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1

Investigation of velocity profile in time dependent boundary layer flow of a modified power-law fluid of fourth grade

Yurusoy M.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 2

176--191

EN

This paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the y direction increases.

2

Yurusoy M.

Journal of Theoretical and Applied Mechanics

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2003

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Vol. 41 nr 4

775-787

EN

Two dimensional equations of steady motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the ...-coordinates and the velocity potential lines are ...-coordinates which form an orthogonal curvilinear set of coordinates. The outcome, boundary layer equations, is then shown to be indepedent of the bidy shape immersed into the flow. As the first approximation, it is assumed that the second grade terms are negligible compared to the viscous and third grade terms. The second grade terms spoil scanling transformation which is the only transformation leading to similarity solutions for a third grade fluid. By using Lie's group methods, infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions to the outcoming nonlinear differential equations are found by using a combination of the Runge-Kutta algorithm and a shooting technique.

PL

W pracy przedstawiono dwuwymiarowe równania ruchu dla stacjonarnego przepływu cieczy trzeciego rzędu w specjalnym układzie współrzędnych. Równania wyprowadzono na bazie przepływu potencjalnego cieczy nielekkiej. Przy nielepkim opływie dowolnego obiektu linie prądu tworzą współrzędną ..., a linie potencjału prędkości współrzędną ... . Obydwie generują ortogonalny układ współrzędnych krzywoliniowych. Przy takim opisie postać równań warstwy przyściennej nie zależy od kształtu zanurzonego ciała poddanego opływowi. W pierwszym przybliżeniu założono, że wyrażenia drugiego rzędu są pomijalne w stosunku do członów wiskotycznych i trzeciego rzędu. Człony drugiego rzędu uniemożliwiają transformację skalowania, będącąjedynym przekształceniem prowadzącym do rozwiązań podobieństwa cieczy trzeciego rzędu. W pracy zastosowano metodę opartą na grupie Lie'a w generowaniu równań warstwy przyściennej przy pomocy wyrażeń infitezymalnych. Równania przekształcono do układu równań różniczkowych zwyczajnych. Numeryczne rozwiązanie równań nieliniowych uzyskano w drodze kombinacji algorytmu Runge-Kutta i techniki trymowania.

3

On flow past a continuously moving semi-infinite vertical plate in the upward direction

Soundalgekar V. M., Takhar H. S.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 3

553-559

EN

Flow past a continuously moving semi-infinite vertical plate in the upward direction is studied here. With usual boundary layer transformations, the boundary layer equations are reduced to local non-similar ordinary differential equations which are solved numerically. Velocity and temperature profiles are shown on graphs and the numerical values of the skin-friction and the rate of heat transfer are listed in a Table. It is observed that there occurs separation of low Prandtl number fluids at large values of Gr/Re2 where Gr is the Grashof number and Re is the Reynolds number. Greater viscous dissipative heat causes a fall in both the skin-friction and the rate of heat transfer.

4

Analysis of polymers flow through dies of forming devices

Walicka A.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 2

341-361

EN

The steady laminar flow of molten polymer modelled by viscoplastic fluid is considered, through a narrow space between two fixed surfaces of revolution. The problem is described by boundary layer equations. Using the method of averaged inertia one obtains the formulae expressing the pressure distribution. Generally, the flow of viscoplastic fluids given by the nonlinear model of Shulman is considered. The flows of polymers modelled by the viscoplastic fluids of Vočadlo, Herschel - Bulkley, Ostwald - de Waele and Newtonian are discussed in detail. Numerical examples of pressure distributions in the clearance between parallel disks and concentric spherical surfaces are presented.