MASS TRANSFER EFFECTS ON MHD BOUNDARY LAYER FLOW OVER AN UNSTEADY STRETCHING CYLINDER DUE TO SPACE DEPENDENT HEAT SOURCE

In this article important effort has been dedicated toward the learn about of warmth and mass switch for MHD boundary layer float evaluation previous an unsteady continually shifting stretching cylinder beseeching the restricted slip apparatus. Additionally we have analysed our exploration along with the presence of non-uniform warmth supply in the go with the flow field. Moreover first order chemical response is taken into account. The rising primary go with the flow associated non-linear equations have been solved mathematically by RK-4 strategy which consists of capturing procedure. The influence of pertinent parameters on speed and temperature silhouette has been pondered with bodily justification thru tables and graphs. Our research explores that the temperature escalates attributable to the improvisation of curvature parameter. The mass switch price is increased via bettering chemical response parameter.

On Beta Exponentiated Moment Exponential Distribution with Mathematical Characteristics and Application to Engineering Sectors

A new BEME distribution known as beta Exponentiated moment exponential (BEME) distribution is proposed. We provide here some shape properties, moments in the form of special functions, mean deviations of BEME distribution. We derive mathematical properties of the BEME distribution including the reliability measures, the Bonferroni and the Lorenz curves, rth order statistics, measures of uncertainty: the Shannon entropy measure and the s-entropy measure. The parameters of the BEME distribution are estimated by the method of maximum likelihood estimation and estimated non-linear equations for these estimates are presented. The application of BEME distribution is explored in three different fields of engineering.

Methodology of Adaptive Instantaneous Overcurrent Protection Setting

This paper proposed a methodology of adaptive instantaneous overcurrent protection (AIOCP) setting that ensures that the protection coverage remains unchanged regardless of the operating condition of the electrical network. The methodology calculates the protection setting parameters based on the real-time estimation of the Thevenin equivalent circuit (TEC). The estimation algorithm uses the positive-sequence voltage and current values and a system of non-linear equations, which is solved iteratively by the Gauss–Newton method. The proposed methodology calculates the IOCP settings in real time by using the real-time estimation of the TEC; therefore, any change in the electric network conditions is represented in the TEC, and the calculated setting keeps the desired protection coverage constant. Simulation results demonstrate that the proposed AIOCP can keep constant the protection coverage overcoming the classical problems of classical IOCP: sub-allocation and over-coverage.

Three-point iterative algorithm in the absence of the derivative for solving nonlinear equations and their basins of attraction

In this paper, we suggested and analyzed a new higher-order iterative algorithm for solving nonlinear equation $$g(x)=0$$ g ( x ) = 0 , $$g:{\mathbb {R}}\longrightarrow {\mathbb {R}}$$ g : R ⟶ R , which is free from derivative by using the approximate version of the first derivative, and we studied the basins of attraction for the proposed iterative algorithm to find complex roots of complex functions $$g:{\mathbb {C}}\longrightarrow {\mathbb {C}}$$ g : C ⟶ C . To show the effectiveness of the proposed algorithm for the real and the complex domains, the numerical results for the considered examples are given and graphically clarified. The basins of attraction of the existing methods and our algorithm are offered and compared to clarify their performance. The proposed algorithm satisfied the condition such that $$|x_{m}-\alpha |<1.0 \times 10^{-15}$$ | x m - α | < 1.0 × 10 - 15 , as well as the maximum number of iterations is less than or equal to 3, so the proposed algorithm can be applied to efficiently solve numerous type non-linear equations.

DEVELOPMENT OF NEW ITERATIVE SCHEME FOR SOLVING NON-LINEAR EQUATIONS

Within our study a special type of 〖iterative method〗^ω is developed by upgrading Newton-Raphson method. We have modified Newton’s method by using our newly developed quadrature rule which is obtained by blending Trapezoidal rule and open type Newton-cotes two point rule. Our newly developed method gives better result than the Newton’s method. Order of convergence of our newly discovered quadrature rule and iterative method is 3.

Evaluating Diesel/Biofuel Blends Using Artificial Neural Networks and Linear/Nonlinear Equations

The use of biomass-derived additives in diesel fuel mixtures has the potential to increase the fuel’s efficiency, decrease the formation of particulate matter during its combustion, and retain the fuel’s behavior in cold weather. To this end, identifying compounds that enable these behaviors is paramount. The present work utilizes a series of linear and non-linear equations in series with artificial neural networks to predict the cetane number, yield sooting index, kinematic viscosity, cloud point, and lower heating value of multi-component blends. Property values of pure components are predicted using artificial neural networks trained with existing experimental data, and these predictions and their expected errors are propagated through linear and non-linear equations to obtain property predictions for multi-component blends. Individual component property prediction errors, defined by blind prediction median absolute error, are 4.91 units, 7.84 units, 0.06 cSt, 4.00 °C, and 0.55 MJ/kg for cetane number, yield sooting index, kinematic viscosity, cloud point, and lower heating value respectively. On average, property predictions for blends are shown to be accurate to within 6% of the blends’ experimental values. Further, a multitude of compounds expected to be produced from catalytically upgrading products of fast pyrolysis are evaluated with respect to their behavior in diesel fuel blends.

Multi-parametric Dynamic Analysis of a Rolling Bearings System

A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

Optimization by parameters in the iterative methods for solving non-linear equations

In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods.

A symbolic framework for flexible multibody systems applied to horizontal axis wind turbines

The article presents a symbolic framework that is used to obtain the linear and non-linear equations of motion of a multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitate the creation and manipulation of models with various levels of fidelity. The symbolic treatment provides analytical gradients and linearized equations of motion. The linear and non-linear equations can be exported to Python code or dedicated software. The application are multiple such as: time-domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, digital twins, etc. In this paper, we describe the method we used to systematically generate the equations of motion of multibody systems. We apply the framework to generate illustrative onshore and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. A Python implementation is provided as an opensource project.