The article explores the effect of Hall current, thermal radiation, and magnetic field on hybrid nanofluid flow over the surface of a spinning disk. The motive of the present effort is to upgrade the heat transmission rate for engineering and industrial purposes. The hybrid nanofluids as compared to the conventional fluids have higher thermal properties. Therefore, in the present article, a special class of nanoparticles known as carbon nanotubes (CNTs) and iron ferrite nanoparticles are used in the base fluid. The system of modeled equations is depleted into dimensionless differential equations through similarity transformation. The transform equations are further solved through the Parametric Continuation method (PCM). For the parametric study, the physical parameters impact on velocity, energy, mass transmission, and motile microorganism’s concentration profiles have been sketched. The obtained results are compared with the existing literature, which shows the best settlement. It concluded that the heat transmission rate reduces for Hall current and rises with radiative parameter. The results perceived that the addition of CNTs in carrier fluid is more efficacious than any other types of nanoparticles, due to its C–C bond. CNTs nanofluid can be more functionalized for the desired achievement, which can be utilized for a variety of applications by functionalization of non-covalent and covalent modification.

The study explored the 3D numerical solution of an unsteady Ag-MgO/water hybrid nanofluid flow with mass and energy transmission generated by a wavy rotating disc moving up and down. The nanofluid is generated in the context of Ag-MgO nanomaterials. Magnesium oxide and silver nanoparticles have been heavily reported to have broad-spectrum antibacterial operations among metal oxides and metals. Silver nanoparticles are without a doubt the most commonly used inorganic nanoparticles, with numerous innovations in biomaterial’s detection and antimicrobial operations. However, in current paper, the intention of the analysis is to boost thermal energy transmitting rates for a range of industrial implementations. When compared to a flat surface, energy transition is increased up to 15% due to the wavy swirling surface. The problem has been formulated as a system of PDEs, which included the Navier Stokes and Maxwell equations. Following that, the modeled equations are reduced to a dimensionless system of differential equations. The derived equations are then solved numerically using the Parametric Continuation Method (PCM). The findings are displayed graphically and debated. The geometry of a spinning disc is thought to have a positive impact on velocity and heat energy transfer. The insertion of nanostructured materials (silver and magnesium-oxide) increased the carrier fluid’s thermal properties considerably. It is more effective at dealing with low energy transmission.

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An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis of functions, consisting of first derivatives of Chebyshev polynomials, has been used. Consequently, new operational matrices for derivatives of any integer order have been introduced. An error analysis is performed to ensure the convergence of the presented method. In addition, the accuracy and the efficiency are verified by solving BVPs examples, including real-life problems.

In this article, we study the JF iterative algorithm to approximate the fixed points of a non-linear operator that satisfies condition (E) in uniformly convex Banach spaces. Further, some weak and strong convergence results are presented for the same operator using the JF iterative algorithm. We also demonstrate that the JF iterative algorithm is weakly w2G-stable with respect to almost contractions. In connection with our results, we provide some illustrative numerical examples to show that the JF iterative algorithm converges faster than some well-known iterative algorithms. Finally, we apply the JF iterative algorithm to estimate the solution of a functional non-linear integral equation. The results of the present manuscript generalize and extend the results in existing literature and will draw the attention of researchers.