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1

Periodic flow of a second grade fluid due to the disks executing non-torsional oscillations in an orthogonal rheometer under the influence of a magnetic field

Ersoy H. Volkan

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 3

62--71

EN

The present paper studies the periodic flow of a second grade fluid generated by non-torsional oscillations of the disks rotating in the eccentric form under the application of a magnetic field. Subsequent to the rotational motion of the disks at a common angular velocity about two vertical axes, they perform oscillations horizontally in a symmetrical manner. The exact analytical solutions are derived for both the velocity field and the tangential force per unit area exerted on one of the disks by the fluid. Special attention is paid to the influence of the applied magnetic field and it is investigated how the magnetic field controls the flow when the frequency of oscillation is less than or equal to or greater than the angular velocity of the disks. It is found that the application of the magnetic field leads to thinner boundary layers developed on the disks and the changes in the values of the shear stress components which represent the tangential force exerted on the disks occur at larger amplitude.

2

Exact solutions for fractionalized second grade fluid flows with boundary slip effects

Dehraj S., Malookani R. A., Aasoori S. K., Bhutto G. M., Arain L.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 1

88--103

EN

In this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under the influence of slip has been obtained. A coupled system of partial differential equations representing the equation of motion has been re-written in terms of fractional derivatives form by using the Caputo fractional operator. The Discrete Laplace transform method has been employed for computing the expressions for the velocity field […] and the corresponding shear stress […]. The obtained solutions for the velocity field and the shear stress have been written in terms of Wright generalized hypergeometric function pqψ and are expressed as a sum of the slip contribution and the corresponding no-slip contribution. In addition, the solutions for a fractionalized, ordinary second grade fluid and Newtonian fluid in the absence of slip effect have also been obtained as special case. Finally, the effect of different physical parameters has been demonstrated through graphical illustrations.

3

Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall

Khan N. A., Naz F.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 2

359--376

EN

This investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

4

Heat and mass transfer in a second grade fluid over a stretching vertical surface in a porous medium

Baoku I. G., Onifade Y. S., Adebayo L. O., Yusuff K. M.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 2

239--255

EN

The investigation deals with the combined heat and mass transfer in a mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic second grade fluid. The partial differential equations governing the model have been transformed by a similarity transformation and the system of coupled-ordinary differential equations is solved by employing the shooting method with the fifth-order Runge-Kutta-Fehlberg iteration technique. Effects of various values of physical parameters embedded in the flow model on the dimensionless velocity, temperature and concentration distributions are discussed and shown with the aid of graphs. Numerical values of physical quantities, such as the local skin-coefficient, local Nusselt number and local Sherwood number are presented in a tabular form. It is observed that the boundary layer fluid velocity increases as the second grade parameter, mixed convection parameter and Prandtl number increase.

5

Rotation of a heated impervious disk in a second grade fluid bounded by a porous medium

Srivastava A. C., Saxena P.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 2

523-538

EN

The flow and the heat transfer due to the rotation of a disk at a small distance from a porous medium of finite thickness have been discussed when the entire space between the disk and the bottom of the porous medium is filled with a second grade fluid. The disk and the bottom of the porous medium are maintained at constant temperatures; the temperature of the disk being higher. It is observed that with the increase of the Darcy number, all the components of velocity and temperature decrease in the entire region but the rate of heat transfer from the interface increases. With the increase of the non-Newtonian parameter (i) rotational velocity increases but radial and axial velocity components decrease in the entire region, (ii) the temperature increases in the entire region, (iii) the rate of heat transfer from the interface increases. Results of this paper have applications in engineering, biomedical and ground water problems.

6

Wpływ efektów bezwładnościowych oraz parametrów reologicznych na rozkład ciśnienia w przepływie uogólnionego płynu drugiego rzędu typu potęgowego w zakrzywionej szczelinie

Ratajczak P., Walicka A., Walicki E., Ratajczak M.

Inżynieria i Aparatura Chemiczna

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2006

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Nr 6s

205-207

EN

Rheodynamics of the generalized second grade fluids in curvilinear channels with a constant gap thickness are discussed in the paper. A power-law type model of the generalized second grade fluid was assumed. Based on the analytical solutions of movement equations, dependences describing the pressure distribution were given. The influence of a modified Reynolds number and viscoelastic parameters on pressure profiles was examined. . •

7

The unsteady Couette flow of a second grade fluid n a layer of porous medium

Hayat T., Khan M., Ayub M., Siddiqui A. M.

Archives of Mechanics

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2005

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Vol. 57, nr 5

405--416

EN

In this work, the two Couette flows of a second grade fluid are discussed in a porous layer when (i) bottom plate moves suddenly (ii) bottom plate oscillates. Laplace transform method is used to determine the analytic solutions. Expressions for the velocities, volume fluxes and frictional forces are constructed.