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

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.

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

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2020-0042 ◽

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.

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

Mathematical Problems in Engineering ◽

10.1155/2021/5539007 ◽

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.

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Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

Open Physics ◽

10.2478/s11534-010-0073-1 ◽

2011 ◽

Vol 9 (3) ◽

Cited By ~ 8

Author(s):

Constantin Fetecau ◽

Dumitru Vieru ◽

Corina Fetecau

Keyword(s):

Shear Stress ◽

Steady State ◽

Viscous Fluid ◽

Fourier Transforms ◽

Fluid Motion ◽

Infinite Plate ◽

Unsteady Motion ◽

Side Walls ◽

Oscillating Shear Stress ◽

Radiative and Porous Effects on Free Convection Flow near a Vertical Plate that Applies Shear Stress to the Fluid

Zeitschrift für Naturforschung A ◽

10.5560/zna.2012-0083 ◽

2013 ◽

Vol 68 (1-2) ◽

pp. 130-138 ◽

Cited By ~ 13

Author(s):

Corina Fetecau ◽

Mehwish Rana ◽

Constantin Fetecau

Keyword(s):

Shear Stress ◽

Free Convection ◽

Viscous Fluid ◽

Thermal Radiation ◽

Vertical Plate ◽

Fluid Motion ◽

Convection Flow ◽

Free Convection Flow ◽

Special Cases ◽

Infinite Vertical Plate

General solutions for the unsteady free convection flow of an incompressible viscous fluid due to an infinite vertical plate that applies a shear stress f (t) to the fluid are established when thermal radiation and porous effects are taken into consideration. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different motions with technical relevance. The velocity is presented as a sum of thermal and mechanical components. Finally, some special cases are brought to light, and effects of pertinent parameters on the fluid motion are graphically underlined.

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-2021-0212 ◽

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.

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Permanent solutions for some oscillatory motions of fluids with power-law dependence of viscosity on the pressure and shear stress on the boundary

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0135 ◽

2020 ◽

Vol 75 (8) ◽

pp. 757-769

Author(s):

Constantin Fetecau ◽

Abdul Rauf ◽

Tahir Mushtaq Qureshi ◽

Masood Khan

Keyword(s):

Shear Stress ◽

Power Law ◽

Fluid Motion ◽

Viscosity Coefficient ◽

Shear Stresses ◽

Parallel Plates ◽

Constant Shear Stress ◽

Starting Solutions ◽

The Effect of Wall Shear Stress on Two Phase Fluctuating Flow of Dusty Fluids by Using Light Hill Technique

Water ◽

10.3390/w13111587 ◽

2021 ◽

Vol 13 (11) ◽

pp. 1587

Author(s):

Dolat Khan ◽

Ata ur Rahman ◽

Gohar Ali ◽

Poom Kumam ◽

Attapol Kaewkhao ◽

...

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Base Fluid ◽

Perturbation Technique ◽

Fluid Velocity ◽

Dust Particles ◽

Stress Effect ◽

Parallel Plates ◽

Dusty Fluid ◽

Wall Shear

Due to the importance of wall shear stress effect and dust fluid in daily life fluid problems. This paper aims to discover the influence of wall shear stress on dust fluids of fluctuating flow. The flow is considered between two parallel plates that are non-conducting. Due to the transformation of heat, the fluid flow is generated. We consider every dust particle having spherical uniformly disperse in the base fluid. The perturb solution is obtained by applying the Poincare-Lighthill perturbation technique (PLPT). The fluid velocity and shear stress are discussed for the different parameters like Grashof number, magnetic parameter, radiation parameter, and dusty fluid parameter. Graphical results for fluid and dust particles are plotted through Mathcad-15. The behavior of base fluid and dusty fluid is matching for different embedded parameters.

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

Mathematics ◽

10.3390/math9040334 ◽

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.

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Computational Analysis of Fluid Flow Within a Device for Applying Biaxial Strain to Cultured Cells

Journal of Biomechanical Engineering ◽

10.1115/1.4029638 ◽

2015 ◽

Vol 137 (5) ◽

Cited By ~ 2

Author(s):

Jason Lee ◽

Aaron B. Baker

Keyword(s):

Shear Stress ◽

Cultured Cells ◽

Fluid Velocity ◽

Mechanical Strain ◽

Cell Types ◽

Linear Increase ◽

Shear Stresses ◽

Biaxial Strain ◽

Maximal Strain

In vitro systems for applying mechanical strain to cultured cells are commonly used to investigate cellular mechanotransduction pathways in a variety of cell types. These systems often apply mechanical forces to a flexible membrane on which cells are cultured. A consequence of the motion of the membrane in these systems is the generation of flow and the unintended application of shear stress to the cells. We recently described a flexible system for applying mechanical strain to cultured cells, which uses a linear motor to drive a piston array to create biaxial strain within multiwell culture plates. To better understand the fluidic stresses generated by this system and other systems of this type, we created a computational fluid dynamics model to simulate the flow during the mechanical loading cycle. Alterations in the frequency or maximal strain magnitude led to a linear increase in the average fluid velocity within the well and a nonlinear increase in the shear stress at the culture surface over the ranges tested (0.5–2.0 Hz and 1–10% maximal strain). For all cases, the applied shear stresses were relatively low and on the order of millipascal with a dynamic waveform having a primary and secondary peak in the shear stress over a single mechanical strain cycle. These findings should be considered when interpreting experimental results using these devices, particularly in the case when the cell type used is sensitive to low magnitude, oscillatory shear stresses.

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Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2014.m588 ◽

2016 ◽

Vol 8 (5) ◽

pp. 784-794 ◽

Cited By ~ 2

Author(s):

Vatsala Mathur ◽

Kavita Khandelwal

Keyword(s):

Shear Stress ◽

Velocity Field ◽

Newtonian Fluid ◽

Outer Cylinder ◽

Fluid Motion ◽

Maxwell Fluid ◽

Circular Cylinders ◽

Generalized Solutions ◽

Special Cases ◽

Graphical Illustration

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

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