Set Of Equations Research Articles

Quarkonium dynamics in the quantum Brownian regime with non-abelian quantum master equations

We present numerical solutions in a one-dimensional setting of quantum master equations that have been recently derived. We focus on the dynamics of a single heavy quark-antiquark pair in a Quark-Gluon Plasma in thermal equilibrium, in the so-called quantum Brownian regime where the temperature of the plasma is large in comparison with the spacing between the energy levels of the QQ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ Q\\overline{Q} $$\\end{document} system. The one-dimensional potential used in the calculations has been adjusted so as to produce numbers that are relevant for the phenomenology of the charmonium. The equations are solved using different initial states and medium configurations. Various temperature regimes are studied and the effects of screening and collisions thoroughly analyzed. Technical features of the equations are analyzed. The contributions of the different operators that control the evolution are discussed as a function of the temperature. Some phenomenological consequences are addressed.

Analytical modeling of desublimation of a phase change material (PCM) in a porous medium with temperature-dependent volumetric heat sink and convection due to air-mixed vapor

The desublimation phase change heat and mass transfer process in a porous medium occurs during the conversion of vapor into solid form, which has several applications in chemical deposition and industrial coating. For economic feasibility, reducing the operating time of the conventional desublimation technique is of much interest. Toward this goal, current work presents a mathematical model for desublimation that accounts for a volumetric heat sink connected with temperature. A linear profile of the volumetric heat sink varying with temperature is modeled within the frozen region. Further, the rate of water vaporization (with mixed air) produces a convective term, which is also accounted for in the frozen region. Despite previous studies on desublimation phase change process, there is still insufficient mathematical modeling of this particular phenomena. The solution to the governing set of dimensionless partial differential equations is obtained analytically by employing the space-time transformation. Results indicate that the rate of desublimation process becomes faster with increasing the strength of the volumetric heat sink, which results in the reduction of the total operating time to desublimate of a phase change material. Higher values of the dimensionless temperature parameters also accelerate the desublimation process. On the other hand, a larger value of the convective term is found to slow down the desublimation process. The dimensionless moisture concentration profile in the vapor region increases with increasing the value of the Luikov number. Observations from this study are expected to aid in the fundamental design of processes including industrial coating, preservation of biological products, and evaporative deposition where desublimation plays a key role.

On the thermal performance of radiative stagnation-point hybrid nanofluid flow across a wedge with heat source/sink effects and sensitivity analysis

The present article aims to examine the thermal performance and the sensitivity analysis of a GO−TiO2/water hybrid nanofluid in the presence of different nanoparticle shapes along with heat absorption and thermal radiation effects over a wedge geometry. Analyzing the effects of heat generation and radiation effects is one of the key studies conducted by researchers in various nanofluid flows over some required geometries. However, a combined study of these effects has yet to be studied over a moving wedge, and that combination defines the novelty of the work. Similarity transformations are implemented to the governing equations to obtain the final set of nondimensional equations, which are solved using the bvp4c code in MATLAB. The results obtained were in close agreement with the published results. The Nusselt number decreased with an increase in the heat source parameter Q, and it increased with an increasing Hartree pressure gradient β and thermal radiation parameter Rd. The sensitivity is statistically analyzed for the variations in radiation effect, heat source, and pressure gradient parameters on the Nusselt number. The high values for R2=99.99% and Adj R2=99.96% validate the ANOVA results obtained using a Box–Behnken design (BBD) model in the response surface methodology (RSM) with 14 degrees of freedom. The input parameters Rd and β show positive sensitivity, while Q shows negative sensitivity toward the skin friction. The Nusselt number proves to be most sensitive toward the pressure gradient parameter. TiO2, graphene (Gr), and the derivative forms of graphene, are gaining much importance due to their wide applications in the oil and petroleum industries. Thus, this study contributes to lubrication purposes, emulsion stabilizers, oxalic acid removal, anti-corrosive properties, etc.

Analytical method for systems of nonlinear singular boundary value problems

The standard Lane–Emden equations model several physical phenomena such as isotropic continuous media, thermal behaviour of a spherical cloud of gas, and isothermal gas spheres. Systems of Lane–Emden-type equations appear in the modelling of the concentration of carbon substrate and oxygen, catalytic diffusion reactions, the steady state concentration of carbon dioxide, dusty fluid models, and pattern formation. In solving singular boundary value problems, one faces challenges resulting from the divergence of the associated variable coefficients at the singular points. This research article explores the power series approach to analytically approximate solutions to a class of systems of strongly nonlinear singular boundary value problems of Lane–Emden-type. The nonlinear terms in the proposed problems are transformed into power series using the generalised Cauchy product before establishing explicit recursion formulae for the expansion coefficients of the system of series solutions. The initial conditions required in the proposed boundary value problems are assumed and determined from a set of nonlinear algebraic equations resulting from the given right boundary conditions. Three special systems of nonlinear singular boundary value problems of Lane–Emden type are presented to demonstrate the proposed method’s reliability, effectiveness, and accuracy. The obtained approximate solutions are compared with the exact solutions (where they are available), or with other existing results (where the exact solution is not readily available). The series solution of the first example has a slow convergent rate, while the results of the other two examples are in excellent agreement with the exact solutions and other published results.

Computational workflow to monitor the electroosmosis of nanofluidic flow in the vicinity of a bounding surface

This investigation studies the flow of a boundary layer with electroosmotic forces on a nanofluid with gyrotactic microorganisms along the vertical Riga plate. This sort of fluid movement necessitates specific mathematical techniques and numerical simulations. In addition, the boundary-layer flow is induced by the mass and heat transfer, Joule heating, and viscous dissipation. A mathematical model is simulated by non-linear partial differential equations (PDEs). The combination of PDEs is turned into a set of non-linear ordinary differential equations using proper transformations. Some analysis tools are used to investigate the morphological characteristics of the problem while applying suitable boundary conditions. The influence of parameters on the derived solutions is numerically and visually explained through sets of figures. It is elucidated that the concentration of the microorganisms reduces due to an increase in Lewis number which leads to a decrease in the motile microorganism’s density profile. It is seen that the temperature distribution is improved when the chemical reaction and Casson parameter increase. In addition, we find that the application of electro-osmotic forces applied to the surfaces helps to dewater and separate microorganisms from incompressible solid and liquid mixtures.

Numerical study of Carreau fuzzy nanofluid across a stretching cylinder using a modified version of Buongiorno's nanofluid model

The principal intention of the currently analysis is to investigate the impacts of the naturally convective nanofluid using a model of Carreau fluid with engine oil (CnH2n+2)as the base fluid and Manganese Zinc Ferrite (MnZnFe2O4)as the nanoparticle, the fluid flowing through a stretched cylinder in a fuzzy ambient. It examines the impact of assorted parameters, Weissenberg number(We), Prandtl numeral(Pr), Schmidt numeral (Sc), and curvature (k)with magnetic field(B) and nanoparticle parameter, in order to manipulate an analogous conversion, the regulating equations of velocity, energy, and concentration profiles permute from a set of partial differential equations stand to ordinary differential equations. The present analysis focuses on the no slip assumption, which gives rise to a nonlinear Dirichlet boundary condition in axial velocity. The bvp5c approach was utilized to solve the resulting series of equations by the MATLAB. This is a highly effective approach with minimal computing expenditure. The volume quantity of nanoparticles in MnZnFe2O4 is considered an uncertain parameter respect to TFNs (triangular fuzzy numbers) ranging [0, 0.5, 0.1]. Triangular membership function (TMF) is used to study the uncertainty variability while α − cut controls the TFNs. Fuzzy linear regression analysis makes use of TFNs to determine the middle (crisp), left, and right values of the fuzzy velocity profile. In comparison to the crisp velocity profile (mid value), the study's result and the fuzzy velocity profile have the maximum rate of flow. Tables and graphs are used to illustrate the outputs.

Minimum connected dominating set and backbone of a random graph

We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected subgraph makes the problem rather nontrivial to investigate by statistical physics methods. Here, we convert this global connectivity constraint into a set of local vertex constraints and build a spin glass model with only five coarse-grained vertex states. We derive a set of coarse-grained belief-propagation equations and obtain theoretical predictions of the relative sizes of the minimum dominating sets for regular random and Erdös–Rényi random graph ensembles. We also implement an efficient message-passing algorithm to construct close-to-minimum connected dominating sets and backbone subgraphs for single random graph instances. Our theoretical strategy may also be applicable to some other global topological constraints.

Quasi-Newton positivity-preserving scheme for the Spalart-Allmaras turbulence model using unstructured grids

A new implicit method for solving the Spalart-Allmaras (SA) turbulence model is proposed using a formal second-order upwind scheme on unstructured grids for steady-state flows. The mean-flow set of equations and the SA model equation are solved in a loosely coupled manner. While the Jacobian of the mean-flow equations is derived from a low-order approximation of the residual (i.e. the defect-correction approach), the SA Jacobian is obtained by modifying a direct linearization of the second-order residual. The modified Jacobian is designed to form an M-matrix without the artificial time derivative commonly used for steady-state problems. Namely, no time step is involved in solving the SA model equation. Thanks to a special design of the M-matrix, the positivity of the SA model working variable and the convergence of the SA model linearized problem (fixed-point iterative problem) is guaranteed. To further enhance the overall stability of the flow solver, the Runge-Kutta implicit algorithm is employed, allowing CFL numbers as high as one to two thousand for the mean-flow equations. A second-order upwind scheme is achieved with a least-square method using a limiter to suppress oscillation in the solution. However, second-order upwind scheme discretization of turbulence models may lack robustness, especially when using unstructured grids. The limiter can hinder the convergence of the non-linear iterations, especially of the turbulence model. A square root transformation is applied to the dependent variable of a baseline SA model to improve the non-linear convergence characteristics. Three variants of the SA model are implemented and tested together with two limiters. Numerical simulations of a broad range of aerodynamic applications are conducted. The transformed variant exhibits the least sensitivity to the limiter type.

Heat transfer in a reversible esterification process of hydromagnetic Casson fluid with Arrhenius activation energy

Engineering technology is rapidly changing, and activation and binary chemical reactions have many uses in the fields of chemical engineering, processing food, and mobility and Geothermal reservoir, etc. Energy activation stimulates reactants with the least energy whenever a chemical transition occurs. The thermophysical features of viscoelastic fluids are based on internal energy change, which has been discussed for years. With this significance the current proposal focuses on the heat transfer process in reversible esterification reactions. The reversible chemical reaction and the activation energy with hydromagnetic movement of Casson fluid are considered. A complex multivariate partial differential equation set can be reduced to ordinary differential equations using appropriate variables. A numerical method is utilized to determine the solutions. In order to examine the outcomes of the concentration boundary layer utilizing the R-K-based shooting technique, the study primarily considers the reversible esterification process, which involves an ethanol-based reversible chemical reaction. Also, the bvp4c solver was employed to validate the results and appraise the precision of the R-K methodology. The temperature field, the momentum field, and the volumetric concentration of the esterification process are analysed in relation to a variety of numerical values. Graphical analysis considers the pertinent physical ramifications for temperature, velocity, and concentration contours. Explications that furnish a comprehension of the values accompany the tabular depictions of the heat transfer rate, local Sherwood number and skin friction. Reversible and irreversible flows differ considerably in the assessment of Sherwood number, local Nusselt number and rate of shear stress, when the inertial parameter, temperature difference parameter and activation energy are measured.

Geometric Design Methodology for Deployable Self-Locking Semicylindrical Structures

Due to their unique bistable characteristics, deployable self-locking structures are suitable for many engineering fields. Without changing the geometrical composition, such structures can be unfolded and locked solely by the elastic deformation of materials. However, their further applications are hampered by the lack of simple and systematic geometric design methodologies that consider arbitrary structural curvature profiles. This paper proposes such a methodology for double-layer semicylindrical grid structures to simplify their cumbersome geometric design. The proposed methodology takes joint sizes into account to ensure that the design results can be applied to actual projects without further adjustments. By introducing symmetry into the structural units (SUs) and selecting reasonable geometric parameters that describe the structural side elevation profile, a concise set of simultaneous nonlinear geometric constraint equations is established, the solution of which provides the geometric parameter values of the grid shape. On this basis, the remaining geometric parameter values, i.e., the geometric parameter values of the inner scissor-like elements (SLEs) of each SU, can be achieved from the equations derived from general SLEs. Design examples and the assembled physical grid structure indicate the feasibility and wide applicability of the proposed geometric design methodology.

New robust remote reference estimator using robust multivariate linear regression

SUMMARY The solution of the remote reference method, a frequently used technique in magnetotelluric (MT) data processing, can be viewed as a product of the two-input–multiple-output relationship between the local electromagnetic field and the reference field at a remote station. By applying a robust estimator to the two-input–multiple-output system, one can suppress the influence of outliers in the local magnetic field as well as those in the local electric field based on regression residuals. Therefore, this study develops a new robust remote reference estimator with the aid of robust multivariate linear regression. By applying the robust multivariate regression S-estimator to the multiple-output system, the present work derives a set of equations for robust estimates of the transfer function, noise variances, and the scale of the Mahalanobis distance simultaneously. The noise variances are necessary for the multivariate analysis to normalize the residuals of dependent variables. The Mahalanobis distance, a distance measure for multivariate data, is a commonly used indicator of outliers in multivariate statistics. By updating those robust estimates iteratively, the new robust remote reference estimator seeks the transfer function that minimizes the robust scale estimate of the Mahalanobis distance. The developed estimator can avoid bias in the MT transfer function even if there are significant noises in the reference magnetic field and handle outlying data more robustly than previously proposed robust remote reference estimators. The authors applied the developed method to a synthetic data set and real-world data. The test results demonstrate that the developed method downweights outliers in the local electric and magnetic fields and gives an unbiased transfer function.

Honeycomb-configured dissipative nanofluid flow within a squeezed channel with entropy generation: regression and numerical evaluations

PurposeNanosized honeycomb-configured materials are used in modern technology, thermal science and chemical engineering due to their high ultra thermic relevance. This study aims to scrutinize the heat transmission features of magnetohydrodynamic (MHD) honeycomb-structured graphene nanofluid flow within two squeezed parallel plates under Joule dissipation and solar thermal radiation impacts.Design/methodology/approachMass, energy and momentum preservation laws are assumed to find the mathematical model. A set of unified ordinary differential equations with nonlinear behavior is used to express the correlated partial differential equations of the established models, adopting a reasonable similarity adjustment. An approximate convergent numerical solution to these equations is evaluated by the shooting scheme with the Runge–Kutta–Fehlberg (RKF45) technique.FindingsThe impression of pertinent evolving parameters on the temperature, fluid velocity, entropy generation, skin friction coefficients and the heat transference rate is explored. Further, the significance of the irreversibility nature of heat transfer due to evolving flow parameters are evaluated. It is noted that the heat transference rate performance is improved due to the imposition of the allied magnetic field, Joule dissipation, heat absorption, squeezing and thermal buoyancy parameters. The entropy generation upsurges due to rising magnetic field strength while its intensification is declined by enhancing the porosity parameter.Originality/valueThe uniqueness of this research work is the numerical evaluation of MHD honeycomb-structured graphene nanofluid flow within two squeezed parallel plates under Joule dissipation and solar thermal radiation impacts. Furthermore, regression models are devised to forecast the correlation between the rate of thermal heat transmission and persistent flow parameters.

Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction

Abstract Non-uniform heat sources and sinks are used to control the temperature of the reaction and ensure that it proceeds at the desired rate. It is worldwide in nature and may be found in all engineering applications such as nuclear reactors, electronic devices, chemical reactors, etc. In food processing, heat is used to cook such as microwave ovens, pasteurize infrared heaters, and sterilize food products. Non-uniform heat sources are mainly used in biomedical applications, such as hyperthermia cancer treatment, to target and kill cancer cells. Because of its ubiquitous nature, the idea is taken as our subject of study. Heat and species transfer analysis of a non-Newtonian fluid flow model under magnetic effects past an extensible moving sheet is modelled and examined. Homogeneous chemical reaction inside the fluid medium is also investigated. This natural phenomenon is framed as a set of Prandtl boundary layer equations under the assumed convective surface boundary constraint. Self-similarity transformation is employed to convert framed boundary layer equations to ordinary differential equations. The resultant system is solved using the efficient finite difference utilized Keller box method with the help of MATLAB programming. The influence of various fluid-affecting parameters on fluid momentum, energy, species diffusion and wall drag, heat, and mass transfer coefficients is studied. Accelerating the Weissenberg number decelerates the fluid velocity. The temperature of the fluid rises due to variations in the non-uniform heat source and sink parameters. Ohmic dissipation affects the temperature profile significantly. Species diffusion reduces when thermophoresis parameter and non-uniform heat source and sink parameters vary. The Eckert number enhances the heat and diffusion transfer rate. Increasing the chemical reaction parameter decreases the shear wall stress and energy transmission rate while improving the diffusion rate. The wall drag coefficient and Sherwood number decrease as the thermophoretic parameter increases whereas the Nusselt number increases. We hope that this work will act as a reference for future scholars who will have to deal with urgent problems related to industrial and technical enclosures.

Computational analysis of the bioconvective flow of Williamson–Sutterby fluid with microorganisms and activation energy subject to Cattaneo–Christov double-diffusion effects

This research aims to develop a mathematical model and outline the implications of the free convection flow within a non-Newtonian Williamson–Sutterby type nonfluid through a stretching surface placed horizontally with magnetic dipole effect. The present attempt establishes the influence of multiple factors, including double diffusion, and heat flux. Utilizing the Cattaneo–Christov heat mass flux model approximations, to shape the thermal and concentration balance equations, incorporating various generalized transport laws. Furthermore, the transportation mechanism incorporates Arrhenius activation energy and binary chemical reactions. The impact of bioconvection resulting from self-propelled microorganisms is incorporated into the fluidic model. A nonlinear set of partial differential equations (PDEs) are appropriately formulated, employing boundary layer approximations theory, to comprehensively describe the convective flow. The PDEs are converted to ordinary differential equations via similarity transformation, and then computationally computed via a well-structured RKF45 technique with a shooting algorithm. To validate the results, a comparison is made with published findings in limiting cases. It is observed that the velocity profiles exhibit an escalation in tandem with ascending values of the electric parameter and mixed convection. Conversely, the velocity diminishes with the augmentation of the magnetic factor, ferrohydrodynamic interaction parameter, porosity parameter, and Sutterby fluid parameter. Temperature profiles elevate in response to escalating values of the Eckert number, radiation parameter, and Brownian motion parameter while diminishing with the augmentation of the thermal relaxation constant, Prandtl number, and Sutterby fluid parameter. The concentration distribution exhibits an augmentation with the increasing magnitude of the thermophoresis parameter and activation energy while experiencing a reduction with the improvement in the behavior of Schmidt number and Brownian parameter. The ongoing investigation encompasses a wide spectrum of applications within the field of applied sciences, placing particular emphasis on thermal oil recovery, geothermal reservoirs, chemical engineering, and the cooling processes pertinent to nuclear reactors.

Analytical solution for the interfacial stress and energy release rate at failure initiation of the three-point bending test (ISO 14679:1997)

Determining adhesive failure in adhesively bonded joints is still challenging in the field. While the three-point bending test (3PBT) (ISO 14679:1997) has been helpful in identifying critical forces and displacements related to bond strength, it only allows for a qualitative assessment of the bond line. Recently, a new quantitative methodology has been developed to determine critical stress and fracture toughness using the coupled stress–energy criterion and the 3PBT. However, these assessments require a significant effort using semi-analytical or finite element (FE) analysis. Therefore, the present study proposes a reliable set of analytical equations to determine peel and shear stress distributions using a weak interface formulation and 1D Euler–Bernoulli approach. More precisely, a particular numerical method computes the integration constants from these equations. A new method has been proposed for calculating the interfacial stiffness in peel and shear mode, based on the material and geometrical parameters of the geometry. This method differs from the previous approach, where the interfacial stiffness was calibrated from the experimental behavior of the test. The whole approach has been validated through experimental and numerical analysis, including the costly 3D FE analysis. An analytical expression for interfacial energy release is suggested, developed following the works of Fraisse and Schmit on J-integral assessment of sandwich-type overlaps and depending on the applied force and a rotation, which could be experimentally measured. Therefore, this work is significant progress in determining bond strength using a simple mechanical test and equations applicable to various industries.

Asymptotic generalization errors in the online learning of random feature models

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the last layer is trainable, known as the random feature model. We study over-parametrization in the context of a student-teacher framework by deriving a set of differential equations for the learning dynamics. For any finite ratio of hidden layer size and input dimension, the student cannot generalize perfectly, and we compute the non-zero asymptotic generalization error. Only when the student's hidden layer size is exponentially larger than the input dimension, an approach to perfect generalization is possible. Published by the American Physical Society 2024

Optimization of heat transfer rate of trihybrid nanofluid Embedded between two horizontal coaxial cylinders by RSM

Heat pipes are heat transfer devices that carry heat from one point to another efficiently. The thermal conductivity and heat transfer performance of the heat pipe can be increased by integrating nanofluids, making them appropriate for applications such as electronics cooling, spacecraft thermal management, and heat recovery systems. The suggested work is being carried out for the approximate solution of tri-hybrid nanofluid (copper (Cu), silver (Ag) and graphene oxide (GO)) flow between two horizontal coaxial cylinders. The inner cylinder is rotating with constant velocity and the outer cylinder is fixed. Moreover, the flow is under the influence of magnetic field. The system of governing partial differential equations is converted into a set of non-linear ordinary differential equations by incorporating the suitable similarity transformation and then solved numerically by employing Runga-Kutta 4th order technique. Response surface methodology (RSM) is also incorporated in order to optimize the heat transfer rate by the various combinations of the physical parameters involved in the study. The study revealed that the temperature of the nanofluid increased by raising the strength of the Reynolds number and melting parameter. From optimization technique RSM it came to know that the heat transfer rate reached its peak value when the strength of the Reynolds number and concentration of the nanoparticle of the fluid is higher than normal.

Development and validation of reference equations for dual-energy X-ray absorptiometry-derived measures of fat-free mass in adults aged 45-85 years: results from the Canadian Longitudinal Study on Aging.

Reference equations for fat-free mass (FFM) and lean soft tissue mass (LM) measures obtained from dual-energy X-ray absorptiometry (DEXA) are important for the interpretation of body composition. This study developed and validated reference equations for FFM and LM using DEXA from the Canadian Longitudinal Study on Aging. Reference equations were developed using data from a random population-based sample of ostensibly healthy and functionally independent adults aged 45-85 years. Reference equations for absolute (accounting for age, sex, height, and body mass) and height-adjusted aka index (accounting for age, sex, and body mass index) measures of FFM and LM were developed using quantile regression. Reference equations were respectively developed and validated in derivation (80%) and validation cohorts (20%). Reference equations were applied to symptomatic adults with self-reported chronic obstructive pulmonary disease (COPD) or heart disease to assess discriminant validity; and compared with other published equations to assess performance. Bland-Altman analyses and Lin's concordance correlation coefficients were utilised to assess agreement. Reference equations for 5th, 10th, 50th, 90th, and 95th percentiles were developed for DEXA-derived estimates of FFM and LM based on 1881 healthy participants (57% male) aged 55 [IQR: 50-61] years. Reference equations performed comparably in the validation cohort and discriminated reference values between ostensibly healthy adults and people with symptomatic COPD or heart disease. Previously published reference equations tended to over- or under-predict estimates of LM compared with the current reference equations. This study provides a comprehensive and validated set of reference equations for estimating and interpreting FFM and LM from DEXA in Canadian adults aged 45-85 years, although additional validation may be required for those>75 years.

Fractional dynamics study: analytical solutions of modified Kordeweg-de Vries equation and coupled Burger’s equations using Aboodh transform

The study examines the using of Aboodh residual power series method and the Aboodh transform iteration method (ATIM) to analyze modified Korteweg-de Vries equation (mKdV) beside coupled Burger’s equations in the framework of the Caputo operator. These sets of equations represent the non-linear wave description for various physical systems. Through APM and ATIM, the solution for the coupled Burger’s equations and the mKdV equation get accurate dynamics information that will reveal the nature of their interactions. Using mathematically proven techniques and computational simulations, the developed methods’ efficiency and reliability are illustrated in the complex behaviors of these nonlinear wave equations, so that we can gain deeper insights into their complex dynamics. The research is aimed at an increase of the knowledge about the fractional calculus utilization for nonlinear wave motion and it also provides analytical tools for an analysis of wave acting in different scientific and engineering areas.

Activation energy, Rotational and Hall current Effects of Magnetohydrodynamic 3D flow of Non-Newtonian Hybrid Nanofluid over a Stretched Plate

Nanofluids are of great importance to researchers as they have significant uses industrially due to their high heat transfer rates. Recently, a new class of nanofluid, ‘‘hybrid nanofluid” is being used to further enhance the heat transfer rate. This new model in 3D is employed to examine the impact of activation energy, Rotational and hall current on a Non-newtonian hybrid Fe3O4/Al2O3 nanofluid flow over-stretched plate. Using similarity transformations, the controlling partial differential equations are turned into a set of nonlinear ordinary differential equations. For that system of equations, the shooting method is used to generate numerical solutions. The impact of various entry parameters on transversal and longitudinal velocities, temperature, heat flow and surface shear stress are studied numerically and graphically. A good correlation between the earlier studies is obtained in specific cases showing the convergence criteria of the present procedure. Further, the physical significance of the contributive parameters is presented through graphs and tables. The observation shows that the particle concentration for the hybrid nanofluid augments the fluid velocity. Moreover, the inclusion of dissipative heat favors enhancing the fluid temperature for the involvement of the particle concentration.