Nanofluids holding three distinct sorts of nanosized particles suspended in base fluid possess excellent thermal performance. In light of this novel use in coolant applications, the current work dealt with the optimal design and performance estimation of a ternary hybrid nanofluid, based on a modern machine learning prediction technique. The synthesis of $\left(Cu\right)$, $\left(Ti{O}_2\right)$, and $\left(Si{O}_2\right)$ ternary hybrid nanoparticles suspended in water over a symmetrically stretching sheet was scrutinized. The flow over a stretching sheet is the most noteworthy symmetry analysis for momentum and thermal boundary layers, due to the implications of heat transfer, and is applied in various industries and technological fields. The governing equations were transformed to a dimension-free series of ODEs, by handling similarity transformable with symmetry variables, after which, the series of ODEs were treated scientifically, with the help of the Wolfram Language tool. The precision of the current estimates was assessed by comparison to existing research. Moreover, the natures of the physical phenomena were forecast by designing a support vector machine algorithm with an emphasis on machine learning, which delivers a robust and efficient structure for every fluid application that infers physical influences. To validate the proposed research, some of the statistical metrics were taken for error assessment between true and anticipated values. It was revealed that the presented approach is the best strategy for predicting physical quantities. This investigation established that ternary hybrid nanofluid possesses excellent thermal performance, greater than that of hybrid nanofluid. The current optimization process delivers a new beneficial viewpoint on the production of polymer sheets, glass fiber, petroleum, plastic films, heat exchangers, and electronic devices. Hence, the obtained results are recommended for the development of industrial devices setups.

In this paper, we investigate a (discretization) Caputo fractional glucose-insulin model qualitatively with incommensurate orders that appear in Bergman's minimal model. After intravenous tolerance testing, the model is used to characterize the blood insulin and glucose metabolism. We also prove that the presented model possesses existence, uniqueness, non-negative, and boundedness solution. We also proceed a systematical studies on the stability of the (discretization) Caputo fractional. Comparisons between the results of the fractional-order, the integer order and the measured real data obtained from patients are presented. These comparisons is shown that the presented Caputo fractional order model is better representative of the system than its integer order form. Numerical solutions of the Caputo fractional model are obtained by using the method of Adams-Bashforth-Moulton type to handle the fractional derivatives. Also, numerical simulations of the discretization fractional derivative order model are used to support the analytical results.

The primary goal of this research study is to examine the influence of Brownian motion and thermophoresis diffusion with the impact of thermal radiation and the bioconvection of microorganisms in a symmetrically stretching sheet of non-Newtonian typical Williamson fluid. Structures of the momentum, energy, concentration, and bio-convection equations are interconnected with the imperative partial differential equations (PDEs). Similarity transformations are implemented to translate pertinent complicated partial differential equations into ordinary differential equations (ODEs). The BVP4C approach from the MATLAB assemblage computational methods scheme is extensively impacted by the results of these ODEs. The impact of several physical parameters, including Williamson fluid $We(0.2\le We\le 1.2)$, the magnetic field parameter $M(0.0\le M\le 2.5)$, Brownian motion $Nb(0.0\le Nb\le 1.0)$, thermophoresis diffusion $Nt(0.1\le Nt\le 0.9)$. In addition, various physical quantities of the skin friction ($\sqrt{R{e}_x}{C}_{f_x}$), Nusselt number ($N_{u_x}$), Sherwood number ($S_{h_x}$), and motile microorganisms ($N_{n_x}$) are occupied and demonstrate the visualization of graphs and tabular values. These outcomes are validated with earlier obtained results, displaying excellent synchronicity in the physical parameters. Furthermore, the physical quantities concerning the non-dimensional parameters are anticipated by employing Multiple Linear Regression (MLR) in Machine Learning (ML) as successfully executed a novelty of this study. These innovative techniques can help to advance development and technologies for future researchers. The real-world implications of this research are that bio-remediation, microbial movements in mixed fluids, and cancer prevention therapy are crucial.

A study on the influence of magnesium ferrite nanoparticles on the optical and dielectric attributes of Polyaniline has been conducted. Magnesium nano Ferrite powder is synthesized by the self-propagating solution combustion method. Polyaniline–Magnesium nano ferrite composites are synthesized by chemical oxidative polymerization of aniline with the addition of Magnesium nanoparticles. The samples are characterized with XRD and UV-Vis spectrometer, in the wavelength range of 200–800 nm and studied for optical properties. Dielectric properties are studied in the frequency range of 50 Hz to 5 MHz. X-ray diffraction reveals single phase formation of Magnesium ferrite, whereas Polyaniline shows an amorphous nature. In the XRD of the composites, we see the crystalline peaks of ferrite becoming more intense with the addition of ferrite and whereas the peak of Polyaniline diminishes. The crystallite size is quantified with the Debye—Scherrer formula, and it increases as the content of ferrite in the composites increases. The micro-strain decreases in the composites as the percentage of ferrite enhances in the composites. In the UV-Vis absorption spectra of composites, the peaks of Polyaniline shift to higher wavelength and there is also an absorption band in the spectra of composites corresponding to that of Magnesium ferrite particles. Both direct and indirect band gaps are calculated with the Tauc plot, and both the optical band gap decrease as the percentage of ferrite increases in the composite. The dielectric loss and dielectric constant both decrease with frequency in all the samples, and the dielectric response are in good agreement with Maxwell—Wagner model. Ferrite—polymer composites with both conducting and magnetic properties are considered useful for electromagnetic shielding and microwave absorption.

The main goal of this work is to use the cut and paste method to match the inner flat and outer acoustic Schwarzschild black holes to examine the geometry of a thin-shell. Moreover, the study uses the Klein–Gordon equation and the equation of motion to examine the dynamical evolution of a thin-shell composed of massive as well as massless scalar field. The results of the study show that the collapsing behavior is exhibited by the potential function of a massless scalar shell while the effective potential of a massive scalar shell first collapses and then progressively increases. Additionally, the researchers have analyzed the stable configuration for the phantom-type equation of state encompassing dark energy, quintessence and phantom energy by applying the linearized radial perturbations. As a result, the research suggests that thin-shell Schwarzschild black holes are less stable than acoustic Schwarzschild black holes.