The analysis is carried out to analyze the flow through double stretchable rotating disks with the theory of radiative Cross nanofluid under the influence of variable thermal conductivity, the Hall current, Arrhenius activation energy, and binary chemical reactions. The Buongiorno nanofluid model is adopted for the governing equations of the problem which are transformed into ordinary differential equations through similarity transformations and then solved using the homotopy analysis method. The impact of dimensionless parameters on all profiles and physical quantities is presented and discussed. The radial velocity of the two disks increases with their corresponding ratio stretching rate parameter and decreases with the Hall parameter and the bioconvection Rayleigh number. The heat transfer at the lower disk enhances with the variable thermal conductivity parameter, while at the upper disk, opposite trend is observed. Mass transfer increases with the chemical reactions and temperature difference parameters at the lower disk and decreases with Arrhenius activation energy, whereas an opposite trend is observed at the upper disk. The local density number is enhanced for the larger values of Peclet and Lewis numbers. The comparison of the present work with the published literature authenticates the validation of the present work.

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This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.

This paper investigates the two-dimensional and incompressible flow of viscoelastic nano-liquid dynamic and axisymmetric sprayed thin film deposit on a stretched cylinder. It also looked at how activation energy and entropy evaluation affected mass and heat flow. The governing equations are transformed into nonlinear differential equations using similarity transformation techniques, which are then resolved successively using a strong semi-analytical homotopy analysis method (HAM). The velocity decreases as the magnetic field strength and viscoelastic parameters are increased. The temperature rises as the Brownian motion parameter increases, while it falls as the Prandtl number, film thickness parameter, and thermophoresis parameter increase. The greater the Reynolds number and the activation energy parameter, the higher the concentration of nanoparticles. The film size increases nonlinearly with the spray rate. Entropy generation increases as the Brinkmann number, magnetic field, and thermal radiation parameters increase. A nearby agreement is signed after comparing the current investigation with published results. The results obtained, possibly under ideal conditions, could be useful for determining and architecting coating applications.

In this article, exponentiated U-quadratic distribution (EUq) is proposed by exponentiation procedure. The quantile function and r th moment of the new model are computed. Estimation of parameter by the alternative maximum likelihood and estimation based on percentiles are established and compare their performances through numerical simulations. The results show that both methods are suitable for the parameter estimation of EUq distribution. A real data set is used to compare the fit of the two proposed estimation method using Kolmogorov Smirnov test (KS).