CLOSED NEWTON COTES QUADRATURE RULES WITH DERIATIVES

In this research paper, a new family of numerical integration of closed newton cotes is introduced which uses the mean of arithmetic and geometric means at derivative value for the Evaluation of Definite Integral. These quadrature methods are shown to be more efficient than the existing quadrature rules. The error terms are obtained by using the concept of precision. Finally, the accuracy of proposed method is verified with numerical examples and the results are compared with existing methods numerically and graphically. Keywords – Numerical Integration, Closed Newton-cotes formula, Definite integral, Arithmetic mean, Geometric mean, Numerical examples. DOI: 10.7176/MTM/9-5-06 Publication date: May 31st 201

Simulating Electrohydrodynamic Ion-Drag Pumping on Distributed Parallel Computing Systems

Objectives: This paper aims to simulate EHD ion-drag pumping model using Finite Difference Method (FDM) and to apply the idea of parallelism to reduce the computational time. Methods: The numerical simulation of EHD ion-drag pumping plays an important part not only to understand the different working principles but also enables to model the designs with better performance. Since the performance of EHD pumps depends on the shapes and geometries of the actuator electrodes, therefore the variation in the geometric dimensions of the electrodes require dense and fine meshes for numerical solution. Consequently, the numerical simulations take unacceptably more execution time on sequential computers. For that reason, a Data Parallel Algorithm for EHD model (DPA-EHD) is designed. To implement the parallel algorithm a distributed parallel computing system using MATLAB Distributed Computing Server (MDCS) is configured. The computational time and speedup with respect to the different number of processors is evaluated. Findings: This results show that the parallel algorithm for EHD simulations may provide 4.14 times more speedup over sequential algorithm for large grid sizes. Improvements: This study shows the feasibility of using the parallelism to reduce the computational time in the EHD model enabling to simulate the micropumps with very small dimensions of electrodes

Role of copper and alumina for heat transfer in hybrid nanofluid by using Fourier sine transform

The convection, thermal conductivity, and heat transfer of hybrid nanofluid through nanoparticles has become integral part of several natural and industrial processes. In this manuscript, a new fractionalized model based on hybrid nanofluid is proposed and investigated by employing singular verses and non-singular kernels. The mathematical modeling of hybrid nanofluid is handled via modern fractional definitions of differentiations. The combined Laplace and Fourier Sine transforms have been configurated on the governing equations of hybrid nanofluid. The analytical expression of the governing temperature and velocity equations of hybrid nanofluid have been solved via special functions. For the sake of thermal performance, dimensional analysis of governing equations and suitable boundary conditions based on Mittage-Leffler function have been invoked for the first time in literature. The comparative analysis of heat transfer from hybrid nanofluid has been observed through Caputo-Fabrizio and Atangana-Baleanu differential operators. Finally, our results suggest that volume fraction has the decelerated and accelerated trends of temperature distribution and inclined and declined profile of heat transfer is observed copper and alumina nanoparticles

A comparative analysis of sulfate (SO4-2) ion concentration via modern fractional derivatives: An industrial application to cooling system of power plant

Abro, Irfan Ali/0000-0001-9350-0407WOS: 000514758600061The significance of cooling system of power plant has vividly diverted the scientists, engineers and researchers because of the experimental analyses and numerical approximations on a cooling system of power plant. in fact, the heat exchange processes inside the condenser take worsening place due to uncontrolled increase of the sulfate ion concentration in cooling water which depends upon two main causes (i) an increase in deposition of calcium salts on the surfaces of heat exchangers/cooling towers (ii) the corrosion of power plants in cooling system. in this manuscript, a fractional modeling of sulfate SO4-2 ions concentration for circulating water in a closed cooling system of a power plant is based on the contributions of modern differentiations of Atangana-Baleanu and Caputo-Fabrizio types. the governing equation of Sulfate SO4-2 ions concentration is converted through the law of conservation of mass for volumetric flow rates using modern fractional differentiations, and then solved analytically by invoking Laplace transform method. An interesting comparative analysis of sulfate SO4-2 ions concentration is explored via Atangana-Baleanu and Caputo-Fabrizio fractional operators. Based on both modern differentiation operators our results suggest few similarities and differences for the removal of Sulfate SO4-2 ions concentration. (C) 2019 Elsevier B.V. All rights reserved.Mehran University of Engineering and Technology, Jamshoro, PakistanKashif Ali Abro and Wan Ali Abro acknowledge the support from Mehran University of Engineering and Technology, Jamshoro, Pakistan for the successful completion of this research work

Fractional Treatment of Vibration Equation Through Modern Analogy of Fractional Differentiations Using Integral Transforms

WOS: 000487075500027Although the significance of the vibration equation has recently attracted the researchers because of the experimental, empirical or numerical analyses, there is a lack of modern fractional analytic approaches. The main aim of this investigation is to analyze the dual treatment of vibration equation for large membrane through the modern approaches of Caputo-Fabrizio and Atangana-Baleanu fractional operators. In order to analyze the fractional model of vibration equation for large membrane, an analytic study is carried out by using Laplace and Hankel transforms satisfying the imposed conditions. A comparative analysis of vibration equation is addressed by newly presented non-integer-order derivatives with and without singular kernel, namely Michele Caputo-Mauro Fabrizio and Atangana-Baleanu fractional derivatives. The analytical solutions are obtained via both fractional approaches and then separately expressed in terms of newly presented Wiman special function E eta,xi. The present fractional methods performed extremely well in terms of reliabilities and computational efficiencies. For the accuracy and validations of analytical treatment of fractional model of vibration equation for large membrane, a graphical comparison is made between Caputo-Fabrizio and Atangana-Baleanu fractional derivatives, which results in various similarities and differences on pertinent parameters involved in the vibration equation

Heat Transfer in Magnetohydrodynamic Second Grade Fluid with Porous Impacts using Caputo-Fabrizoi Fractional Derivatives

This article leads to free convection problem of magnetohydrodynamic second grade fluid with porous medium using recently defined Caputo-Fabrizoi fractional derivatives. Analytical expressions for temperature distribution and velocity field have been investigated using Laplace transforms having inverses. The general expressions for Temperature distribution and velocity field are written in terms of Generalized Mittage-Leffler function MP Q,R(Z) and Fox-H function H 1,P P,Q+1(Z) respectively. Both the solutions of Temperature distribution and velocity field satisfy implemented conditions as V (y, 0) = T(y, 0) = 0 and V (0, t) = UH(t)cos(ωt), V (0, t) = UH(t)sin(ωt) and T(0, t) = 1. The general expressions have been reduced for limiting cases. Finally influences of material parameter, non-dimensional parameters, rheological parameters and Caputo-Fabrizoi fractional parameter are analyzed graphically by choosing distinct values on fluid flow

Exact Solutions on the Oscillating Plate of Maxwell Fluids

This work is related to establish the exact solutions of sine hyperbolic and cosine hyperbolic oscillations of Maxwell fluid over the velocity field and shear stress. Under the effects of sine hyperbolic and cosine hyperbolic oscillations, the general solutions are derived for the motions of incompressible Maxwell fluid. For the sack of the general solutions the mathematical techniques of integral transformations (Laplace and Fourier Sine transforms) are applied. We have expressed the obtained solutions under form of theorem of convolutions product and integral notation, satisfying the boundary and initial conditions. The expressions for similar solutions are specialized as a limiting case of Newtonian fluid