scholarly journals Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Ahmed Zeeshan
Keyword(s):  
Steady State ◽  
Porous Plate ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Newtonian Fluids ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Fourier Cosine ◽  
Maxwell Fluids

Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

scholarly journals Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 90
Author(s):  
Constantin Fetecau ◽  
Rahmat Ellahi ◽  
Sadiq M. Sait
Keyword(s):  
Steady State ◽  
Porous Plate ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Physical Parameters ◽  
Maxwell Fluids ◽  
Flow Through ◽  
Starting Solutions ◽  
Plate Channel

Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Mixed initial-boundary value problems describing motions of Maxwell fluids with linear dependence of viscosity on the pressure

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Abdul Rauf ◽  
Tahir Mushtaq Qureshi
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Boundary Value Problems ◽  
Linear Dependence ◽  
Boundary Value ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Shear Stresses ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

Abstract Some mixed initial-boundary value problems are analytically studied. They correspond to unsteady motions of the incompressible upper-convected Maxwell (IUCM) fluids with linear dependence of viscosity on the pressure between infinite horizontal parallel plates. The fluid motion is generated by the upper plate that applies time-dependent shear stresses to the fluid. Exact solutions are established for the dimensionless velocity and nontrivial shear stress fields using a suitable change of the spatial variable and the Laplace transform technique. They are presented as sum of the steady-state and transient components and are used to determine the required time to reach the permanent state. Comparisons between exact and numerical solutions indicate an excellent agreement. Analytical solutions for the unsteady motion of the same fluids induced by an exponential shear stress on the boundary are obtained as limiting cases of the general solutions. Moreover, the steady-state solutions corresponding to the ordinary IUCM fluids performing the initial motions are provided by means of asymptotic approximations of standard Bessel functions. Finally, spatial variation of starting solutions and the influence of physical parameters on the fluid motion are graphically underlined and discussed.

scholarly journals General solutions for the mixed boundary value problem associated to hydromagnetic flows of a viscous fluid between symmetrically heated parallel plates

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1389-1405 ◽  
Author(s):  
Maria Javaid ◽  
Muhammad Imran ◽  
Constantin Fetecau ◽  
Dumitru Vieru
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Viscous Fluid ◽  
Mixed Boundary ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Shear Stresses ◽  
Parallel Plates ◽  
General Solutions ◽  
Special Cases

Exact general solutions for hydromagnetic flows of an incompressible viscous fluid between two horizontal infinite parallel plates are established when the upper plate is fixed and the inferior one applies a time-dependent shear stress to the fluid. Porous effects are taken into consideration and the problem in discussion is completely solved for moderate values of the Hartman number. It is found that the fluid velocity and the non-trivial shear stress satisfy PDE of the same form and the motion characteristics do not depend of magnetic and porous parameters independently but only by a combination of them that is called the effective permeability. For illustration, as well as to bring to light some physical insight of results that have been obtained, three special cases are considered and the influence of Reynolds number as well as combined porous and magnetic effects on the fluid motion are graphically underlined and discussed for motions due to constant or ramped-type shear stresses on the boundary. The starting solutions corresponding to motions induced by the lower plate that applies constant or oscillatory shear stresses to the fluid are presented as sum of steady-state and transient solutions and the required time to reach the steady-state is graphically determined. This time is greater for motions due to sine as compared to cosine oscillating shear stresses on the boundary. The steady-state is rather obtained in the presence of a magnetic field or porous medium.

scholarly journals "Permanent solutions for some motions of UCM fluids with power-law dependence of viscosity on the pressure"

2021 ◽  
Vol 66 (1) ◽  
pp. 197-209
Author(s):  
Constantin Fetecau ◽  
Abdul Rauf
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Fluid Motion ◽  
Steady Motion ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Maxwell Fluids ◽  
Gravity Effects ◽  
Starting Solutions ◽  
Similar Solutions

Steady motion of two types of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure is analytically studied between infinite horizontal parallel plates when the gravity effects are taken into consideration. Simple and exact expressions are established for the permanent components of starting solutions corresponding to two oscillatory motions induced by the lower plate that oscillates in its plane. Such solutions are very important for the experimentalists who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids, as well as the permanent solutions corresponding to ordinary incompressible Maxwell fluids performing the same motions, are obtained as limiting cases of general solutions. The convergence of starting solutions to their permanent components as well as the influence of physical parameters on the fluid motion is graphically underlined and discussed.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Flow of Second Grade Fluid between two Walls Induced by Rectified Sine Pulses Shear Stress

2015 ◽  
Vol 31 (5) ◽  
pp. 573-582
Author(s):  
Q. Sultan ◽  
M. Nazar ◽  
I. Ahmad ◽  
U. Ali
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Fourier Cosine ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Grade Fluid

AbstractThis paper concerns with the unsteady MHD flow of a second grade fluid between two parallel walls through porous media induced by rectified sine pulses shear stress. The analytical expressions for the velocity field and the adequate shear stress are determined by means of the Laplace transform technique and Fourier cosine and sine transforms and are written as a sum of steady state and transient solutions. The influence of side walls on the fluid motion, the distance between walls for which the velocity of the fluid in the middle of the channel is negligible, and the required time to reach the steady state are presented by graphical illustrations. As the second grade fluid parameter → 0 the problem reduces to the Newtonian fluids performing the same motion.

scholarly journals Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure

2020 ◽  
Vol 25 (3) ◽  
pp. 181-197
Author(s):  
D. Vieru ◽  
C. Fetecau ◽  
C. Bridges
Keyword(s):  
Shear Stress ◽  
Linear Dependence ◽  
Mixed Boundary ◽  
Fluid Motion ◽  
Hankel Transform ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Special Cases ◽  
Independent Variable ◽  
Suitable Change

AbstractAn unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid

2013 ◽  
Vol 68 (12) ◽  
pp. 725-734 ◽  
Author(s):  
Mehwish Rana ◽  
Nazish Shahid ◽  
Azhar Ali Zafar
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Integral Transforms ◽  
Second Grade ◽  
Shear Stresses ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions

Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

scholarly journals Hall-current effects on unsteady MHD flow between stretching sheet and an oscillating porous upper parallel plate with constant suction

2011 ◽  
Vol 15 (2) ◽  
pp. 527-536 ◽  
Author(s):  
Raju Changal ◽  
Reddy Ananda ◽  
Kumar Vijaya
Keyword(s):  
Stretching Sheet ◽  
Hall Current ◽  
Porous Plate ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Physical Parameters ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Constant Suction

The unsteady MHD flow of an incompressible viscous electrically conducting fluid between two horizontal parallel non conducting plates, where the lower one is stretching sheet and the upper one is oscillating porous plate, is studied in the presence of a transverse magnetic field and the effects of Hall current. Fluid motion is caused by the stretching of the lower sheet and a constant suction is applied at the upper plate which is oscillating in its own plane. The stretching velocity of the sheet is assumed to be a linear function of distance along the channel. The expressions relating to the velocity distribution are obtained and effects of different values of various physical parameters are calculated numerically and shown graphically.

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