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Dusty time fractional MHD flow of a Newtonian fluid through a cylindrical tube with a non-Darcian porous medium

Imo-Mani-Singha H., Sengupta Sanjib

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

101--114

EN

In this paper, time fractional flow of a Newtonian fluid through a uniform cylindrical tube with a non-Darcy porous medium in the presence of dust particles under the application of a uniform magnetic field along the meridian axis is discussed. The implication of time fractional order differential equations in flow problems and some benefits of fractional order differential equations are highlighted. The Laplace Decomposition Method (LDM) is used to obtain an approximate solution to the proposed problem. The impact of fractional order and integer order of the differential equations and also the effects of some important parameters on the flow system are shown in the forms of graphs and a table. The convergence test of the solution is done. It has been observed that the fractional order differential equation reveals more things like the decrease in dust particle velocity due to the increase in magnetic field for fractional order derivatives, whereas, no noticeable change in dust particle velocity due to the change in magnetic field for integer order derivatives are observed. Also, it is observed that an increase in a fractional order derivative decrease the fluid as well as the dust particle velocities. The skin friction at the walls of the tube are also highlighted.

2

Impact of optical indices on particle size distribution of activated sludge measured by laser diffraction method

Sochan A., Polakowski C., Łagód G.

Ecological Chemistry and Engineering. S

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2014

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Vol. 21, nr 1

137--145

EN

The important factors that strongly influence the particle size distributions measured by the laser diffraction method are the optical parameters of the suspension (refractive index and absorption coefficient). Knowledge of the values of these parameters is necessary for Mie theory. Mie theory is applied for conversion of the intensity of light recorded on detectors into particle size distribution (PSD) of tested material. Both wastewater and activated sludge are mixtures of a variety of elements (mineral or organic, including living organisms). In practice, it is not possible to define clearly the values of the optical parameters, as the composition of the suspension changes over time. The aim of the study was to estimate the impact of assumed values of the optical parameters on particle size distributions obtained. The PSDs of suspensions sampled in different stages of wastewater treatment are the most reproducible when the following optical parameters are defined: absorption coefficients - 1.0 and the refractive index - 1.52.

PL

Czynnikami, które w istotny sposób wpływają na rozkłady granulometryczne wyznaczane za pomocą dyfrakcji laserowej, są parametry optyczne mierzonej zawiesiny (współczynnik załamania światła oraz współczynnik absorpcji). Znajomość wartości tych parametrów jest niezbędna przy zastosowaniu teorii Mie. Teoria Mie jest wykorzystywana do przeliczenia intensywności światła zmierzonego na detektorach na rozkład granulometryczny (PSD) badanego materiału. Zarówno ścieki, jak i osad czynny są mieszaninami bardzo różnych składników (mineralnych i organicznych, w tym żywych organizmów). W praktyce nie ma możliwości określenia rzeczywistych wartości parametrów optycznych mieszanin, tym bardziej, że ich skład zmienia się w czasie. Celem niniejszej pracy było określenie wpływu założonych wartości parametrów optycznych na uzyskiwane rozkłady granulometryczne. Rozkłady granulometryczne zawiesin pobranych na różnych etapach oczyszczania ścieków są najbardziej powtarzalne dla następujących wartości współczynników optycznych: współczynnika absorpcji - 1,0 i współczynnika załamania światła - 1,52.

3

Application of EMTP-RV control devices in lightning overvoltage simulations

Bajorek J., Korzeniowski M., Ziemba R.

Poznan University of Technology Academic Journals. Electrical Engineering

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2009

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No 60

69-80

EN

The possibilities of nonlinear element modeling by control devices in EMTP-RV simulator for lightning overvoltage simulations are analyzed in the paper. The results are presented for back-flashover phenomenon on transmission line air gaps and for substation with nonlinear model of ZnO surge arrester. Tests of the Leader Development Model (LDM) for the flashover mechanism, which is supplied as a standard EMTP-RV device, are presented for the new standard waveshape of the lightning channel-base current. The block diagram of the substation model with last tower and ZnO surge arrester was made using standard control elements. Computer simulations for this model show its effectiveness and possibilities of its development.