the operating numerical approach bvp4c. The impacts of the nanoparticle volume fraction, dimensionless viscosity ratio, stretching ratio parameter, and dimensionless constant on fluid velocity, micropolar angular velocity, fluid temperature, and skin friction coefficient in both x-direction and y-direction are inspected. Graphical outcomes are shown to predict the features of the concerned parameters into the current problem. These results are vital in the future in the branches of technology and industry. The micropolar function Rη increases for higher values of the micropolar parameter and nanoparticle concentration. Micropolar function Rη declines for higher values of the micropolar parameter and nanoparticle concentration. Temperature function is enhanced for higher values of solid nanoparticle concentration. Temperature function declines for higher values of the micropolar parameter. The range of the physical parameters are presented as: 0.005<ϕ2<0.09, Pr=6.2, 0

The numerical analysis for two-dimensional oblique stagnation point flow with the magnetohydrodynamic effects of an incompressible unsteady Jeffrey fluid model caused by an oscillatory and stretching sheet has been presented in this article. The Brownian motion and thermophoresis impacts are taken into consideration. The similarity transformation technique is implemented on the governing partial differential equations of the Jeffrey fluid model to obtain a set of nonlinear coupled ordinary differential equations and then these resulting equations are numerically computed with the help of BVP-Maple programming. The variation in the behavior of velocity, temperature, and concentration profile influenced by the governing parameters, has been explicitly explored and displayed through graphs. The numerical results are highlighted in tabular form and through these outcomes, the skin friction coefficient, Nusselt number, and Sherwood number have been investigated. These physical quantities rise for gradually increasing the Hartmann number and ratio of relaxation to retardation time. However, these reduce for gradually growing Jeffrey fluid parameter.

Analysis of an unsteady two-dimensional magnetohydrodynamic stagnation point flow of second-grade fluid is carried out in this article. It is supposed that the fluid is incompressible and impinges over the oscillatory stretching surface obliquely. The governing PDEs for second-grade fluid have been derived and then transfigured into a system of nonlinear coupled ODEs via appropriate similarity mappings. The BVP arrangement technique in Maple programming is used for the numerical arrangements of these subsequent nonlinear coupled equations. The outcomes are graphically represented and tabulated with the aim of illustrating the physical impacts of governing parameters on the temperature, concentration, and velocity profiles. The skin friction coefficient, Sherwood number, and Nusselt number are also analyzed by computational results, where it is reported that these physical quantities enhance with increment in Hartmann number and diminish with increment in the local second-grade parameter.

In this manuscript, two nonlinear fifth-order partial differential equations, namely, the bidirectional and 2D- Sawada-Kotera equations are analytically treated using an extended form of homoclinic process. In the presence of a bilinear form, novel periodic waves with different categories including periodic soliton, solitary and kinky solitary wave solutions are constructed. In the meantime, The diverse features and mechanical qualities of these acquired solutions are elucidated by 3D figures and some contour plots.

The velocity field and shear stress for unsteady flow of a second grade fluid with fractional derivatives through an infinite long circular cylinder are evaluated. The fluid is initially at rest and at t=0+, the fluid inside the cylinder starts to move longitudinally due to tangential shear stress. Semi analytical solutions are obtained with the help of Laplace transformation and modified Bessel equation. This hybrid technique, which we have used has less computational efforts and time cost as compared to other schemes that are commonly used. The solutions in the transformed domain, are presented in terms of modified Bessel functions I0(·) and I1(·) and satisfy all given conditions. Inverse Laplace transformations have been numerically calculated by using MATLAB. The semi analytical solutions for the motion of second grade fluid with fractional derivatives are reduced to the similar solutions for ordinary second grade and Newtonian fluid. Finally, the effect of different parameters of the flow is graphically examined. Keywords: Second grade fluid, Velocity field, Quadratic shear stress, Fractional derivatives, Laplace transformation, Modified Bessel function

Abstract We design a deterministic model of pine wilt affliction to analyze the transmission dynamics. We obtain the reproduction number in unequivocal form, and global dynamics of the ailment is totally controlled by this number. With a specific end goal to survey the adequacy of malady control measures, we give the affectability investigation of basic reproduction number R 0 $R_{0}$ and the endemic levels of diseased classes regarding epidemiological parameters. From the aftereffects of the sensitivity analysis, we adjust the model to evaluate the effect of three control measures: exploitation of the tainted pines, preventive control to limit vector host contacts, and bug spray control to the vectors. Optimal analysis and numerical simulations of the model show that limited and appropriate utilization of control measures may extensively diminish the number of infected pines in a viable way.

This work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes independent of saturation level by including the transmission through mating.