Axisymmetric motion of a spherical porous particle perpendicular to two parallel plates with slip surfaces

2015 ◽  
Vol 93 (7) ◽  
pp. 784-795 ◽  
Author(s):  
E.I. Saad
Keyword(s):  
Fluid Motion ◽  
Brinkman Equation ◽  
Parallel Plates ◽  
Porous Sphere ◽  
Field Equations ◽  
Clear Fluid ◽  
Stress Jump ◽  
Spherical Coordinate ◽  
Good Convergence ◽  
Special Cases

A combined analytical–numerical approach to the problem of the low Reynolds number motion of a porous sphere normal to one of two infinite parallel plates at an arbitrary position between them in a viscous fluid is investigated. The clear fluid motion governed by the Stokes equation and the Darcy–Brinkman equation is used to model the flow inside the porous material. The motion in each of the homogeneous regions is coupled with the continuity of the velocity components, the continuity of the normal stress, and the tangential stress jump condition. The fluid is allowed to slip at the surface of the walls. A general solution for the field equations in the clear region is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The collocation solutions for the hydrodynamic interactions between the porous sphere and the walls are calculated with good convergence for various values of the slip coefficient of the walls, the separation between the porous sphere and the walls, the stress jump coefficient, and a coefficient that is proportional to the permeability. For the special cases of a solid sphere, our drag results show excellent agreement with the available solutions in the literature for all relative particle-to-wall spacing.

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.

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 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.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

On the isometric motion of a charged fluid in the Einstein-Maxwell theory

1974 ◽  
Vol 336 (1606) ◽  
pp. 273-284 ◽  
Keyword(s):  
Killing Vector ◽  
Fluid Motion ◽  
Fluid Pressure ◽  
Field Equations ◽  
Maxwell Theory ◽  
Charged Fluid ◽  
Spherically Symmetric Solution ◽  
Electromagnetic Field Tensor ◽  
Discrete Values ◽  
Full Solution

It is shown that in the Einstein-Maxwell theory a class of four-dimensional charged fluid space-times exists, with non-zero fluid pressure, satisfying the conditions that (i) the fluid motion is isometric, (ii) the dual of the electromagnetic field tensor has no projection in the direction of a Killing vector - equivalent to the condition that in a static space time the local field of an observer moving with the fluid is purely electric - and (iii) the ratio of charge to mass is constant. For the case of a diagonal static metric it is seen that a group of quasi-conformal transformations may be determined which leaves the field equations unchanged. This may be used to obtain a full solution of the field equations, in three independent variables, from a given solution in one independent variable. A spherically symmetric solution of this kind is obtained which is seen to be expressible in terms of hypergeometric functions. An interesting aspect of this is that the charge/mass ratio can only have discrete values depending on the eigenvalues of a linear boundary-value problem.

scholarly journals Unsteady Heat and Mass Transfer of Chemically Reacting Micropolar Fluid in a Porous Channel with Hall and Ion Slip Currents

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Odelu Ojjela ◽  
N. Naresh Kumar
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Parallel Plates ◽  
Field Equations ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Ion Slip ◽  
Chemically Reacting

This paper presents an incompressible two-dimensional heat and mass transfer of an electrically conducting micropolar fluid flow in a porous medium between two parallel plates with chemical reaction, Hall and ion slip effects. Let there be periodic injection or suction at the lower and upper plates and the nonuniform temperature and concentration at the plates are varying periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations using similarity transformations and then solved numerically by quasilinearization technique. The profiles of velocity components, microrotation, temperature distribution and concentration are studied for different values of fluid and geometric parameters such as Hartmann number, Hall and ion slip parameters, inverse Darcy parameter, Prandtl number, Schmidt number, and chemical reaction rate and shown in the form of graphs.

On uniqueness in dynamic poroelasticity

1963 ◽  
Vol 53 (4) ◽  
pp. 783-788 ◽  
Author(s):  
H. Deresiewicz ◽  
R. Skalak
Keyword(s):  
Porous Media ◽  
Liquid Medium ◽  
Uniqueness Theorem ◽  
Dissimilar Materials ◽  
Elastic Solid ◽  
Porous Solid ◽  
Uniqueness Of Solution ◽  
Biot’S Theory ◽  
Field Equations ◽  
Special Cases

Abstract Conditions are derived sufficient for uniqueness of solution of the field equations of Biot's theory of liquid-filled porous media, particular attention being paid to continuity requirements at an interface between two such dissimilar materials. It is found that at an interface two distinct sets of conditions will satisfy the demands of the mathematical uniqueness theorem, one of them being discarded on physical grounds. The permissible set is then discussed in relation to a number of possible models of the structure of a pair of elements in contact. The special cases of an impermeable elastic solid or a liquid medium in contact with a saturated porous solid are also examined.

Interaction of Free Surface Flows With Unrestrained Solid-Porous Bodies

2003 ◽  
Author(s):  
Razvan Bidoae ◽  
Remus M. Ciobotaru ◽  
Peter E. Raad
Keyword(s):  
Wave Breaking ◽  
Free Surface Flows ◽  
Velocity Fields ◽  
Porous Sphere ◽  
Clear Fluid ◽  
Large Wave ◽  
Free Surfaces ◽  
Surface Flows ◽  
Porous Bodies ◽  
Porous Boundaries

This paper presents an extension of the Eulerian-Lagrangian Marker and Micro Cell (ELMMC) method, developed to numerically simulate the interaction between clear fluid flow and composite obstacles. The method can simulate both transient and pseudo-steady state problems that involve wave breaking, impact between fluid fronts, and impact between free surfaces and solid or porous boundaries. The newest capability added to the ELMMC method can simulate interaction between fluid fronts and unrestrained solid/porous obstacles. The extension of the ELMMC method is presented here in detail, including the estimation of the hydrodynamic forces induced by the flow on the solid/porous obstacles, the calculation of the final velocity fields, and the computation of the velocity of the solid/porous obstacles. The capabilities of the new method are demonstrated by simulating two representative problems, namely, a solid/porous sphere falling in a reservoir and a single large wave impacting an unrestrained solid/porous structure.

Heat Transfer Enhancement in a Horizontal Channel by the Addition of Curved Baffles

2006 ◽  
Author(s):  
J. L. Luviano ◽  
A. Hernandez ◽  
C. Rubio ◽  
D. Banerjee
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Transfer Rate ◽  
Fluid Motion ◽  
Horizontal Channel ◽  
Parallel Plates ◽  
Energy Transfer Rate ◽  
Transfer Enhancement ◽  
The Heat Transfer Coefficient

This paper presents the heat transfer and fluid dynamics analysis of a horizontal channel formed by parallel plates with periodic insertions of heated blocks, having curved deflectors to direct the flow. The heat transfer coefficient investigated is compared with that of the horizontal channel without deflectors. The aim of the deflectors is to lead the fluid to the space between the heated blocks increasing the dynamics in this area. This zone will normally, without deflectors, become a stagnant fluid zone in which low energy transfer rate occurs. The results show that the heat transfer coefficient is larger as compared to that of the case without deflectors. The increment in the heat transfer coefficient is due primarily to the fluid motion stirred in the area between the heated block due to the deflectors. However, it must be pointed out. This implementation also increases the pressure drop in the channel.

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