Exploring optical solitary wave solutions in the (2+1)-dimensional equation with in-depth of dynamical assessment.

The current study explores the (2+1)-dimensional Chaffee-Infante equation, which holds significant importance in theoretical physics renowned reaction-diffusion equation with widespread applications across multiple disciplines, for example, ion-acoustic waves in optical fibres, fluid dynamics, electromagnetic wave fields, high-energy physics, coastal engineering, fluid mechanics, plasma physics, and various other fields. Furthermore, the Chaffee-Infante equation serves as a model that elucidates the physical processes of mass transport and particle diffusion. We employ an innovative new extended direct algebraic method to enhance the accuracy of the derived exact travelling wave solutions. The obtained soliton solutions span a wide range of travelling waves like bright-bell shape, combined bright-dark, multiple bright-dark, bright, flat-kink, periodic, and singular. These solutions offer valuable insights into wave behaviour in nonlinear media and find applications in diverse fields such as optical fibres, fluid dynamics, electromagnetic wave fields, high-energy physics, coastal engineering, fluid mechanics, and plasma physics. Soliton solutions are visually present by manipulating parameters using Wolfram Mathematica software, graphical representations allow us to study solitary waves as parameters change. Observing the dynamics of the model, this study presents sensitivity in a nonlinear dynamical system. The applied mathematical approaches demonstrate its ability to identify reliable and efficient travelling wave solitary solutions for various nonlinear evolution equations.

A novel probabilistic q-rung orthopair linguistic neutrosophic information-based method for rating nanoparticles in various sectors.

The idea of probabilistic q-rung orthopair linguistic neutrosophic (P-QROLN) is one of the very few reliable tools in computational intelligence. This paper explores a significant breakthrough in nanotechnology, highlighting the introduction of nanoparticles with unique properties and applications that have transformed various industries. However, the complex nature of nanomaterials makes it challenging to select the most suitable nanoparticles for specific industrial needs. In this context, this research facilitate the evaluation of different nanoparticles in industrial applications. The proposed framework harnesses the power of neutrosophic logic to handle uncertainties and imprecise information inherent in nanoparticle selection. By integrating P-QROLN with AO, a comprehensive and flexible methodology is developed for assessing and ranking nanoparticles according to their suitability for specific industrial purposes. This research contributes to the advancement of nanoparticle selection techniques, offering industries a valuable tool for enhancing their product development processes and optimizing performance while minimizing risks. The effectiveness of the proposed framework are demonstrated through a real-world case study, highlighting its potential to revolutionize nanoparticle selection in HVAC (Heating, Ventilation, and Air Conditioning) industry. Finally, this study is crucial to enhance nanoparticle selection in industries, offering a sophisticated framework probabilistic q-rung orthopair linguistic neutrosophic quantification with an aggregation operator to meet the increasing demand for precise and informed decision-making.

Significance of Dufour and Soret aspects on dynamics of water based ternary hybrid nanofluid flow in a 3D computational domain.

The prime motive to conduct this communication is to explicate hydrothermal attributes of water by inducing new composition of nanoparticles termed as ternary particles. For this purpose, two differently natured groups one with lesser densities (Carbon nanotubes, Graphene and Aluminium oxide) and with higher densities (Copper oxide, Copper and Silver) are accounted. A 3D permeable surface is considered as a physical configuration of problem by providing dual stretching. Initially, mathematical structuring in dimensional representation expressing the constitutive relations for mass, momentum and energy conservation is manifested. Later on, a set of similar variables are executed to express attained coupled system into ordinary form. Numerical simulations are performed to find solution by employing shooting and RK-4 methods in conjunction. Description about change is displayed through graphical visualization. Subsequently, temperature distribution and heat flux coefficient against sundry variables are also measured and comprehensively discussed in pictorial and tabular format. Wall drag coefficients along (x, y) directions are also computed. It is inferred from the outcomes that velocity, temperature and concentration of base fluid is higher for ternary group 1 containing particles of low densities than for group 2 with more denser particles. It is also deduced that elevation in temperature of fluid is revealed against Soret number whereas contrary aspects is observed in view of concentration distribution. Dufour number has declining impact on temperature profile whereas it upsurges the mass distribution. It is depicted that skin friction in case of group containing particles with less densities are more than other group.

The weakly non-linear waves propagation for Kelvin-Helmholtz instability in the magnetohydrodynamics flow impelled by fractional theory.

The weakly nonlinear wave propagation that occurs in the presence of magnetic fields, in which energy is concentrated in a narrow band of wave-numbers in a dispersive and dissipative fluid. The main objective of this paper is to analyze the ( 2 + 1 ) - dimensional elliptic nonlinear Schrodinger equation under the influence of three different fractional operators. The generalized fractional soliton solutions and propagation of magnetohydrodynamics fluid in sort of solition will be visualized. The Conformable, ß and M-truncated fractional operator applied to classical evolution Schrodinger equation. In order to get the analytical closed form solution, one of the generalized approach new extended direct algebraic method is utilized. The fractional nonlinear elliptic Schrodinger equation is developed in three different fractional sense. The similarity transformation technique converted the controlling fractional system to ordinary differential equations. The fractional analytical solutions such as, plane solution, mixed hyperbolic solution, periodic and mixed periodic solutions, mixed trigonometric solution, trigonometric solution, shock solution, mixed shock singular solution, mixed singular solution, complex solitary shock solution, singular solution and shock wave solutions are obtained. The graphical 2-D and 3-D representation of the results is shown to express the propagation of fluid with the magnetic field by assuming the appropriate values of the involved parameters. The graphical performance of the obtained solution at various settings of parametric values and fractional order reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.

Flow Characteristics of Heat and Mass for Nanofluid under Different Operating Temperatures over Wedge and Plate.

BACKGROUND AND PURPOSE: Nanofluids are a new class of heat transfer fluids that are used for different heat transfer applications. The transport characteristics of these fluids not only depend upon flow conditions but also strongly depend on operating temperature. In respect of these facts, the properties of these fluids are modified to measure the temperature effects and used in the governing equations to see the heat and mass flow behavior. Design of Model: Consider the nanofluids which are synthesized by dispersing metallic oxides (SiO2, Al2O3), carbon nanostructures (PEG-TGr, PEG-GnP), and nanoparticles in deionized water (DIW), with (0.025-0.1%) particle concentration over (30-50 °C) temperature range. The thermophysical properties of these fluids are modeled theoretically with the help of experimental data as a function of a temperature and volume fraction. These models are further used in transport equations for fluid flow over both wedge and plate. To get the solution, the equations are simplified in the shape of ordinary differential equations by applying the boundary layer and similarity transformations and then solved by the RK method. RESULTS: The solution of the governing equation is found in the form of velocity and temperature expressions for both geometries and displayed graphically for discussion. Moreover, momentum and thermal boundary layer thicknesses, displacement, momentum thicknesses, the coefficient of skin friction, and Nusselt number are calculated numerically in tabular form. FINDING: The maximum reduction and enhancement in velocity and temperature profile is found in the case of flow over the plate as compared to the wedge. The boundary layer parameters are increased in the case of flow over the plate than the wedge.

Application of Ternary Nanoparticles in the Heat Transfer of an MHD Non-Newtonian Fluid Flow.

This paper introduces a novel theoretical model of ternary nanoparticles for the improvement of heat transmission. Ternary nanoparticles in a heat conductor are shown in this model. Ternary nanoparticles consist of three types of nanoparticles with different physical properties, and they are suspended in a base fluid. Analytical solutions for the temperature and velocity fields are found by using the Laplace transform approach and are modeled by using a novel fractional operator. As a result, the ternary nanoparticles are identified, and an improved heat transfer feature is observed. Further experimental research on ternary nanoparticles is being carried out in anticipation of a faster rate of heat transmission. According to the graphed data, ternary nanoparticles have greater thermal conductivity than that of hybrid nanoparticles. Moreover, the fractional approach based on the Fourier law is a more reliable and efficient way of modeling the heat transfer problem than the artificial approach. The researchers were driven to create a concept of existing nanoparticles in order to boost heat transfer, since there is a strong demand in the industry for a cooling agent with improved heat transfer capabilities.

New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach.

The existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier's law were converted into non-dimensional equations. In order to obtain a fractional model, a fractional operator known as the Prabhakar operator is used. To find a generalized solution for temperature as well as a velocity field, the Laplace transform is used. With the help of graphs, the impact of various parameters on velocity as well as temperature distribution is obtained. As a result, it is noted that ternary nanoparticles approach can be used to increase the temperature than the results obtained in the recent existing literature. The obtained solutions are also useful in the sense of choosing base fluids (water, kerosene and engine oil) for nanoparticles to achieved the desired results. Further, by finding the specific value of fractional parameters, the thermal and boundary layers can be controlled for different times. Such a fractional approach is very helpful in handling the experimental data by using theoretical information. Moreover, the rate of heat transfer for ternary nanoparticles is greater in comparison to hybrid and mono nanoparticles. For large values of fractional parameters, the rate of heat transfer decreases while skin friction increases. Finally, the present results are the improvement of the results that have already been published recently in the existing literature. Fractional calculus enables us to control the boundary layers as well as rate of heat transfer and skin friction for finding suitable values of fractional parameters. This approach can be very helpful in electronic devices and industrial heat management system.

Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques.

The wave propagation has the significant role in the field of coastal engineering and ocean. In the geographical fields, waves are primary source of environmental process owed to energy conveyance on floating structure. This study aims to investigate the system of cold bosonic atoms in zig-zag optics lattices. The solitonic patterns of the considered model successfully surveyed by using two integrated analytical techniques new extended direct algebraic and G ' G 2 expansion method. The exact solutions are presented by rational, trigonometric, hyperbolic and exponential functions. On the basis of solitons, we need to show that which one is more integrated and robust scheme. These solutions will help to understood the dynamics of cold bosonic atoms in zig-zag optical lattices and the several other systems. Three dimensional as well as two dimensional comparison presented for a cold bosonic atoms model solutions which are revealed diagrammatically for appropriate parameters by using Mathematica. This study will help physicists to predict some new hypothesis and theories in the field of mathematical physics.

Convective Heat and Mass Transport in Casson Fluid Flow in Curved Corrugated Cavity with Inclined Magnetic Field.

Convection in fluids produced by temperature and solute concentration differences is known as thermosolutal convection. It has valuable utilization in wide industrial and technological procedures such as electronic cooling, cleaning, and dying processes, oxidation of surface materials, storage components, heat exchangers, and thermal storage systems. In view of such prominent physical significance, focus is made to explicate double (thermal and solutal)-diffusive transport in viscoelastic fluid characterized by the Casson model enclosed in a curved enclosure with corrugations. An incliningly directed magnetic field is employed to the flow domain. A uniformly thermalized and concentrated circular cylinder is installed at the center of the enclosure to measure transport changes. Dimensionally balanced governing equations are formulated in 2D, representing governed phenomenon. Finite element-based open-sourced software known as COMSOL is utilized. The domain of the problem is distributed in the form of triangular and quadrilateral elements. Transport distributions are interpolated by linear and quadratic polynomials. The attained non-linear system is solved by a less time and computation cost consuming package known as PARDISO. Convergence tests for grid generation and validation of results are executed to assure credibility of work. The influence of involved physical parameters on concerned fields are revealed in graphical and tabular manner. Additionally, heat and mass fluxes, along with, kinetic energy variation are also evaluated.

The Influence of Aligned MHD on Engine Oil-Based Casson Nanofluid with Carbon Nanotubes (Single and Multi-Wall) Passing through a Shrinking Sheet with Thermal Radiation and Wall Mass Exchange.

The optimization of heating or cooling during an industrial system may result in power savings, reduced processing time, enhanced thermal efficiency, and increased equipment operating lifespan. The advancement of high-efficiency thermal systems for heat and mass transport improvement has become increasingly popular in recent years. The analysis of aligned magnetohydrodynamics (MHD) on engine oil-based Casson nanofluid with carbon nanotubes (single and multi-wall) passing a shrinking sheet following the thermal radiation and wall mass transport phenomena is carried out in this aspect. The dynamic model is utilized to reduce difficult ordinary differential equations into nondimensional forms, which are then analytically assessed. To study the repercussions of a physical parameter on the velocity field, skin friction at the wall, the stream pattern, the temperature distribution, isotherm, and the local Nusselt, numeric data and visualizations are generated. When the value of ϕ increases, the velocity field decelerates, and the velocity pattern of multi-walled CNTs drops considerably when compared to single-walled CNTs. The local Nusselt number is a decreasing function of N and ϕ and the opposite trend is shown for Pr. The local Nusselt number is a decreasing function of N and ϕ and the opposite trend is shown for Pr. The single-walled CNTs have a higher degradation rate as compared to multi-walled CNTs. It is found that higher temperature distribution occurs in the case of multi-walled CNT-based fluid as compared to single-walled CNT-based fluid.

Biochar-Mediated Zirconium Ferrite Nanocomposites for Tartrazine Dye Removal from Textile Wastewater.

To meet the current challenges concerning the removal of dyes from wastewater, an environmentally friendly and efficient treatment technology is urgently needed. The recalcitrant, noxious, carcinogenic and mutagenic compound dyes are a threat to ecology and its removal from textile wastewater is challenge in the current world. Herein, biochar-mediated zirconium ferrite nanocomposites (BC-ZrFe2O5 NCs) were fabricated with wheat straw-derived biochar and applied for the adsorptive elimination of Tartrazine dye from textile wastewater. The optical and structural properties of synthesized BC-ZrFe2O5 NCs were characterized via UV/Vis spectroscopy, Fourier transform Infra-red (FTIR), X-Ray diffraction (XRD), Energy dispersive R-Ray (EDX) and Scanning electron microscopy (SEM). The batch modes experiments were executed to explore sorption capacity of BC-ZrFe2O5 NCs at varying operative conditions, i.e., pH, temperature, contact time, initial dye concentrations and adsorbent dose. BC-ZrFe2O5 NCs exhibited the highest sorption efficiency among all adsorbents (wheat straw biomass (WSBM), wheat straw biochar (WSBC) and BC-ZrFe2O5 NCs), having an adsorption capacity of (mg g-1) 53.64 ± 0.23, 79.49 ± 0.21 and 89.22 ± 0.31, respectively, for Tartrazine dye at optimum conditions of environmental variables: pH 2, dose rate 0.05 g, temperature 303 K, time of contact 360 min and concentration 100 mg L-1. For the optimization of process variables, response surface methodology (RSM) was employed. In order to study the kinetics and the mechanism of the adsorption process, kinetic and equilibrium mathematical models were used, and results revealed 2nd order kinetics and a multilayer chemisorption mechanism due to complexation of hydroxyl, Fe and Zr with dyes functional groups. The nanocomposites were also recovered in five cycles without significant loss (89 to 63%) in adsorption efficacy. This research work provides insight into the fabrication of nanoadsorbents for the efficient adsorption of Tartrazine dye, which can also be employed for practical engineering applications on an industrial scale as efficient and cost effective materials.

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order.

The purpose of this paper is to investigate the approximate solution of the casting-mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional-order partial differential equations. We apply Yang transform homotopy perturbation method (𝒴T-HPM) to find the approximate solution of temperature distribution in the casting-mould heterogeneous system. The 𝒴T-HPM is a combined form of Yang transform (𝒴T) and the homotopy perturbation method (HPM) using He's polynomials. Some examples are provided to demonstrate the superiority of the suggested technique. The significant findings reveal that 𝒴T-HPM minimizes the enormous without imposing any assumptions. Due to its powerful and robust support for nonlinear problems, this approach presents a remarkable appearance in the functional studies of fractal calculus.

Study of Results of Katugampola Fractional Derivative and Chebyshev Inequailities.

In this work, we use generalized form of Caputo-type fractional derivative and Riemann-Liouville fractional Integral which is known as Katugampola fractional derivative. This work deals with some results having applications of Katugampola fractional derivative. We discuss commutative and inverse property of Katugampola fractional derivative. We have also introduced Chebyshev inequalities and some other integrals inequalities applying the Katugampola fractional derivative.

Insight into the Dynamics of Fractional Maxwell Nano-Fluids Subject to Entropy Generation, Lorentz Force and Heat Source via Finite Difference Scheme.

In recent times, the loss of useful energy and solutions to those energy challenges have a wide scope in different areas of engineering. This work focuses on entropy analysis for unsteady viscoelastic fluids. The momentum boundary layer and thermal boundary layer are described under the effects of a magnetic field in the absence of an induced magnetic field. The study of a fractional model of Maxwell nanofluid by partial differential equation using Caputo time differential operator can well address the memory effect. Using transformations, the fractional ordered partial differential equations (PDEs) are transfigured into dimensionless PDEs. Numerical results for fractional Maxwell nanofluids flow and heat transfer are driven graphically. The Bejan number is obtained following the suggested transformation of dimensionless quantities like entropy generation. A mathematical model of entropy generation, Bejan number, Nusselt number and skin friction are developed for nanofluids. Effects of different physical parameters like Brickman number, Prandtl number, Grashof number and Hartmann number are illustrated graphically by MAPLE. Results depict that the addition of nanoparticles in base-fluid controls the entropy generation that enhances the thermal conductivity and application of magnetic field has strong effects on the heat transfer of fractional Maxwell fluids. An increasing behavior in entropy generation is noticed in the presence of source term and thermal radiation parameter.

Construction of optical solitons of magneto-optic waveguides with anti-cubic law nonlinearity.

Two efficient integration schemes, new extended hyperbolic function and generalized tanh are employed to discover optical soliton solutions to magneto-optic waveguides that retains anti-cubic form of nonlinear refractive index. Bright, dark, periodic singular, singular, and combo soliton solutions have created. These solutions expose the comprehensive variety of soliton solutions.

Higher-Dimensional Fractional Order Modelling for Plasma Particles with Partial Slip Boundaries: A Numerical Study.

We integrate fractional calculus and plasma modelling concepts with specific geometry in this article, and further formulate a higher dimensional time-fractional Vlasov Maxwell system. Additionally, we develop a quick, efficient, robust, and accurate numerical approach for temporal variables and filtered Gegenbauer polynomials based on finite difference and spectral approximations, respectively. To analyze the numerical findings, two types of boundary conditions are used: Dirichlet and partial slip. Particular methodology is used to demonstrate the proposed scheme's numerical convergence. A detailed analysis of the proposed model with plotted figures is also included in the paper.

MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection.

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge-Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter λ, variable viscosity parameter Λµ and wall thickness parameter ς impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter Nb and thermophoresis parameter Nt. The boosted value of Brownian motion Nb and Lewis number Le reduce the concentration of nanoparticles. The higher inputs of Peclet number Pe and bioconvection Lewis number Lb decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.

Application of water based drilling clay-nanoparticles in heat transfer of fractional Maxwell fluid over an infinite flat surface.

In the present paper, unsteady free convection flow of Maxwell fluid containing clay-nanoparticles is investigated. These particles are hanging in water, engine oil and kerosene. The values for nanofluids based on the Maxwell-Garnett and Brinkman models for effective thermal conductivity and viscosity are calculated numerically. The integer order governing equations are being extended to the novel non-integer order fractional derivative. Analytical solutions of temperature and velocity for Maxwell fluid are build using Laplace transform technique and expressed in such a way that they clearly satisfied the boundary conditions. To see the impact of different flow parameters on the velocity, we have drawn some graphs. As a result, we have seen that the fractional model is superior in narrate the decay property of field variables. Some limiting solutions are obtained and compared with the latest existing literature. Moreover, significant results can be observed for clay nanoparticles with different base fluids.

Heatline visualization of MHD natural convection heat transfer of nanofluid in a prismatic enclosure.

Temperature transfer by virtue of natural convection for visualizing heat transport characteristics through heatline method within a prismatic cavity filled with Cu-H2O nanofluid considering two different temperature boundary conditions is performed numerically. Two top inclined walls are warmed-up at low temperature whilst the bottom wall is heated two different heated conditions such as uniform temperature condition and linear temperature condition. Two vertical walls are insulated. Finite element technique of Galerkin weighted residual form is employed for solving nonlinear partial differential equations for numerical calculation. Heatlines, isotherm contours, streamline contours, and Nusselt number are employed for displaying numerical simulated results for the model parameters entitled nanoparticles volume fraction, Hartmann number and Rayleigh number. The outcomes indicate that heat transfer rate has a significant impact on thermal boundary condition and shape of the nanoparticles. The temperature transfer value enhances significantly for higher Rayleigh number as well as nanoparticles volume fraction. Hartmann number has a positive impact on fluid flow and temperature transport. The characteristics of heat transport using heatlines method are also performed for predicting the better energy transform compared to isotherm contours. In addition, different types of nanofluids are also employed to examine the best heat transport performance.

Numerical analysis of thermal conductive hybrid nanofluid flow over the surface of a wavy spinning disk.

A three dimensional (3D) numerical solution of unsteady, Ag-MgO hybrid nanoliquid flow with heat and mass transmission caused by upward/downward moving of wavy spinning disk has been scrutinized. The magnetic field has been also considered. The hybrid nanoliquid has been synthesized in the presence of Ag-MgO nanoparticles. The purpose of the study is to improve the rate of thermal energy transmission for several industrial purposes. The wavy rotating surface increases the heat transmission rate up to 15%, comparatively to the flat surface. The subsequent arrangement of modeled equations is diminished into dimensionless differential equation. The obtained system of equations is further analytically expounded via Homotopy analysis method HAM and the numerical Parametric continuation method (PCM) method has been used for the comparison of the outcomes. The results are graphically presented and discussed. It has been presumed that the geometry of spinning disk positively affects the velocity and thermal energy transmission. The addition of hybrid nanoparticles (silver and magnesium-oxide) significantly improved thermal property of carrier fluid. It uses is more efficacious to overcome low energy transmission. Such as, it provides improvement in thermal performance of carrier fluid, which play important role in power generation, hyperthermia, micro fabrication, air conditioning and metallurgical field.