Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation.

In this research, we investigate the integrability properties of the Schamel-Korteweg-de Vries (S-KdV) equation, which is important for understanding the effect of electron trapping in the nonlinear interaction of ion-acoustic waves. Using the optimal system, we come over reduced ordinary differential equations (ODEs). To deal with reduced ODEs for this problem, Lie symmetry analysis is combined with the modified auxiliary equation (MAE) procedure and the generalized Jacobi elliptic function expansion (JEF) method. The analytical solutions reported here are novel and have a wide range of applications in mathematical physics.

Galerkin finite element analysis for the augmentation in thermal transport of ternary-hybrid nanoparticles by engaging non-Fourier's law.

Boosting of thermal transportation is the demand of current era. Several techniques have been used to do so. One of an important way is the mixing of nanoparticles to boost thermal performance. Current investigation has been prepared to study the inclusion of tri hybrid nanoparticles in Prandtl fluid model past over a stretched heated sheet. Modelling of consider problem has been done due to consideration of movement in flow in Cartesian coordinates which results coupled partial differential equation system thermal transport in presented by considering generalized heat flux model and heat generation/absorption. The derived coupled complex partial differential equations (PDEs) system is simplified by engaging boundary layer theory. Such developed model is used in coolants regarding automobiles, dynamics in fuel and production of solar energy, fuel cells, optical chemical sensors, automotive parts, dental products, cancer therapy, electrical insulators and dental products. Handling of complex PDEs for the solution is a challenging task. Due to complexity in computational work these PDEs have been transformed into ordinary differential equations (ODEs) after applying similarity transformation afterwards converted ODEs have been approximated via finite element algorithm coded in MAPLE 18.0 symbolic computational package. Comparative study has been presented for the validity of code and authenticity of obtained result. It is observed that fluid velocity for tri-hybrid nanoparticles is higher than fluidic motion for pure fluid, nanofluid and hybrid nanomaterial.

Modeling of three dimensional Prandtl hybrid nano-material over a heated rotating cone involving hall and ion slip currents via finite element procedure.

Flow in a rotating cone for magnetized Prandtl fluid model is inspected in this investigation. The momentum equation of Prandtl model is derived under the consideration of Hall and ion slip effects and heat transport phenomenon is considered with Joule heating and viscous dissipation effects. The model of Hamilton Crosser and Yamada Ota are considered for the empirical relations of nanofluid mixture. The flow presenting expression of Prandtl fluid model with thermal transport is modeled under boundary layer approximation in the form of partial differential equations (PDEs). The derived PDEs have been converted into set of coupled nonlinear ordinary differential equations (ODEs) by engaging an appropriate scaling group transformation and these converted nonlinear set of ODEs have been tackled numerically via finite element scheme (FES). Impact of different emerging parameters has been displayed graphically and the physics behind the observed phenomena is explained in detail. The convergence of FES is established by carrying the grid independent survey. From the performed investigation, it is recorded that the parameters appear due to Hall and Ion slip currents enhance the fluid velocity but the inverse behavior is recorded for temperature profile.

A study of triple-mass diffusion species and energy transfer in Carreau-Yasuda material influenced by activation energy and heat source.

The mechanism of thermal transport can be enhanced by mixing the nanoparticles in the base liquid. This research discusses the utilization of nanoparticles (tri-hybrid) mixture into Carreau-Yasuda material. The flow is assumed to be produced due to the stretching of vertical heated surface. The phenomena of thermal transport are modeled by considering Joule heating and heat generation or absorption involvement. Additionally, activation energy is engaged to enhance heat transfer rate. The mathematical model composing transport of momentum, heat and mass species is developed in Cartesian coordinate system under boundary layer investigation in the form of coupled nonlinear partial differential equations. The complex partial differential equations are converted into coupled nonlinear ordinary differential equations by using the appropriate similarity transformation. The conversion of PDEs into ODEs make the problem easy to handle and it overcome the difficulties to solve the PDEs. The transformed ordinary differential equations are solved with the help of help of finite element scheme. The obtained solution is plotted against numerous involved parameters and comparative study is established for the reliability of method and accuracy of obtained results. An enhancement in fluid temperature is recorded against magnetic parameter and Eckert number. Also, decline in velocity is recorded for Weissenberg number and concentration is controlled against higher values of Schmidt number. Furthermore, it is recommended that the finite element scheme can be implemented to handle complex coupled nonlinear differential equation arising in modeling of several phenomena occurs in mathematical physics.

A wind power plant site selection algorithm based on q-rung orthopair hesitant fuzzy rough Einstein aggregation information.

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method's capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects.

Applications of Cattaneo-Christov fluxes on modelling the boundary value problem of Prandtl fluid comprising variable properties.

Stretched flows have numerous applications in different industrial, biomedical and engineering processes. Current research is conducted to examine the flow phenomenon of Prandtl fluid model over a moveable surface. The phenomenon of mass and thermal transportation is based on generalized theory of Cattaneo-Christov which considers the involvement of relaxation times. In addition to these, variable characteristics of thermal conductivity and diffusion coefficient are considered as a function of temperature. The physical problem in Cartesian coordinate system is modeled via boundary layer theory which yields a coupled system of partial differential equations. Group scaling transportation is applied to model these PDEs system. The converted equations have been approximated via optimal homotopic scheme. The efficiency and validity of used approach has been shown by computing the error analysis and establishing a comparative study. It is noted that the enhancement in magnetic parameter plays a controlling role for velocity field and it augment the concentration and temperature fields. Furthermore, increase in thermal relaxation parameter and Prandtl number maintains the fluid temperature.

Inclusion of hybrid nanoparticles in hyperbolic tangent material to explore thermal transportation via finite element approach engaging Cattaneo-Christov heat flux.

This report is prepared to examine the heat transport in stagnation point mixed convective hyperbolic tangent material flow past over a linear heated stretching sheet in the presence of magnetic dipole. Phenomenon of thermal transmission plays a vital role in several industrial manufacturing processes. Heat generation is along with thermal relaxation due to Cattaneo-Christov flux is engaged while modeling the energy equation. In order to improve the thermal performance, inclusion of hybrid nanoparticles is mixed in hyperbolic tangent liquid. The conservation laws are modeled in Cartesian coordinate system and simplified via boundary layer approximation. The modeled partial differential equations (PDEs) system are converted into ordinary differential equations (ODEs) system by engaging the scaling group transformation. The converted system of modeled equations has been tackled via finite element procedure (FEP). The efficiency of used scheme has been presented by establishing the grid independent survey. Moreover, accurateness of results is shown with the help of comparative study. It is worth mentioning that the inclusion of hybrid nanoparticles has significant higher impact on heat conduction as compared with nanoparticle. Moreover, hybrid nanoparticles are more efficient to conduct maximum production of heat energy as compared with the production of heat energy of nanoparticles. Hence, hybrid nanoparticles (MoS2/Ag) are observed more significant to conduct more heat energy rather than nanoparticle (Ag).

Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube.

In this article, we provide new formulas to compute the reduced reciprocal randic index, Arithmetic geometric1 index, SK index, SK 1 index, SK 2 index, edge version of the first zagreb index, sum connectivity index, general sum connectivity index, and the forgotten index using the M-polynomial and finding these topological indices for a boron triangular nanotube. We also elaborate the results with graphical representations.