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1

A fractional study of mhd casson fluid motion with thermal radiative flux and heat injection/suction mechanism under ramped wall condition: application of rabotnov exponential kernel

Rehman Aziz Ur, Jarad Fahd, Riaz Muhammad Bilal

Acta Mechanica et Automatica

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2024

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Vol. 18, no. 1

84--92

EN

The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as 𝑢0. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as 𝛼, 𝛽, 𝑃𝑟, 𝑄, 𝐺𝑟, 𝑀, 𝑁𝑟 and 𝐾, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.

2

Mesomechanical model for concrete creep with viscoelastic interface transition zone

Xu Zehua, Zhao Qingxin, Guo Weichao

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e65, 1--15

EN

The interface transition zone (ITZ) effect on concrete creep performance was analyzed in this study. The ITZ was treated as a weakened matrix, which mechanical behavior could be described by the Burgers model. The proposed prediction model of concrete creep took account of the ITZ's viscoelasticity by combining the generalized self-consistent Mori–Tanaka method with the Laplace transformation principle. The model's experimental validation confirmed that it accurately simulated the creep behavior of concrete specimens with various fly ash and ground slag ratios. The existence of viscoelastic ITZ promotes the creep of concrete, and the maximum creep growth rate was attained in the concrete specimen with 60% ratio of fly ash. The effects of ITZ thickness and other parameters, the volume fraction of aggregates, and particularly ITZ contribution to concrete creep in the concrete specimens with five mix proportions at different loading ages were clarified and discussed in detail.

3

On theoretical and practical aspects of Duhamel’s integral

Różański Michał, Sikora Beata, Smuda Adrian, Wituła Roman

Archives of Control Sciences

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2021

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Vol. 31, No. 4

815--847

EN

The paper is a new approach to the Duhamel integral. It contains an overview of formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.

4

Analyzing fuid fow characteristics in a dual porosity reservoir with an elastic outer boundary

Kim Song Chol, Han Chol Gwang, Rim Myong Won, Kim Ju Song, Ryang Myong Jun

Acta Geophysica

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2021

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Vol. 69, no. 5

1843--1853

EN

When we develop petroleum and natural gas reservoirs, we can see a lot of dual-porosity reservoirs with both pores and fractures. Many researchers have studied characteristics of fluid flow in dual-porosity reservoirs with the ideal outer boundary (infinite boundary, closed boundary or constant pressure boundary) but nobody has considered dual-porosity model with the elastic outer boundary (EOB) reflecting the real condition. So there could be large errors in analyzing well-test data for dual-porosity model. In this paper, we establish a percolation model for dual-porosity reservoirs with the EOB and consider the skin factor and wellbore storage. And we obtain its solution in Laplace space by introducing the effective well radius and applying the Laplace transformation. An approximation in Laplace space is also derived by using an asymptotic formula of I0(x) and I1(x). By using Stehfest numerical inversion of Laplace transformation, the solution in the real space is obtained. We compare this model to homogeneous model with the EOB and conventional dual-porosity model, respectively. Comparison results show that the conventional outer boundary conditions are three special cases of the EOB and homogeneous model with the EOB is a special case of dual-porosity model with the EOB. Flow characteristics are analyzed and it is shown that the EOB affects analysis of well-test data through simulation. This study may improve the accuracy of well-test analysis for dual-porosity reservoir.

5

Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab

Kukla S., Siedlecka U.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

105--113

EN

In this paper the Laplace transformation for solving the problem of fractional heat conduction in a two-layered slab has been applied. The different orders of Caputo derivative in the time-fractional equation governed the heat transfer in the layers are assumed. The inverse Laplace transform by using a numerical method is determined. The numerical results obtained by using of the eigenfunctions method and by numerically inverting the Laplace transform are compared.

6

Research Methods for the Dynamic Properties of Textiles

Tumajer P., Ursíny P., Bílek M., Moučková E.

Fibres & Textiles in Eastern Europe

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2011

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Vol. 19, no. 5 (88)

33--39

EN

This paper is concerned with a theoretical description of the dynamic properties of textiles and their experimental analysis. In the theoretical section of the paper, the dynamic properties of textiles are described based on rheological models. To describe their dynamic characteristics, the Laplace transformation has been employed. The experimental section of the paper describes special equipment - VibTex and the possibilities of its use in the experimental analysis of the dynamic properties of textiles. The experimental section includes a description of the manner of determining the dynamic properties of textiles based on the results of measurement.

PL

W artykule omówiono zależności dotyczące właściwości dynamicznych tekstyliów oraz opisano badania eksperymentalne. Zależności teoretyczne oparto na opracowanych modelach. Dla opisania właściwości dynamicznych zastosowano transformaty Laplacea. W części eksperymentalnej przedstawiono VidTex - specjalne urządzenie do badan dynamicznych oraz możliwości jego zastosowania. Artykuł zawiera opis sposobu uzyskiwania parametrów dynamicznych tekstyliów.

7

Tools of control object identification

Goncharov V., Rudnicki V.

Systems Science

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2008

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Vol. 34, no 2

43-47

EN

In this paper, the problem of construction of the hardware-software means intended for maintenance of manual and automated regimes of automatic control system adjustment is considered. For the solution of the problem, the Real Interpolation Method is offered. Two important procedures which guarantee decreasing of computation costs in comparison with traditional methods are in its basis. Firstly, a special discrete transformation of time functions is used and derivable functions-images have real argument. Secondly, these functions are replaced with discrete forms, which can describe control system, its elements and signals. The offered way of problem decision is illustrated with numerical example.

8

Cardinality and Probability Under Intuitionistic and Interval-Valued Fuzzy Sets

Mańko J., Niewiadomski A.

Journal of Applied Computer Science

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2006

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Vol. 14, nr 1

31-41

EN

The paper focuses on probability and cardinalities in terms of intuitionistic and interval-valued fuzzy sets under classic Laplace's approach. We use the necessity and possibility operators for intuitionistic fuzzy sets, and the type-reduction operations for interval-valued fuzzy sets. In both cases, formulae for the classic probability of an intuitionistic and interval-valued fuzzy event are discussed.

9

Wyznaczanie niestacjonarnych pól temperatury : porownanie metod numerycznych w obszarach 2D

Fraska A.

Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją

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2005

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Nr 2

5-16

PL

W artykule porównano dokładność metod numerycznych. Jako przykłady testowe wykorzystano dwuwymiarowe zagadnienia początkowo-brzegowc mające dokładne rozwiązania. Porównano dwie różne wersje metody kolokacji brzegowej. Pierwsza z nich to metoda źródeł pozornych, w której jest wykorzystana metoda kolokacji brzegowej i metoda rozwiązań podstawowych. Druga jest oparta na transformacji Laplace'a oraz na metodzie rozwiązań podstawowych. Na podstawie otrzymanych wyników można stwierdzić, że metoda oparta na transformacji Laplace'a jest lepsza pod względem dokładności niż metoda źródeł pozornych.

10

Transient free convection MHD flow through a porous medium between two vertical plates

Kalita B., Borkakati A. K.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 1

87-94

EN

An analysis is presented to investigate the flow and heat transfer characteristic of a viscous incompressible and electrically conducting fluid through a porous medium bounded by two long vertical parallel plates in the presence of a uniform magnetic field applied transversely to the flow. The governing momentum and energy equations are solved by the Laplace transform technique and the solutions are presented for velocity and temperature distributions and shear stress. The effects of the four parameters, namely, the Darcy number, viscosity ratio parameter, magnetic Hartmann number, and Prandtl number on temperature and velocity distributions are shown in graphs and presented through the results and discussion. Also, the effects of these four parameters on skin friction are given.

11

Diagnosing of automatic control systems based on their dynamic characteristics under field conditions.

Goncharov V., Liepinch A., Rudnicki W.

Prace Naukowe Instytutu Technologii Maszyn i Automatyzacji Politechniki Wrocławskiej. Konferencje

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2000

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Vol. 78, nr 36

107-110

EN

The automatic control systems of industrial plants lose optimum tuning during their operation. Therefore, appreciable economic and time expenditures are demanded for correction of settings. Recently the tendency of using systems dynamic characteristics was designed for their diagnosing. This is destined for decrease of expenditures and raise of control systems state analysis exactitude. However, there are appreciable difficulties on this way, which are caused by lack of the sufficiently cost-effective algorithmic basis for creation of portative hardware-software diagnostic tools. It does not allow to solve all complex of problems under field conditions immediately: it is impossible to gain the information about the system, to process it, to form current dynamic characteristics and to compare them with etalon. In this is offered the Real Interpolation Method (RIM) for the diagnosing with the purpose of softening the mentioned deficiency. It is founded on usage of a special case of the Laplace transformation when the complex variable p= +j is degenerated in real . The number of operations is diminish more than 2 times in comparison with the frequency method. Real Interpolation Method is equivalent to the frequency method from positions of noise proof features. The possibilities of RIM allow to use it for identification diagnostic of liearized continuous and discrete systems, and also for their subsequent tuning.

PL

Brak odpowiednio efektywnych algorytmów utrudnia stworzenie przenośnych urządzeń diagnostycznych. W referacie opisano zaproponowaną do diagnostyki układów sterowania metodą interpolacji RIM (Real Interpolation Method). Polega ona na zastosowaniu szczególnym przypadku transformaty Laplaca, gdy zmienna zespolona p= +j jest zredukowana do jej części rzeczywistej . W ten sposób zmniejsza się liczba operacji podczas diagnostyki o więcej jak 2 razy w porównaniu z przypadkiem gdy są znane charakterystyki częstotliwościowe. Metoda RIM, gdy idzie o zakłócenia, jest równa metodom, w których stosuje się charakterystyki częstotliwościowe. Metoda RIM nadaje się do diagnostyki i identyfikacji ciągłych i dyskretnych układów sterowania automatycznego