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<abstract> <p>The present work is to design a novel Neuro swarm computing standards using artificial intelligence scheme to exploit the Gudermannian neural networks (GNN)accomplished with global and local search ability of particle swarm optimization (PSO) and sequential quadratic programming scheme (SQPS), called as GNN-PSO-SQPS to solve a class of the second order Lane-Emden singular nonlinear model (SO-LES-NM). The suggested intelligent computing solver GNN-PSO-SQPS using the Gudermannian kernel are unified with the configuration of the hidden layers of GNN of differential operators for solving the SO-LES-NM. An error based fitness function (FF) applying the differential form of the differential model and corresponding boundary conditions. The FF is optimized together with the combined heuristics of PSO-SQPS. Three problems of the SO-LES-NM are solved to validate the correctness, effectiveness and competence of the designed GNN-PSO-SQPS. The performance of the GNN-PSO-SQPS through statistical operators is tested to check the constancy, convergence and precision.</p> </abstract>

This article focuses on the three‐dimensional Cross fluid flow of a radiative nanofluid over an expanding sheet with aligned magnetic field, chemical reaction, and heat generation phenomenon. The stretching sheet has convective heat and slip boundary conditions. The similarity variables are properly used for the conversion of a dimensional mathematical model into a nondimensional one. The transformed ordinary differential equations are handled for the numerical outcomes of the suggested fluidic model by incorporating the shooting scheme. Furthermore, the numeric investigations are also compared by bvp4c MATLAB built‐in package. In a limited case, both the techniques are checked with already published articles, thereby revealing good agreement. Furthermore, the effects of few parameters like Prandtl number, Weissenberg number, heat generation, stretching rate parameter, magnetic parameter, thermal radiation, Brownian and thermophoresis parameters, and Lewis number on concentration, temperature, and velocity profiles have been presented using figures and numerical tables. The strong intensity of the magnetic field across the fluid and increment in the inclination angle (ϑ) result in a lower velocity profile. Temperature is more prominent for the higher slip mechanism. Furthermore, there in an increase in thermophoretic force, which pushes the nanoparticles, and this mixing of nanoparticles helps to increase the concentration profile. A higher Cross fluid index responds to a larger velocity.

Key developments in the field of nanotechnology have drawn the attention of many scholars toward the interaction of nanoparticles due to their capturing applications in solar energy systems and thermal engineering. Larger consumption of energy posed a challenge for thermal science, so thermal engineering is trying to solve this issue by increasing the thermal conductivity of the fluid. The thermal conductivity of conventional fluid is increased by incorporating the nanoparticles in the base fluid. Keeping this in mind, the present research project addresses the utilization of nanoparticles in a steady three-dimensional rotating flow of magnetohydrodynamic water-based hybrid fluid over an extending sheet. Nanoparticles of aluminum oxide (Al 2 O 3 ) and silver (Ag) are being used with water (H 2 O) as base fluid. The velocity of nanoparticles is being captured under the influence of an inclined magnetic field and the transport of heat is scrutinized through thermal radiation. The physical model generates partial differential equations and then transported into an equivalent set of a nonlinear ordinary differential equations. The purpose of numerical computation is made by the Lobatto IIIA method, which is

Heat transference in fluid mechanism has a deep influence in real-life applications like hot-mix paving, recovery of energy, concrete heating, heat spacing, refineries, distillation, autoclaves, reactors, air conditioning, and so forth. In this attempt, findings related to energy exchange with features of infinite shear rate viscosity model of Carreau nanofluid by placing inclined magnetic dipole over the wedge are made. The main role in the transportation of heat is exercised by incorporating facts of radiation, nonuniform heat sink source, Brownian motion, thermophoresis, and chemical reaction. The mathematical system of the infinite shear rate viscosity model of Carreau nanofluid gives a system of partial differential equations and furthermore, these are moved into ordinary differential equations. A numerical procedure is applied via shooting/bvp4c to obtain numerical results. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor velocity of Carreau fluid gets down. A* causes to generate the heat internally, so due to this, temperature increases

Fluid viscosity manages several engineering processes and keeps its leading role in lubrication models, biological models, polymer processes, melt solutions, colloidal suspensions, and mayonnaise. The cross viscosity model is the most appropriate model, which interprets the key features of non-Newtonian fluids in the region of shear-thinning/thickening when very high and very low shear rates are applied. This article focuses on the mathematical model of threedimensional Cross nanofluid and interprets its aspect of infinite shear rate of viscosity over the expanding sheet. Velocity is studied through placing inclined magnetic dipole effect, transportation phenomenon is brought by considering the radiation effects, heat generation and chemical process is engaged for concentration of nanoparticles. The geometry of this mathematical model is expanding the stretching sheet with velocity slip, and convective heat conditions are associated. Similarity variables are being utilized for conversion dimensional mathematical model into nondimensional one. For the pursuit of numerical solution of the system of nondimensional

Here, modeling and computations are performed to explore the impact of variable molecular diffusivity, nonlinear thermal radiation, convective boundary conditions, momentum slip, and variable molecular diffusivity on Prandtl fluid past a stretching sheet. By using the compatible transformation, the partial differential equations regarding momentum, energy, and concentration are reformed into ordinary differential equations and furthermore, these equations are handled numerically via the shooting method. The behavior of intricate parameters that emerge during numerical simulation is displayed in the form of tables and graphs. These outcomes are supplemented with the information for the heat transfer rate and surface drag coefficients. It is perceived that an uplift in the temperature profile occurs by virtue of augmentation in the temperature convection parameter, and furthermore, mass fraction field escalates owing to an amplification in the chemical reaction coefficient.

Solar energy is the basic source of renewable energy, and it is being used for controlling global pollution/warming. As the Cross nanofluid is very useful for cooling solar devices, in this paper analysis of the global warming effect is investigated by incorporating the nonlinear thermal radiation over the exponentially extendable surface because it plays a major role related to solar energy absorption of nanofluid. Furthermore, the mathematical modeling of Cross nanofluid involving magnetic effect and diffusion is discussed by using the fact of chemical reaction. Chemical reaction finds astonishing applications in pollution studies, chemical processing equipment, and polymer production. As a result of this study, it is noticed that more magnetized conducting fluid controls the motion of fluids for both cases of shear thinning and shear thickening. Brownian motion parameter Nb affects the rate of the random motion of nanoparticles. Increased Nb temperature also increases due to these random movements of nanoparticles. That is the reason why pollutant nanoparticles spread in air as a result of global warming increase.