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1

Magnetohydrodynamic flow around an elongated cylinder in non-Darcian porous regime with higher order chemical reaction and Soret/Dufour effects

Das Utpal Jyoti, Begum Jubi

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 1

11--22

EN

Here, we consider magnetohydrodynamic flow of an incompressible, time independent fluid past an elongated cylinder surrounded in a non-Darcian porous regime with magnetic flux supplied at an acute angle. The Soret/Dufour effects and the higher order chemical reactions are also included in the present study. The subsequent governing equations are resolved using the MATLAB-bvp4c method. The flow velocity appears to decrease with the growth of the Reynolds number, inertia parameter, magnetic field and angle of inclination of the magnetic flux, but improves with the Darcy number. The inertia parameter enhances the fluid temperature and skin friction. Further order of chemical reaction, Soret/ Dufour number plays a significant role in the system.

2

Effects of viscous dissipative MHD fluid flow past a moving vertical plate with rotating system embedded in porous medium

Kumari D. Santhi, Sajja Venkata Subrahmanyam, Kishore P. M.

International Journal of Applied Mechanics and Engineering

|

2023

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Vol. 28, no. 3

112--126

EN

An incompressible unsteady free convective viscous MHD rotating flow past a moving plate embedded in a porous medium is considered with the influence of viscous dissipation, heat source effects. It is assumed that the flow rotates with angular velocity which is normal to the plate and also that a transverse magnetic field is applied along the normal to the plate. Appropriate dimensionless quantities are applied to change the governing equations into dimensionless form. Then the equations are solved numerically using the Galerkin finite element method. Some important characteristics of the fluid are studied. The results are in good agreement with the available literature.

3

Biomagnetic flow over a flat plate embedded by a magnetic dipole in a porous media

Ferdows Mohammad, Jumana Sadia Anjum

International Journal of Applied Mechanics and Engineering

|

2023

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Vol. 28, no. 4

69--78

EN

The present study used a simplified axisymmetric biomagnetic fluid dynamics and porous mediamodel which includes FHD (Ferrohydrodynamics), porosity and inertia effects saturated by magnetic dipole to study the influences of the leading parameters on various flow variables along a flat plate.The governing equations are simplified and solved by finite difference approach. We clarify how the ferromagnetic interaction parameter, B and porosity,ε assumptions contribute in the bio-background of the problem of interest. Moreover, from the results of the flow profiles, accelerating and decelerating phenomena are noticed for B, and ε interaction.

4

Radiation and magnetohydrodynamic effects on convective nanofluid past an inclined plate in the presence of a chemical reaction

Palani G., Arutchelvi A.

International Journal of Applied Mechanics and Engineering

|

2022

|

Vol. 27, no. 3

115--126

EN

This computational work explores the heat and mass transfer of copper water nanofluid flowing along an inclined plate with varying surface temperature and concentration in the presence of a magnetic field and radiation through a permeable medium. The dimensionless governing equations are solved numerically using an efficient finite-difference technique, which is fast convergent and unconditionally stable. The findings are reviewed and illustrated through graphs for pertinent parameters.

5

Combined effects of helical force and rotation on stationary convection of a binary ferrofluid in a porous medium

Kpossa M., Monwanou A. V.

International Journal of Applied Mechanics and Engineering

|

2022

|

Vol. 27, no. 2

158--176

EN

This work studies the simultaneous effects of helical force, rotation and porosity on the appearance of stationary convection in a binary mixture of a ferrofluid and on the size of convection cells. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. The effect of each parameter on the system is studied. The consideration of the simultaneous effect of the basic characteristics made it possible to determine the evolution of the convection threshold in the ferrofluid and then the size of convection cells. The analyzes of the various results obtained allowed us to deduce whether the convection sets in quickly or with a delay when the various effects taken into account in the study are considered simultaneously.

6

Exact solution of flow in a composite porous channel

Singh Sanjeeva Kumar, Verma Vineet Kumar

Archive of Mechanical Engineering

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2020

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LXVII, nr 1

97--110

EN

This article concerns fully developed laminar flow of a viscous incompressible fluid in a long composite cylindrical channel. Channel consist of three regions. Outer and inner regions are of uniform permeability and mid region is a clear region. Brinkman equation is used as a governing equation of motion in the porous region and Stokes equation is used for the clear fluid region. Analytical expressions for velocity profiles, rate of volume flow and shear stress on the boundaries surface are obtained and exhibited graphically. Effect of permeability variation parameter on the flow characteristics has been discussed.

7

Electrohydrodynamic instability of a rotating Walters’ (model B’) fluid in a porous medium: Brinkman model

Rana G. C., Chand R., Sharma Veena

Mechanics and Mechanical Engineering

|

2019

|

Vol. 23, nr 1

138--143

EN

In this study, the instability of Walters’ (model B’) viscoelastic fluid in a Darcy-Brinkman-Boussinesq system heated from below saturating a porous medium in electrohydrodynamics is considered. By applying the linear stability analysis and normal modes, the dispersion relations accounting for the effect of Prandtl number, electric Rayleigh number, Darcy number, Brinkman-Darcy number, Taylor number and kinematic viscoelasticity parameter is derived. The effects of electric Rayleigh number, Darcy number, Brinkman-Darcy number and Taylor number on the onset of stationary convection have been investigated both analytically and graphically.

8

Niestacjonarna analiza wymiany ciepła w gruntowym wymienniku ciepła posadowionym na gruntach niewysyconych

Sławiński Daniel

Instal

|

2019

|

nr 9

24--30

PL

Wydajność wymiany ciepła w gruntowych wymiennikach ciepła (GHE) w wielu projektach zmniejsza się wraz z długością czasu eksploatacji. Zaobserwowano duże wahania temperatury w trakcie ładowania wymiennika oraz w trakcie naturalnego stygnięcia. Problem wynika głównie z braku pogłębionych badań dotyczących wpływu ogrzewania oraz migracji wilgotności na pracę gruntowego wymiennika w glebie nienasyconej. W pracy wykorzystano model numeryczny ośrodka porowatego z przepływem płynu wieloskładnikowego. Opis matematyczny wyposażono w dodatkowe strumienie, opisujące wymianę ciepła w elementach podsypki oraz szkielecie modelu porowatego. Odwzorowano geometrycznie oraz matematycznie porowatość gruntu. Wprowadzono definicję temperatury całkowitej. Wyniki porównano z symulacjami wykonanymi dla modelu rozwiązującego klasyczne równanie wymiany ciepła. Model weryfikowano na danych pomiarowych odczytanych dla 3 czujników zamontowanych na różnej głębokości jednego otworu oraz przy różnych przedziałach czasowych. Parametry modelu są oparte na lokalnych warunkach klimatycznych w Jabłonnej w okolicy Warszawy. Odwzorowano numerycznie 24 godzinną pracę pojedynczego otworu. Uzyskane wyniki wykazały dużo większą zbieżność z danymi pomiarowymi niż te uzyskane dla klasycznego modelu opisującego wymianę ciepła. Punktem krytycznym przyjętego modelu był dobór współczynników opisujących opory przepływu i-tych składników w ośrodku porowatym oraz poszczególne człony składowe zaproponowanej definicji temperatury całkowitej. Rozszerzoną dyskusje przeprowadzono w punkcie dotyczącym weryfikacji modelu. Wykonano przegląd prac o podobnej tematyce opublikowanych w ostatnim czasie.

EN

The efficiency of heat exchange in ground heat exchangers (GHE) in many projects decreases throughout their service life. Large temperature fluctuations were observed during feeding of the exchanger and during its natural cooling. This problem stems mainly from the lack of in-depth studies on the impact of heating and humidity migration on the operation of ground heat exchanger in unsaturated soil. In our work we applied a numerical model of a porous medium with multi-component fluid flow. The mathematical description was expanded with additional streams describing the exchange of thermal energy in the backfill material and the structure of the porous model. Ground porosity was mapped geometrically and mathematically. We introduced the definition of total temperature. The results were compared with the simulations performed for the model solving the classic heat exchange equation. The model was verified on the measurement data read for 3 sensors installed at different depths of one hole and at different time intervals. The parameters of the model are based on local climatic conditions of Jabłonna near Warsaw. 24-hour operation of a single hole has been numerically mapped. The results proved a much greater convergence with the actual data than those obtained for the classic model describing heat exchange. The critical point of the model was the selection of coefficients describing the flow resistance of i-components in the porous medium and the individual components of the adopted definition of the total temperature. Extended discussions were carried out in the section on model verification. We also performed a review of works on similar topics published recently.

9

Computer modelling of the dynamic system «porous medium – moisture – chemical substance» in the case of soil desalinization by rainfalls (a three-dimensional case)

Kozhushko Oksana D, Martyniuk Petro M.

Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

|

2018

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nr 21

47--60

EN

Mathematical model of moisture transport taking into account variable porosity has been investigated numerically. Changes in porosity are caused by dissolution of chemical substances associated with soil skeleton. The finite element solution of the problem in the case of regular rainfall has been found. Program realization of the corresponding algorithms has been implemented in FreeFem++ computational environment. Numerical experiments have been carried out and the impact of rainfall on desalinization of soil with high concentration of salts in the solid component has been determined.

PL

Numerycznie badano model matematyczny transportu wilgoci o zmiennej porowatości. Zmiany porowatości są spowodowane rozpuszczaniem substancji chemicznych związanych ze szkieletem gruntu. Znaleziono numeryczne rozwiązanie problemu w przypadku regularnych opadów. Programowa realizacja odpowiednich algorytmów została zaimplementowana w środowisku obliczeniowym FreeFem++. Przeprowadzono eksperymenty numeryczne i określono wpływ opadów na odsalanie gruntu przy wysokim stężeniu soli w twardym komponencie.

10

Impact of pre-stress, inhomogeneity and porosity on the propagation of Love wave

Gupta S., Pramanik A., Ahmed M.

Acta Geophysica

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2018

|

Vol. 66, no. 5

855--866

EN

This work presents a mathematical modelling of Love wave transference through a pre-stress influenced anisotropic medium with heterogeneity between a sandy medium and an initially stressed anisotropic porous medium. Variable separation method has been induced in order to derive the frequency relation. Using appropriate boundary conditions at two interfaces, the dispersion equation has been obtained in its closed form. Possible particular cases are considered, and the corresponding results are consonant with the classical cases. Numerical computations have been employed to demonstrate the role of inhomogeneity factors, initial stresses and porosity, and are depicted by means of graphs which substantiates that those parameters immensely affect the Love wave velocity. In mineral prospecting and exploring technique in earth, the method and the results of this problem may be applicable.

11

Zastosowanie sondy areometrycznej do pomiaru przepuszczalności in situ za pomocą sprężonego gazu

Szpunar T., Budak P.

Nafta-Gaz

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2017

|

R. 73, nr 12

935--942

PL

W artykule podano sposób określania przepuszczalności in situ oraz skin effect ośrodków porowatych w otworach pionowych i poziomych przy pomocy tzw. sondy areometrycznej i sprężonego gazu. Sonda areometryczna skonstruowana została w Głównym Instytucie Górnictwa w Katowicach i aktualnie wykorzystywana jest do pomiaru szczelinowatości węgli. Wykazano możliwość wykorzystania tego urządzenia do pomiaru przepuszczalności i skin effect. Podano model matematyczny, który to umożliwia, oraz przeprowadzono przykładowe obliczenia dla danych zebranych w jednej z polskich kopalń węgla.

EN

The paper presents a procedure for the evaluation of in situ permeability and skin effect of porous rocks in vertical and horizontal wells, using areometric probe and pressurized gas. A mathematical model is provided, which shows that the measured values of logarithm of dimensionless pressure versus time should plot along the straight line in a vertical coordinate system. Provided are exemplary calculations of permeability and skin of coal seams in horizontal drainage wells using compressed air. The calculations were done using real world data collected from a Polish coal mine.

12

A study of chemically reactive species and thermal radiation effects on an unsteady MHD free convection flow through a porous medium past a flat plate with ramped wall temperature

Pandit K. K., Sarma D., Singh S. I.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

945--964

EN

An investigation of the effects of a chemical reaction and thermal radiation on unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous, incompressible fluid past a vertical infinite flat plate embedded in a porous medium is carried out. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. An exact solution of the governing equations is obtained in closed form by the Laplace Transform technique. Some applications of practical interest for different types of plate motions are discussed. The numerical values of fluid velocity, temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters for both ramped temperature and isothermal plates.

13

Numerical Modeling of Physical Dispersionin Porous Medi

Gołąbek A., Szott W.

Prace Naukowe Instytutu Nafty i Gazu

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2016

|

nr 209 wyd. konferencyjne

843--850

EN

The paper addresses the problem of physical dispersion mechanism in modeling fluid transport in porous media. It includes the analysis of numerical dispersion effects in numerical solution of the transport equations. Two methods to reduce the effects are proposed and implemented in a typical reservoir simulator. The results of these methods are presented in various models related to gas – gas mixing processes. Finally, a full term of physical dispersion phenomena is included into a reservoir simulator and examples of simulation results for physical dispersion effects are presented and discussed.

PL

Praca dotyczy problemu dyspersji fizycznej w modelowaniu przepływu płynów przez ośrodek porowaty. Obejmuje analizę efektów dyspersji numerycznej pojawiających się w numerycznych rozwiązaniach równań przepływu. Zaproponowano dwie metody redukcji tych efektów zaimplementowane w typowym symulatorze złożowym. Rezultaty tych metod przedstawiono dla kilku przykładowych modeli procesów mieszania się gazów w złożu. Do algorytmu numerycznych rozwiązań równań przepływu zmodyfikowanego ze względu na dyspersję numeryczną, włączono człony opisujące zjawisko dyspersji fizycznej. Przedstawiono wyniki symulacji uwzględniających to zjawisko na przykładowych modelach złożowych.

14

Garg P., Purohit G. N., Chaudhary R. C.

International Journal of Applied Mechanics and Engineering

|

2016

|

Vol. 21, no. 4

827--836

EN

This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

15

Thermal instability of a Rivlin-Ericksen nanofluid saturated by a Darcy-Brinkman porous medium: a more realistic model

Rana G. C., Chand R., Sharma V.

Engineering Transactions

|

2016

|

Vol. 64, iss. 3

271--286

EN

In this paper, we study thermal instability in a horizontal layer of Rivlin-Ericksen elasticoviscous nanofluid in porous medium. Brinkman model is used as a porous medium and RivlinEricksen fluid model is used to describe the rheological behavior of nanofluid. In the earlier model (Chand and Rana [18]), we constrained both temperature and nanoparticle volume fractions at the boundaries of Rivlin-Ericksen nanofluid layer. In this paper, we assume that the value of temperature can be constrained on the boundaries, while the nanoparticle flux is zero on the boundaries. The considered boundary condition neutralizes the possibility of oscillatory convection due to the absence of two opposing forces, and only stationary convection occurs, in which Rivlin-Ericksen elastico-viscous nanofluid behaves like an ordinary nanofluid. The effects of Lewis number, medium porosity, modified diffusivity ratio, Darcy-Brinkman number and concentration Rayleigh number in stationary convection are discussed analytically and numerically. The results of this study are in good agreement with the results published earlier.

16

Dynamics of particle loading in deep-bed filter. Trasport, deposition and reentrainment

Przekop R., Gradoń L.

Chemical and Process Engineering

|

2016

|

Vol. 37, nr 3

405--417

EN

Deep bed filtration is an effective method of submicron and micron particle removal from the fluid stream. There is an extensive body of literature regarding particle deposition in filters, often using the classical continuum approach. However, the approach is not convenient for studying the influence of particle deposition on filter performance (filtration efficiency, pressure drop) when non-steady state boundary conditions have to be introduced. For the purposes of this work the lattice-Boltzmann model describes fluid dynamics, while the solid particle motion is modeled by the Brownian dynamics. For aggregates the effect of their structure on displacement is taken into account. The possibility of particles rebound from the surface of collector or reentrainment of deposits to fluid stream is calculated by energy balanced oscillatory model derived from adhesion theory. The results show the evolution of filtration efficiency and pressure drop of filters with different internal structure described by the size of pores. The size of resuspended aggregates and volume distribution of deposits in filter were also analyzed. The model enables prediction of dynamic filter behavior. It can be a very useful tool for designing filter structures which optimize maximum lifetime with the acceptable values of filtration efficiency and pressure drop.

17

Criteria Parameters for Fluid Flow Simulation in Tight Reservoir Rocks

Krakowska P., Madejski P.

Logistyka

|

2014

|

nr 4

4537--4542, CD6

EN

Combination of computed microtomography and fluid flow simulation approach leads to rock permeability estimation as a reservoir parameter deciding about the rock potential to fluid (hydrocarbons and/or formation water) flow in porous space. For the proper simulation run and results two aspects are needed to be considered: modelling approach and the flow regime. The Knudsen number classifies the modelling approach and Reynolds number – flow regime. The Knudsen number and Reynolds number were calculated for the Carboniferous sandstone sample, cored at 3154 m depth and with total porosity obtained from micro-CT equal to 12.6%.

PL

W pracy zostały omówione parametry kryterialne oraz sposoby ich wyznaczania w celu poprawnego modelowania zjawiska przepływu płynu przez ośrodki porowate z zastosowaniem komputerowej mechaniki płynów. Poprawny dobór poszczególnych równań i modeli podczas komputerowej symulacji przepływu płynu wymaga obliczenia kryterialnych parametrów, jakimi są liczba Knudsena i liczba Reynoldsa. Wartości liczb kryterialnych determinują możliwe do zastosowania podejście w modelowaniu przepływów oraz określają zakres charakteru przepływu, jaki występuje w analizowanym przypadku. W pracy przedstawione zostały wyniki obliczeń parametrów kryterialnych dla piaskowca karbońskiego.

18

Study of magnetic field dependent viscosity on a soret driven ferrothermohaline convection in a rotating porous medium

Hemalatha R.

International Journal of Applied Mechanics and Engineering

|

2014

|

Vol. 19, no. 1

61--77

EN

The effect of a magnetic field dependent viscosity on a Soret driven ferro thermohaline convection in a rotating porous medium has been investigated using the linear stability analysis. The normal mode technique is applied. A wide range of values of the Soret parameter, magnetization parameter, the magnetic field dependent viscosity, Taylor number and the permeability of porous medium have been considered. A Brinkman model is used. Both stationary and oscillatory instabilities have been obtained. It is found that the system stabilizes only through oscillatory mode of instability. It is found that the magnetization parameter and the permeability of the porous medium destabilize the system and the Soret parameter, the magnetic field dependent viscosity and the Taylor number tend to stabilize the system. The results are presented numerically and graphically.

19

Dynamika ośrodków wielofazowych na przykładzie dynamiki gruntów

Wrana B.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

|

2013

|

z. 101

95--96

PL

Grunt jest materiałem niejednorodnym składającym się głównie z ziaren mineralnych albo cząstek organicznych czy też antropogenicznych o różnej wielkości oraz porów zajętych przez płyn (głównie wodę) i gaz (głównie powietrze). Grunt jest zatem materiałem trójfazowym składającym się z fazy stałej (struktury zbudowanej z cząstek), fazy ciekłej i fazy gazowej. W modelowaniu obszaru gruntu stosowane są modele jednofazowe, jako mieszaniny trzech faz, modele dwufazowe składające się z fazy szkieletu i płynu w porach oraz modele trójfazowe obejmujące trzy fazy wzajemnie oddziaływujące na siebie. Obciążenia działające na grunt mogą być obciążeniami statycznymi, nie zmiennymi w czasie, lub/i obciążeniami dynamicznymi zmiennymi w czasie. Niniejsza artykuł dotyczy obciążeń dynamicznych, których analiza rozszerza się (w stosunku do obciążeń statycznych) o określenie sił bezwładności zależnych od gęstości gruntu i wielkości przyspieszenia oraz o określenie sił tłumienia, które w gruncie są definiowane przez zjawisko lokalnego przepływu wody w porach oraz tłumienia lepkiego związanego z modelami teorii sprężysto-lepko-plastyczności.

20

Triple-diffusive convection in Walters' (Model B') fluid with varying gravity field saturating a porous medium

Kango S. K., Rana G. C., Chand R.

Studia Geotechnica et Mechanica

|

2013

|

Vol. 35, nr 3

45--56

EN

The Triple-Diffusive convection in Walters’ (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.