Emissivity: A Program for Atomic Emissivity Calculations

In this article we report the release of a new program for calculating the emissivity of atomic transitions. The program, which can be obtained with its documentation from our website www.scienceware.net, passed various rigorous tests and was used by the author to generate theoretical data and analyze observational data. It is particularly useful for investigating atomic transition lines in astronomical context as the program is capable of generating a huge amount of theoretical data and comparing it to observational list of lines. A number of atomic transition algorithms and analytical techniques are implemented within the program and can be very useful in various situations. The program can be described as fast and efficient. Moreover, it requires modest computational resources.Comment: 20 pages, 0 figures, 0 table

Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.Comment: 27 pages, 6 figure

One-Dimensional Navier-Stokes Finite Element Flow Model

This technical report documents the theoretical, computational, and practical aspects of the one-dimensional Navier-Stokes finite element flow model. The document is particularly useful to those who are interested in implementing, validating and utilizing this relatively-simple and widely-used model.Comment: 46 pages, 1 tabl

Modeling the Flow of Yield-Stress Fluids in Porous Media

Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modeling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modeling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modeling strategies are required to tackle this problem in the future.Comment: 27 pages and 5 figure

Variational approach for the flow of Ree-Eyring and Casson fluids in pipes

The flow of Ree-Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress. The variationally-obtained solutions are compared to the analytical solutions derived from the Weissenberg-Rabinowitsch-Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.Comment: 18 pages, 2 figure

Flow of Navier-Stokes Fluids in Converging-Diverging Distensible Tubes

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes fluids. We employ an analytical formula derived from a one-dimensional version of the Navier-Stokes equations to describe the underlying flow model that provides the residual function. This formula correlates the flow rate to the boundary pressures in straight cylindrical elastic tubes with constant-radius. We validate our findings by the convergence toward a final solution with fine discretization as well as by comparison to the Poiseuille-type flow in its convergence toward analytic solutions found earlier in rigid converging-diverging tubes. We also tested the method on limiting special cases of cylindrical elastic tubes with constant-radius where the numerical solutions converged to the expected analytical solutions. The distensible model has also been endorsed by its convergence toward the rigid Poiseuille-type model with increasing the tube wall stiffness. Lubrication-based one-dimensional finite element method was also used for verification. In this investigation five converging-diverging geometries are used for demonstration, validation and as prototypes for modeling converging-diverging geometries in general.Comment: 31 pages, 9 figures, 2 table

Special Relativity: Scientific or Philosophical Theory?

In this article, we argue that the theory of special relativity, as formulated by Einstein, is a philosophical rather than a scientific theory. What is scientific and experimentally supported is the formalism of the relativistic mechanics embedded in the Lorentz transformations and their direct mathematical, experimental and observational consequences. This is in parallel with the quantum mechanics where the scientific content and experimental support of this branch of physics is embedded in the formalism of quantum mechanics and not in its philosophical interpretations such as the Copenhagen school or the parallel worlds explanations. Einstein theory of special relativity gets unduly credit from the success of the relativistic mechanics of Lorentz transformations. Hence, all the postulates and consequences of Einstein interpretation which have no direct experimental or observational support should be reexamined and the relativistic mechanics of Lorentz transformations should be treated in education, academia and research in a similar fashion to that of quantum mechanics.Comment: 12 page

Flow of non-Newtonian Fluids in Converging-Diverging Rigid Tubes

A residual-based lubrication method is used in this paper to find the flow rate and pressure field in converging-diverging rigid tubes for the flow of time-independent category of non-Newtonian fluids. Five converging-diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel-Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging-diverging tubes, convergence to analytical solutions found earlier for the flow in converging-diverging tubes of Newtonian fluids as special cases for non-Newtonian, and convergence to analytical solutions found earlier for the flow of power-law fluids in converging-diverging tubes. A brief investigation was also conducted on a sample of diverging-converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically-symmetric converging-diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range.Comment: 36 pages, 14 figures, 5 table

Reply to "Comment on Sochi's variational method for generalised Newtonian flow" by Pritchard and Corson

In this article we challenge the claim that the previously proposed variational method to obtain flow solutions for generalized Newtonian fluids in circular tubes and plane slits is exact only for power law fluids. We also defend the theoretical foundation and formalism of the method which is based on minimizing the total stress through the application of the Euler-Lagrange principle.Comment: 9 page