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Investigation of expanding sheet flow in the existence of tiny particles is an interesting field of research and this type of mathematical model is usually expressed in the form of partial differential equations. Present exploration has been made to describe the unsteady 3D dynamics of MHD tangent-hyperbolic fluid impinging over an expanded sheet with the characteristics of haphazard movement and thermo migration of nanoparticles. Moreover, securitization has been accomplished in the environment of prescribed temperature and prescribed concentration restrictions at the stretchable surface. Novel combination of scaling transformations has been accustomed to exchange the governing equations into complicated system of ordinary differential equation and then solved by an innovative analytical scheme, namely, homotopy analysis method. The significance of involved scientific factors on temperature phase, concentration phase, condensed Nusslet number and condensed Sherwood number has been explained through various contours. It has been noticed that increasing choices of random movement 0 ≤ N b ≤ 1.0 and thermo-migration of nanoparticles 0 ≤ N t ≤ 3.0 reduce the estimate of heat transaction along with the estimate of mass transaction. Moreover, temperature and concentration circulations have improved with the advanced choices of Weissenberg number 0 ≤ W e x ≤ 10.0 and flow behavior index 0 ≤ n ≤ 2.1. [ABSTRACT FROM AUTHOR]

Wire coating is a commercial method to insulate wires for mechanical intensity and environmental protection. In this experimental study, the technique of computational intelligence is used for nonlinear wire coating analysis by soaking the wires in Oldroyd 8-constant fluid under a constant pressure gradient with the help of feed forward artificial neural networks (ANNs). The system of partial differential equations generated for the process of wire coating is transformed into a nonlinear dimensionless ordinary differential equation. One of the salient features of ANNs is the mathematical modeling of transformed equations by exploring the unsupervised error. A new scheme based on inverse multiquadric neural networks (IMQNNs) is used with a hybridization process of well-known genetic algorithms (GAs) and sequential quadratic programming (SQP) to obtain expeditious convergence, i.e., IMQNNs-GA-SQP. The applicability of the problem is investigated by altering the values of the dilatant constant, pressure gradient, shear stress, and pseudo-plastic constant, the outcome of which is in the form of varying polymer coating thickness. Comparison of highly accurate results in the shape of error analysis based on absolute errors of obtained results with those of the reference solution, calculated using the Adams numerical technique using MATHEMATICA software, statistical analysis such as root-mean-square error, Theil's coefficient for inequality, E-R2 (error function based on the coefficient of determination), E-VAF (variance accounted for), E-NSE (Nash–Sutcliffe efficiency), mean absolute error, box plot analyses, and the cumulative distributive function through histogram analyses, is also carried out in this research, which guarantees the effectiveness of the used scheme. [ABSTRACT FROM AUTHOR]

Inspired by spectacular applications of nonlinear resources in the field of nanotechnology, we formulate a mathematical relation for unsteady radiative flow of a magneto-Carreau nanoliquid as the consequence of a bidirectionally stretchable surface using the Buongiorno model. Practically, this newly mentioned approach is more genuine where we account for the fact that the surface temperature and surface heat flux are adjusted themselves on the boundaries, accordingly. With the utilization of this approach, industrial and engineering quantities of interest are investigated in a more effective manner. A suitable combination of variables is used to alter the partial differential equations into ordinary differential equations and then computationally solved by employing the Keller box method. The great significance of the involved constraints on the Carreau nanomaterial velocity components, temperature, and concentration fields is depicted graphically and elucidated in detail. The foremost outcomes for drag forces, surface temperature gradient, and concentration gradient for the Carreau nanomaterial are anticipated and arranged through tables. For endorsement of the present solution, the attained outcomes are linked with formerly published work in a particular case and found in marvelous agreement. It is observed that an escalating amount of radiative parameter Rd enhances the temperature of the Carreau nanomaterial. Moreover, the amounts of heat and mass fluxes are significantly improved by increasing the temperature of the surface. [ABSTRACT FROM AUTHOR]

In this research-based study, the electro-magneto impacts are numerically observed during Darcy-Forchheimer (DF) viscous fluid flow having nonlinear form of thermal radiation. This two-dimensional fluid flow over a stretchable sheet is exposed to joule heating, thermal convection and viscous dissipation. The entire computational work is successfully performed using reliable neuro computing technique (NCT) through a viable combination of genetic algorithms (GAs) a well-known global solver and a famous local solver named sequential quadratic programming (SQP) i-e NCT-GA-SQP. Partial differential equations (PDEs) that express the DF viscous fluid flow are successfully converted into a third order nonlinear system of ordinary differential equations (ODEs) through manipulation of similarity variables. Numerical illustrations with strong accuracy and effective graphical representations are adopted to visualize the velocity profile, thermal distribution and concentration of fluid flow due to the variational effects of various physical parameters namely the electric field parameter (E), magnetic parameter (M), the porosity parameter (λ), the radiation parameter (Rd), the Prandtl number (Pr), the chemical reaction parameter (γ) and the Schmidt number (Sc). The reference solutions attained through well-known Adams method are used to validate the numerical results gathered through complexity analysis and different statistical operators and are closely matched which guarantees the reliability of the proposed solver. [ABSTRACT FROM AUTHOR]

This article addresses the unsteady three-dimensional flow of second grade nanofluid due to thermophoresis and Brownian motion effects. The flow is generated due to unsteady stretching in two lateral directions. The zero nanoparticles mass flux boundary conditions are imposed to find the desired solutions. By introducing the dimensionless variables the governing system of partial differential equations are transformed into the system of ordinary differential equations. Series solutions of the transformed ordinary differential equations are computed. Solutions are carried out for dimensionless temperature and nanoparticles concentration. The behavior of physical parameters on the temperature and nanoparticles concentrations is examined through graphs and tabular data. The temperature and concentration distribution at the surface are also computed and analyzed. It can be noted that both the temperature and nanomaterial are reduced for higher values of unsteadiness parameter. It is also observed that the friction factor of second grade fluid parameter is less compared with viscous nanofluid. • Time-dependent 3D flow of viscoelastic nanofluid is examined. • Brownian motion and thermophoresis effects are considered. • The condition requiring zero nanoparticles mass flux is implemented. • Series solutions are obtained through homotopy analysis method (HAM). [ABSTRACT FROM AUTHOR]

The main theme of the present communication is to analyze the flow of micropolar Casson fluid with the influence of dissipation effects and inclined magnetic field upon a stretching surface by incorporating the Lobatto IIIA based numerical solver. In the presented study, the Navier–Stokes theory is exploited to model the governing fluidic system and similarity variables are used to reduce the system of governing partial differential equations into the equivalent ordinary differential equation-based model. A graphical and tabular illustration of the result of the system using the Lobatto IIIA method for the study of influential effects of various sundry parameters against the velocity profile, temperature, and microrotation are presented with brief interpretations. Results show that the increment of the inclination angle diminishes the velocity and upsurges the temperature, while, the Eckert number reduces the rate of heat transfer and shear stress, however, on the other hand, enhances the temperature and velocity profiles. [ABSTRACT FROM AUTHOR]