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In the present article, the intelligence based numerical investigation by Levenberg–Marquardt algorithm with Back‐propagated Artificial Neural Networks (LMA–BANN) is exploited to analyze the nonlinear radiative stagnation point flow of cross nanofluid system (NRS‐CNFS) past a stretching surface. The designed NRS‐CNFS, initially represented by system of partial differential equations (PDEs), is converted into system of non‐linear ODEs through the applicability of mathematical conversion analysis. The desired reference solution in the form of a dataset for LMA–BANN is achieved from the Adam method for NRS‐CNFS's different scenarios by varying the magnetic parameter (Ha), Prandlt number (Pr), thermal radiation parameter(R), Eckert number (Ec), thermophoresis diffusion coefficients (Nt), and non‐dimensional activation energy (E). The obtained results are construed for the NRS‐CNFS through the performances of the testing, validation, and training. In addition, the comparison is provided using the LMA ‐BANN analysis, which is validated in terms of regression, fitness estimations, and histograms along with MSE performances. Hence, the article provides an impeccable innovative approach to problem‐solving by implementing a soft computation paradigm. It promotes the use of an effective and dependable alternative framework that is based on soft computing environments and emphasizes descriptive analysis to successfully handle the problems brought on by varied physical features. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNF) are the advanced form of nanofluids used for improved heat transfer purposes. Taking this point in mind, the objective of the presented endeavor is to examine the Yamada–Ota HNF flow model comprising (gold–silver/engine oil) over a stretched cylindrical surface and a sheet (as a limiting case) in a permeable medium. The novelty of this research is the consideration of the surface-catalyzed reaction along with the homogeneous–heterogeneous reactions to accelerate the chemical reactions in the shortest possible time. The heat transport phenomenon is strengthened with the support of Joule heating, heat absorption/generation, and the convective heat boundary condition at the surface of the cylinder. The obtained ordinary differential equations are reduced from the partial differential equations using boundary layer theory and are numerically computed using the Keller box method. It is witnessed that for varied estimates of the magnetic parameter, the thermal profile enhances while the velocity field reduces. It is also noted that the fluid concentration is reduced when the surface-catalyzed parameter is enhanced. The validation of the envisioned model in a limiting case is also added to this investigation. [ABSTRACT FROM AUTHOR]

This study discusses entropy generation analysis for a peristaltic flow in a rotating medium with generalized complaint walls. The goal of the current analysis is to understand the fluid flow phenomena particular to micro devices. Nano materials with a size less than 100 nm have applications in micro heat exchangers to cool electronic circuits, blood analyzers, biological cell separations, etc. For this study, we considered the effects of radiation, viscous dissipation and heat flux on the flow of nanomaterial inside a cylindrical micro-channel. To investigate the slip effects on the flow, the second order slip condition for axial velocity, the first order slip condition for secondary velocity and the thermal slip conditions were used. The flow was governed by partial differential equations (PDE's), which were turned into a system of coupled ordinary differential equations (ODE's) that were highly non-linear and numerically solved using the NDSolve command in Mathematica. The impacts of different involved parameters on the flow field were investigated with the aid of graphical illustrations. Entropy generation and the Bejan number were given special attention, and it was found that they decreased as the Hartman number, rotation, and radiation parameters increased. [ABSTRACT FROM AUTHOR]

The free convective unsteady fluctuating, MHD flow of electrically conducting viscoelastic dusty fluid in a channel-driven with the impact of oscillating pressure gradient and the motion of the upper plate has been studied in this article. The noteworthy heat generation/absorption has also taken into account, the heat generation established the mechanism of heat transfer by both the momentum of fluid and the motion of dust particle and absorption of heat by the dust particle is because of conduction. The coupled governing partial differential equations are reduced to the ordinary differential equation through the assumed periodic solutions. Analytical solutions for the velocity of the fluid as well as the velocity of dust particles and for energy equation of the fluid and for dust particles are obtained by using Poincare-Light Hill Perturbation Technique. The influence of various parameters of interest is discussed on the velocity and temperature profiles of the fluid and particles. The evolution of fluid-phase and dusty-phase with dual behavior of the magnetic parameter for both boundary layer and free stream velocities has been discussed. The boundary layer velocity decreased with an increase in magnetic parameter, while at the free stream flow, the result is quite opposite. The above result of magnetic field is worthwhile and can be used to control the boundary layer thickness. The current work also concludes that by increasing the Peclet number and concentration of the dust particles retards the boundary layer velocity. Furthermore, various physical parameters like coefficient of heat absorption, concentration of the dust particles, peclet number, magnetic parameter, and temperature relaxation time parameter retard the motion of dusty-phase, while Grashof number enhances the flow of dusty-phase. Other properties of fluid, which have great importance for engineers are, the rate of heat transfer and skin friction. It is shown in Table 1 that by increasing the value of Peclet number from 1 to 2 it increases the rate of heat transfer from 1.3263 to 1.3387. Furthermore, Table 2 shows that by increasing the concentration parameter from 2 to 4 the skin friction increases from 2.3872 to 4.7799. [ABSTRACT FROM AUTHOR]

The major purpose of this article is to exploit the strength of the Intelligent Back-propagated Neural Networks of Levenberg Marquardt Technique (IBNN-LMT) to study three-dimensional (3D) squeezed flow model of carbon nanotubes (SFM-CNTs) relying on water in a revolving network with a rigid ground wall. The impact of magnetohydrodynamic (MHD) and thermal radiation has been investigated. Similarity transformation is utilized to convert partial differential equations (PDEs) into ordinary differential equations (ODEs). For numerous nanofluids constructed of SWCNT and MWCNT, the influence of each parameter on velocity, temperature, Bejan number, and entropy production is estimated. The overall entropy optimization was also computed. The major outcome of this research is to examine the impacts of flowing parameters on CNTs when squeezing parameters are changed. Moreover, the estimated solution is evaluated for designed SFM-CNTs by using a testing method and comparing it to a standard solution that has been backed up by performance studies based on MSE convergence, error histogram, and regression studies. The velocity profile f (χ) along y-axis intensifies with the intensification in S , φ ,and A. Where Ω gives a dual performance with the increment in the function, as with the increase in M , f (χ) provides decreasing performance. The temperature function θ (χ) increase as the increment in S , Ec ,and Ec m and decrease with the increase in φ and R. The solution is accurate up to 4 to 10 decimal places which proves the worth and effectiveness of the proposed IBNN-LMT solver. [ABSTRACT FROM AUTHOR]

Titanium alloy nanoparticle has a variety of applications in the manufacturing of soap and plastic, microsensors, aerospace design material, nano-wires, optical filters, implantation of surgical, and many biological treatments. Therefore, this research article discussed the influence of nonlinear radiation on magneto Williamson fluid involving titanium alloy particles through a thin needle. The arising system of partial differential equations is exercised by the similarity transformations to get the dimensional form of ordinary differential equations. The dual nature of solutions is obtained by implementing bvp4c. The study of stability has been carried out to check which of the results are physically applicable and stable. Influences of pertinent constraints on the flow field are discussed with the help of graphical representations and the method validation is shown in Table 1. The results imply that more than one result is established when the moving needle and the free-stream travel in the reverse directions. Moreover, the magnetic parameter accelerates the severance of boundary-layer flow, while the separation delays in the absence of the nanoparticle. The velocity gradient of nanofluid decays owing to the Williamson parameter in both branches of the outcome, while the temperature shrinks in the first or upper branch solution (stable one) and uplifts in the second or lower branch solution (unstable one). The size of the needle decreases the velocity in the upper solution and accelerates in the lower solution. The patterns of streamlines are more complicated due to the reverse direction of the free stream and thin needle. [ABSTRACT FROM AUTHOR]

Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial differential equations into nonlinear ordinary differential equations and then these ordinary differential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form A < 0 . However, the unique result is obtained for flow in accelerating form A ≥ 0 . In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result. [ABSTRACT FROM AUTHOR]