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1

Chemical reaction effects on MHD flow past an impulsively started isothermal vertical plate with uniform mass diffusion

Chandrakala P., Narayana Bhaskar P.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

419--426

EN

A numerical technique is employed to derive a solution to the transient natural convection flow of an incompressible viscous fluid past an impulsively started infinite isothermal vertical plate with uniform mass diffusion in the presence of a magnetic field and homogeneous chemical reaction of first order. The governing equations are solved using implicit finite-difference method. The effects of velocity, temperature and concentration for different parameters such as the magnetic field parameter, chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the fluid velocity decreases with increasing the chemical reaction parameter and the magnetic field parameter.

2

Reflection and transmission of waves from a plane interface between viscous liquid and magneto elastic solid half space with voids

Acharya D. P., Maji C.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 1

21-54

EN

This paper investigates the propagation of plane waves as well as their reflection and transmission from the plane interface which separates a viscous liquid half space and a magneto elastic solid semi infinite medium containing a distribution of void pores. From the analysis of the propagation of plane waves in a magneto elastic solid medium with voids, it is found that the longitudinal wave in a void solid medium is subject to dispersion of the general wave form. In this case, short wave and long wave approximations have been made. A 'cut of frequency', which depends upon the void parameter, exists below which one of the longitudinal waves cannot propagate at all. Amplitude and energy ratios of various reflected and transmitted waves are presented in each of the four cases when (i) a set of coupled longitudinal waves (ii) a similar set of coupled waves (iii) a transverse wave, propagating through the solid half space (iv) a longitudinal wave propagating through the viscous liquid half space, are made incident at the interface. Numerical computations are made for a specific model and results are presented graphically to highlight the modulations of these ratios due to the variation of incident angle of the incident wave. It is found that the amplitude and energy ratios of various reflected and transmitted waves are functions of angle of incidence and frequency. The effects of viscosity of the liquid, magnetic field as well as void nature of the solid medium on the amplitude and energy ratios have been analyzed from the graphical representations.

3

Modelling of flow and heat transfer in a generalized second grade fluid

Hayat T., Ellahi R., Asghar S.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 1

101-121

EN

The flow of a second grade fluid past a porous plate has been studied using a modified model of second grade fluid that has shear dependent viscosity and can predict the normal stress difference. The boundary value problem subject to two different sets of boundary conditions is investigated. In the first instance, we consider that the plate is at temperature higher than the fluid. The second case deals with the analysis of an insulated plate. The differential equations governing the flow are solved using the homotopy analysis method (HAM). Expressions for velocity and temperature profiles are plotted and discussed.

4

Heat and mass transfer flow with variable thermal conductivity and variable mass diffusivity in an MHD visco-elastic fluid over a non-isothermal stretching sheet

Veena P. H., Pravin V. K., Shahjahan S. M.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 2

515-541

EN

In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco-elastic fluid flow over a non-isothermal stretching sheet with variable thermal conductivity and variable mass diffusivity. Similarity transformation are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux and mass flux are obtained in the form of confluent hypergeometric functions for two different types of the boundary conditions, namely: (i) wall with prescribed second-order power law temperature and second-order power law concentration (PST) and (ii)wall with prescribed second-order power law heat flux and second-order power law mass flux (PHF). The effect of various physical parameters such as the suction/blowing parameter , heat source/sink parameter [...], Prandtl number Pr, Schmidt number Sc, visco-elastic parameter and permeability parameter on the temperature and concentration profiles are analyzed.

5

Generalized Rayleigh waves in thermoelastic solids under viscous fluid loading

Sharma J. N., Sharma R., Sharma Y. D.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 1

217-238

EN

The paper is aimed to study the propagation of Rayleigh surface waves in a homogeneous isotropic, thermally condueting, and elastic solid halfspace underlying a viscous liquid semi space in the context of generalized theories of thermoelasticity. The investigation is based on modelling the viscous liquid as a hypothetical solid in addition to conduction-convection condition of heat transfer at the interface. After developing the mathematical model, boundary conditions and formal solutions, the secular equations for a thermoelastic solid in closed form and isolated mathematical conditions for generalized Rayleigh waves (Stoneley waves), in complete forms are derived. The amplitude ratios of solid and liquid displacements and temperature change on the surface (interface) are obtained analytically. The surface particle motion has also been discussed and found to be elliptical. The semi-major and semi-minor axes, eccentricity and inclination of major axes with the wave normal are computed analytically and analyzed numerically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum-epoxy composite material solid (half space) underlying water, in the case of both light and heavy semi spaces. The dispersion curves, attenuation coefficient profiles and amplitude ratios of surface displacements, temperature change in the solid half space for generalized Rayleigh waves are presented and illustrated graphically in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The present analysis is useful in electronics and navigation applications.

6

Exact solutions for unsteady incompressible viscous fluid flows

Jamil M., Ahmed F., Khan N. A.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 4

975-988

EN

Two-dimensional, unsteady, laminar equations of motions of an incompressible fluid with variable viscosity are considered. The problem investigated is the flow for which the vorticity distribution is proportional to the stream function perturbed by a generalized uniform stream making an angle with the positive x-axis. Employing transformation variables, the goveming Navier-Stocks Equations (NSE) are transformed into steady state equations and then simple ordinary differential equations and a class of exact solutions are obtained. Several graphs of physical interest of streamline are also displayed and discussed.

7

Ruch pęcherzy gazowych w płynach o wysokiej lepkości w polu sił odśrodkowych

Kiljański T.

Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka

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2005

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Z. 345

3-154

PL

Praca dotyczy ruchu pęcherzy gazowych w polu sił odśrodkowych w płynach o bardzo wysokiej lepkości - newtonowskich, nienewtonowskich rozrzedzanych ścinaniem i plastycznolepkich. Głównym celem pracy jest określenie warunków oddzielania pęcherzy od takich płynów z użyciem wirówki i zbadanie wpływu zwiększonych sił masowych w wirówce na zjawiska powierzchniowe, prowadzące do unieruchomienia powierzchni poruszającego się pęcherza. Opracowano metodę obliczania czasu potrzebnego do usunięcia za pomocą wirówki pęcherza w płynach newtonowskich, nienewtonowskich bez granicy płynięcia opisanych równaniem potęgowym i plastycznolepkich opisanych równaniem Herschela-Bulkleya, potwierdzono ją doświadczalnie dla płynów newtonowskich i nienewtonowskich bez granicy płynięcia. W przypadku płynów plastycznolepkich zaproponowana metoda okazała się zadowalająca jedynie w dostatecznie dużej odległości od miejsca ostatecznego zatrzymania pęcherza, w którym pozostaje on nieruchomy mimo działającej na niego siły wyporu. Wykazano, że pęcherze gazowe poruszające się w substancji plastycznolepkiej przybierają kształt wydłużony. Sformułowano postaci kryterium ruchu - warunku, który musi być spełniony, aby pęcherz mógł się poruszać w substancji plastycznolepkiej, dla pęcherzy o kształcie wydłużonym i kulistym, z powierzchnią swobodną i unieruchomioną. Określono wartość tego kryterium na drodze teoretycznej i wyznaczono je na drodze eksperymentu. Wyznaczono też warunek rozpoczęcia ruchu pęcherzy o kształcie nieregularnym, typowym dla pęcherzy w substancjach plastycznolepkich przed rozpoczęciem ich ruchu. Badania ruchu pęcherzy w wirówce wykazały, że unieruchomienie powierzchni pęcherza, prowadzące do spadku prędkości jego ruchu jest w wirówce trudniejsze, niż w polu grawitacyjnym - wzrost przyspieszenia odśrodkowego powoduje przejście powierzchni ze stanu unieruchomionego w swobodny. Wprowadzono pojęcie bezwymiarowej średnicy pęcherza, które pozwoliło uogólnić warunek unieruchomienia powierzchni w polu grawitacyjnym na pole sił odśrodkowych. Wykazano na drodze teoretycznej możliwość ruchu pęcherzy gazowych w dół w polu grawitacyjnym w cieczy w warunkach izotermicznych, jeśli przedtem pęcherz poddany był działaniu siły odśrodkowej i potwierdzono występowanie takiego zjawiska doświadczalnie. Stwierdzono, że zjawisko takie zachodzi, jeśli podczas odwirowywania pęcherza jego powierzchnia była chociaż częściowo unieruchomiona przez gradient napięcia powierzchniowego. Pozwala to sądzić, że zgodnie z przedstawioną teorią, taki wymuszony ruch pęcherza w dół jest spowodowany zjawiskami powierzchniowymi, takimi samymi, jakie prowadzą również do unieruchomienia powierzchni i spadku prędkości naturalnego ruchu pęcherza. Na podstawie badań kryterium ruchu sztywnych kuł w substancji plastycznolepkiej wyprowadzono zależność opisującą siłę oporu ruchu kuli w płynie nienewtonowskim opisanym prawem potęgowym o wykładniku n dążącym do zera. Opracowano metodę wyznaczania granicy płynięcia substancji plastycznolepkiej za pomocą wirówki.

EN

The work is concerned with the motion of gas bubbles in the field of centrifugal forces in highly viscous liquids - Newtonian, non-Newtonian shear-thinning and viscoplastic ones. The main topic of the work is to define the condition for separation of bubbles from liquids of those kinds by means of a centrifuge and to investigate the influence of increased mass forces in the centrifuge on the surface phenomena which lead to the immobilisation of the moving bubble surface. Formulae were derived for the time needed for bubble separation in the centrifuge from Newtonian, shear-thinning power-law liquids as well as viscoplastic Herschel-Bulkley bodies. The formulae were confirmed experimentally for Newtonian and shear-thinning liquids. In the case of viscoplastic bodies, the proposed method proved satisfactory only at a sufficient distance from the place of the terminal standstill of the bubble, where it stays motionless in spite of the buoyancy force. The investigation of the bubble motion in a centrifuge showed that the surface immobilisation which leads to velocity decrease occurs with more difficulty in the centrifuge than in the gravitational field - as a result of the increased centrifugal acceleration the surface becomes mobile. The dimensionless bubble diameter was introduced which made it possible to generalise the criterion for surface immobilisation in the gravitational field onto the field of centrifugal forces. It was shown in theoretical way that gas bubbles can move downwards in an isothermal liquid if they were formerly subjected to the centrifugal force. That phenomenon was also experimentally confirmed. It was found that this effect occurs if during centrifugation the bubble surface was at least partially immobilised by the surface tension gradient. This leads to the conclusion that, according to the presented theory, this forced downward movement of a bubble is due to the surface phenomena which also lead to the surface immobilisation and as a result, to the decrease of the natural bubble movement. It was shown that gas bubbles moving in viscoplastic bodies assume strongly prolate shape. The criterion of motion, i.e. the condition which must be fulfilled for a bubble to move in a viscoplastic body, was formulated for spherical and prolate bubbles with free and immobilised surface. The critical value of this criterion was theoretically derived and experimentally proved. The motion/no motion conditions were also evaluated for the bubbles of irregular shape, typical for bubbles in viscoplastic bodies before the motion begins. On the ground of investigations of the criterion of motion of solid spheres in viscoplastic bodies, the formula was derived which describes the drag on a solid sphere moving in a power-law non-Newtonian liquid with the exponent n tending to zero. The method for evaluation of the yield stress of viscoplastic bodies by means of a centrifuge was elaborated.