Friction Factor Comparison Between Mixing Length Theory and Empirical Correlation

Equivalent sand grain roughness is required for estimating friction factor for engineering applications from empirical relation via Haalands equation. The real surfaces are different from the sand grain profile. The correlations for friction factor were derived from use of discrete roughness elements with regular shapes such as cones, bars etc. The purpose of the paper is to derive analytical expression of friction factor for a 2 dimensional semi-cylindrical roughness (not exactly a 3 dimensional sand grain but for the circular profile of cross- section) using Navier Stoke equation and mixing length theory. This is compared with the modified series mathematical representation of Haalands equation for friction factor in terms of equivalent sand grain roughness. The comparison is valid for high Reynolds number where the velocity profile is almost flat beyond boundary layer and approximately linear all throughout the boundary layer. The high Reynolds number approximation for Haalands equation is derived and the series form of the friction factor compares approximately with the series form derived from first principles, where in the exponents of the series expansion are close.

On Effects of a New Method for Fractional Initial Value Problems

The aim of this study is to analyze nonlinear Liouville-Caputo time-fractional problems by a new technique which is a combination of the iterative and ARA transform methods and is denoted by IAM. First, the ARA transform method and its inverse are utilized to get rid of time fractional derivative. Later, the iterative method is applied to establish the solution of the problem in infinite series form. The main advantages of this method are that it converges to analytic solution of the problem rapidly and implementation of method is easy. Finally, outcomes of the illustrative examples prove the efficiency and accuracy of the method.

Porous medium on unsteady Helical flows of Generalized Oldroyd-B with two infinite coaxial circular cylinders

This article deals with the influence of porous media on Helical flows of Generalized Oldroyd-B between two infinite coaxial circular cylinders .The fractional derivative are modeled for this problem and studied by using finite Hankel and Laplace transforms .The velocity fields founded by using the fundamentals of the series form in terms of Mittag-leffler equation . The research focused on the parameters like (permeability parameter z ,fractional parameters(𝛼 , 𝛽) , relaxation 𝜆1 , retardation 𝜆2 , kinematic viscosity v , magnetic parameter M and time t) which effected on the velocity field u and w. MATHEMATICA package used to study and analyze the above variables by drawing many graphs .

Semi-Analytical Solution of Two-Dimensional Viscous Flow through Expanding/Contracting Gaps with Permeable Walls

In this research, the analytical methods of the differential transform method (DTM), homotopy asymptotic method (HAM), optimal homotopy asymptotic method (OHAM), Adomian decomposition method (ADM), variation iteration method (VIM) and reproducing kernel Hilbert space method (RKHSM), and the numerical method of the finite difference method (FDM) for (analytical-numerical) simulation of 2D viscous flow along expanding/contracting channels with permeable borders are carried out. The solutions for analytical method are obtained in series form (and the series are convergent), while for the numerical method the solution is obtained taking into account approximation techniques of second-order accuracy. The OHAM and HAM provide an appropriate method for controlling the convergence of the discretization series and adjusting convergence domains, despite having a problem for large sizes of obtained results in series form; for instance, the size of the series solution for the DTM is very small for the same order of accuracy. It is hard to judge which method is the best and all of them have their advantages and disadvantages. For instance, applying the DTM to BVPs is difficult; however, solving BVPs with the HAM, OHAM and VIM is simple and straightforward. The extracted solutions, in comparison with the computational solutions (shooting procedure combined with a Runge–Kutta fourth-order scheme, finite difference method), demonstrate remarkable accuracy. Finally, CPU time, average error and residual error for different cases are presented in tables and figures.

Extension of the Sophomore’s Dream

In this article, we are going to look at the convergence properties of the integral ∫ 0 1 ( a x + b ) c x + d d x \int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx} , and express it in series form, where a, b, c and d are real parameters.

The similarity of inherited diseases (I): clinical similarity within the phenotypic series

Background Mutations of different genes often result in clinically similar diseases. Among the datasets of similar diseases, we analyzed the ‘phenotypic series’ from Online Mendelian Inheritance in Man and examined the similarity of the diseases that belong to the same phenotypic series, because we hypothesize that clinical similarity may unveil shared pathogenic mechanisms. Methods Specifically, for each pair of diseases, we quantified their similarity, based on both number and information content of the shared clinical phenotypes. Then, we assembled the disease similarity network, in which nodes represent diseases and edges represent clinical similarities. Results On average, diseases have high similarity with other diseases of their own phenotypic series, even though about one third of diseases have their maximal similarity with a disease of another series. Consequently, the network is assortative (i.e., diseases belonging to the same series link preferentially to each other), but the series differ in the way they distribute within the network. Specifically, heterophobic series, which minimize links to other series, form islands at the periphery of the network, whereas heterophilic series, which are highly inter-connected with other series, occupy the center of the network. Conclusions The finding that the phenotypic series display not only internal similarity (assortativity) but also varying degrees of external similarity (ranging from heterophobicity to heterophilicity) calls for investigation of biological mechanisms that might be shared among different series. The correlation between the clinical and biological similarities of the phenotypic series is analyzed in Part II of this study1.

Manuel DeLanda

Edited by John Klacsmann and Andrew Lampert (New York: Anthology Film Archives and J&L Books, 2018), 152 pages.Review of Manuel DeLanda: ISM ISM edited by John Klacsmann and Andrew Lampert. The book consists of a photo series, a short essay and an interview with DeLanda. Through the review, I demonstrate some of the ways in which DeLanda’s film ISM ISM, documented in the book as a photo series, form part of the foundations of his later philosophical explorations.