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1
Content available Stokes flow past a contaminated fluid sphere embedded in a porous medium with slip condition
Meduri P. K., Devi P. N. L.
Archives of Mechanics
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2024
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Vol. 76, nr 3
253--275
EN
In this paper, Stokes flow past a contaminated fluid sphere embedded in a porous medium is considered using interfacial slip on the boundary. The stream functions and drag are computed analytically. Special cases are deduced for drag force and a satisfactory agreement is reached with available data in the literature. It was observed that in viscous fluid and couple stress fluid cases with an increase in the viscosity ratio, the slip parameter, the porous parameter there is an increase in the values of the drag coefficient for varying different parameters, respectively. Also noticed that coefficient of drag values for a uniform flow of the viscous fluid flow over a contaminated viscous fluid sphere in a porous medium with the slip condition are superior to those of a couple stress fluid (CSF) flow.
2
Content available Analytical analysis of thermal conductivity by laminar flow under the influence of mhd using Vogel’s model
Nawaz Rashid, Farooq Muhammad, Rehman Siddiq Ur, Ismail Gamal M., Ahmad Hijaz
Acta Mechanica et Automatica
|
2024
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Vol. 18, no. 3
548--563
EN
The main aim of this work is to study the influence of thermal conductivity of uniform couple stress fluid of inclined Poiseuille flow in the presence of magneto hydrodynamic (MHD) between two parallel plates. A well-known Vogel’s viscosity model is used. The momentum and energy equations are solved analytically by utilizing Homotopy Perturbation method (HPM) and Optimal Homotopy Asymptotic Method (OHAM). The results include the velocity profile, average velocity, volume flux, Shear Stress, Skin friction and the temperature distribution between the plates. Particular attention is given to the effect of MHD Γ on the velocity field and temperature distribution. As can be seen, that there exists direct relation between MHD parameter Γ and velocity profile and bears inverse relation with temperature distribution. In addition to that, influence of non-dimensional parameters like G, A, a, B and γ on the velocity field and temperature distribution are also discussed graphically. The physical characteristics of the problem have been well discussed in graphs for several parameters of interest. The results reveal that both techniques are reliable and are in great agreement with each other.
3
Content available Slow flow of couple stress fluid past a cylinder embedded in a porous medium: slip effect
Sarkar Priya, Madasu Krishna Prasad
Engineering Transactions
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2023
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Vol. 71, iss. 4
537--551
EN
An analytical study for the creeping flow of a couple stress fluid past a cylinder embedded in a porous medium is presented using the slip condition. The uniform flow is considered far away from a cylinder. The boundary conditions used are zero couple stress and tangential slip conditions. The modified Bessel functions represent the stream function (the velocity). The drag exerted on a solid cylinder immersed in a porous medium is derived. The impacts of the couple stress, permeability, and slip parameters on the normalized drag force are presented graphically. The drag forces of well-known exceptional cases are reduced. The drag force is a decreasing function of the permeability and couple stress parameters and an increasing function of the slip parameter.
4
Content available An analytical study of couple stress fluid through a sphere with an influence of the magnetic field
Krishna Prasad Madasu, Sarkar Priya
Journal of Applied Mathematics and Computational Mechanics
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2022
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Vol. 21, nr 3
99--110
EN
The present work concerns to study of the steady, axisymmetric slow flow of couple stress fluid through a rigid sphere in the transverse magnetic field. Boundary conditions on the sphere surface are the zero couple stress condition and tangential slip condition. The stream function, vorticity vector, and pressure term are obtained. The drag acting on the sphere in the presence of MHD is calculated. Here, we graphically represented the Hartmann number, couple stress, and slip parameters effect on the drag coefficient. Some well-known results of the drag are deduced.
5
Content available Couple stress fluid past a sphere embedded in a porous medium
Madasu Krishna Prasad, Sarkar Priya
Archive of Mechanical Engineering
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2022
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LXIX, nr 1
5--19
EN
This paper concerns the analytical investigation of the axisymmetric and steady flow of incompressible couple stress fluid through a rigid sphere embedded in a porous medium. In the porous region, the flow field is governed by Brinkman’s equation. Here we consider uniform flow at a distance from the sphere. The boundary conditions applied on the surface of the sphere are the slip condition and zero couple stress. Analytical solution of the problem in the terms of stream function is presented by modified Bessel functions. The drag experienced by an incompressible couple stress fluid on the sphere within the porous medium is calculated. The effects of the slip parameter, the couple stress parameter, and permeability on the drag are represented graphically. Special cases of viscous flow through a sphere are obtained and the results are compared with earlier published results.
6
Content available Effects of stenosis and dilatation on flow of blood mixed with suspended nanoparticles: a study using homotopy technique
Sudha T., Umadevi C., Dhange M., Manna S., Misra J. C.
International Journal of Applied Mechanics and Engineering
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2021
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Vol. 26, no. 1
251--265
EN
The paper deals with a theoretical study on blood flow in a stenosed segment of an artery, when blood is mixed with nano-particles. Blood is treated here as a couple stress fluid. Stenosis is known to impede blood flow and to be the cause of different cardiac diseases. Since the arterial wall is weakened due to arterial stenosis, it may lead to dilatation /aneurysm. The homotopy perturbation technique is employed to determine the solution to the problem for the case of mild stenosis. Analytical expressions for velocity, shear stress at the wall, pressure drop, and flow resistance are derived. The impact of different physical constants on the wall shear stress and impedance of the fluid is examined by numerical simulation. Streamline patterns of the nanofluid are investigated for different situations.
7
Content available Mixed convective flow of unsteady hydromagnetic couple stress fluid through a vertical channel filled with porous medium
Makhalemele C. R., Rundora L., Adesanya S. O.
International Journal of Applied Mechanics and Engineering
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2020
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Vol. 25, no. 4
148--161
EN
In this paper, the mixed convective flow of an electrically conducting, viscous incompressible couple stress fluid through a vertical channel filled with a saturated porous medium has been investigated. The fluid is assumed to be driven by both buoyancy force and oscillatory pressure gradient parallel to the channel plates. A uniform magnetic field of strength 0B is imposed transverse to the channel boundaries. The temperature of the right channel plate is assumed to vary periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. Under these assumptions, the equations governing the two-dimensional couple stress fluid flow are formulated and exact solutions of the velocity and the temperature fields are obtained. The effects of radiation, Hall current, porous medium permeability and other various flow parameters on the flow and heat transfer are presented graphically and discussed extensively.
8
Content available Transport of MHD couple stress fluid through peristalsis in a porous medium under the influence of heat transfer and slip effects
Sankad G. C., Nagathan P. S.
International Journal of Applied Mechanics and Engineering
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2017
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Vol. 22, no. 2
403--414
EN
An attempt has been made to examine the effects of magnetohydrodynamic couple stress fluid in peristaltic flow with porous medium under the impact of slip, heat transfer and wall properties. The expressions are obtained for temperature, coefficient of heat transfer and velocity. Influences of different parameters, the Hartmann number, Brinkman number and adaptability parameters on the temperature and warmth trade coefficient are discussed through outlines.
9
Content available remote Electrokinetics of Dielectric Non-Newtonian Bio Fluids with Heat Transfer Through a Flexible Channel : Numerical Study
Mekheimer K. S., Hasona W. M., El-Shekhipy A. A., Zaher A. Z.
Computational Methods in Science and Technology
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2017
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Vol. 23, No. 4
331--341
EN
Throughout this paper we investigate the effect of a vertical alternative current AC and heat transfer on the peristaltic flow of a couple stress dielectric fluid (blood flow model) in a symmetric flexible sinusoidal wavy channel. In order to solve the system of coupled non-linear partial differential equations, a program designed by Mathematica software "parametric NDSolve package" is used, which pertains to describe the momentum, the energy, and the electric potential that is obtained from using a regular perturbation method with small amplitude ratio. The numerical formulas of the mean velocity, the mean temperature, and the mean electric field are computed and the phenomenon of reflux (the mean flow reversal) is discussed. Moreover, the physical parameters effects of the problem on these formulas are described and illustrated graphically. The results reveal that the mean time averaged velocity is accelerated in the presence of AC electric field and decelerated for the couple stress fluid model (a special case of non-Newtonian fluid). The mean time averaged temperature is high in the presence of an alternative current AC electric field. This results model imply that the physiological role of AC electric field enhances blood circulation and this might help to eliminate the metabolic waste products and endogenous pains producing.
10
Content available Review of applied mathematical models for describing the behaviour of aqueous humor in eye structures
Dzierka M., Jurczak P.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 4
757--772
EN
In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.
11
Content available The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium
Rana G. C.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
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Vol. 62, nr 2
357--362
EN
In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality R ≤4π2/Pl (1 + 2π2F + PlQ/2ε) the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.
12
Content available remote Stagnation flow of couple stress nanofluid over an exponentially stretching sheet through a porous medium
Rehman A., Nadeem S., Malik M. Y.
Journal of Power Technologies
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2013
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Vol. 93, nr 2
122--132
EN
The present investigation is carried for the problem of boundary layer stagnation point flow and heat transfer of couple stress fluid containing nanoparticles and flowing over an exponentially stretching surface in a porous medium. The governing equations of couple stress fluid model for velocity, temperature and nanoparticle profiles are given under boundary layer approach. The nonlinear partial differential equations are simplified by using similar transformations. The analytical solutions of simplified equations are found with the help of homotopy analysis method. The convergence of the HAM solutions has been discussed by plotting - curves and also through homotopy pade approximation. The physical features of pertinent parameters have been discussed through graphs.
13
Content available remote Global stability for thermal convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity
Sunil, Chodhary S., Bharti P. K.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 2
583-602
EN
We show that the global nonlinear stability threshold for convection in a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that the linearized instability theory has captured completely the physics of the onset of convection. Then the effect of couple stress parameter, variable dependent viscosity and Darcy-Brinkman number on the onset of convection are also analyzed.
14
Content available remote Steady streaming effect on the flow of a couple stress fluid through a constricted annulus
Srinivasacharya D., Srikanth D.
Archives of Mechanics
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2012
|
Vol. 64, nr 2
137-137
EN
The oscillatory flow of an incompressible couple stress fluid through an annulus with mild constriction at the outer wall is considered. The mean pressure drops and the mean wall shear stress are calculated across the constricted region. The steady streaming effect on the flow is presented. The variations in the mean pressure drop and wall shear stress with the size of the catheter, the velocity of the catheter and couple stress fluid parameter, are studied through graphs.
15
Content available remote Flow and heat transfer of a quadratic stretching sheet in a Boussinesq-Stokes suspension
Sekhar G. N., Chethan A. S.
International Journal of Applied Mechanics and Engineering
|
2011
|
Vol. 16, no 4
1109-1128
EN
An analysis is carried out to study the flow and heat transfer in a couple stress fluid over a stretching sheet. The velocity of the sheet is taken as a quadratic polynomial of the distance from the sheet. This results in the manifestation of augmentation of flow in the direction transverse to the sheet. An analytical expression is obtained for velocity components as a function of the couple stress parameter and stretching related parameters. The heat transfer characteristic of a Boussinesq-Stokes suspension over a continuous stretching surface with internal heat generation/absorption is analyzed. Two cases are studied, namely (i) the sheet with prescribed surface temperature (PST-case) and (ii) the sheet with prescribed heat flux (PHF-case). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear differential equation is solved exactly. The solution and heat transfer characteristics are obtained in terms of Kummer's functions. The results have possible technological applications in the liquid-based systems involving stretchable materials.
16
Content available remote Combined effect of magnetic field and rotation on thermal stability of a couple-stress fluid heated from below in the presence of suspended particles
Aggarwal A. K., Makhija S.
International Journal of Applied Mechanics and Engineering
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2011
|
Vol. 16, no 4
931-942
EN
Thermal stability of a couple-stress fluid in the presence of suspended particles, magnetic field and rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, it is found that suspended particles have a destabilizing effect whereas rotation has a stabilizing effect. The magnetic field and couple-stresses have a stabilizing effect under certain conditions. In the absence of rotation, couple-stresses and magnetic field have a stabilizing effect on the system. It is found that the principle of exchange of stabilities is satisfied in the absence of the magnetic field.
17
Content available remote Mechanical parameters of a squeeze film step biobearing with a porous layer lubricated by a couple-stress fluid
Jurczak P.
International Journal of Applied Mechanics and Engineering
|
2010
|
Vol. 15, no 3
707-718
EN
The flow of a synovial fluid modelled as a couple-stress fluid in a squeeze film biological bearing with a permeable layer is considered. The biobearing is modelled by two rotational surfaces and the permeable layer is adhered to the curved impermeable surface. The flow in a squeeze film biobearing is considered with inertia and the Navier-Stokes and Poisson equations are uncoupled by using the Morgan-Cameron approximation. The flow of a couple-stress fluid in permeable layer satisfies the modified Darcy's law. As an example the biological bearing modelled by two parallel surfaces is discussed.
18
Content available remote Stability of superposed viscous - viscoelastic (couple-stress) fluids in the presence of variable magnetic field through porous medium
Kumar P., Sharma P.
International Journal of Applied Mechanics and Engineering
|
2008
|
Vol. 13, no 3
837-845
EN
The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying a couple-stress viscoelastic fluid through a porous medium is considered in the presence of a variable horizontal magnetic field. The stability analysis is carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. For the stable configuration, the system is found to be stable or unstable under certain conditions. However, for the unstable configuration, the magnetic field has got stabilizing effects.
19
Content available remote Flow of a couple-stress fluid in a curvilinear thrust bearing with one porous pad
Jurczak P., Walicka A., Walicki E., Michalski D.
Tribologia
|
2006
|
nr 3
63-75
EN
The flow of a couple stress fluid in the clearance of a curvilinear bearing with a porous pad is considered. The porous pad is connected with the upper impermeable rotating surface which approaches the lower fixed bearing surface. The Reynolds and Poisson equations are uncoupled by using the Morgan-Cameron approximation and a closed-form solution is obtained. As an example the bearing formed by two disks is discussed.
PL
W pracy rozważono przepływ płynu z naprężeniami momentowymi w krzywoliniowej szczelinie łożyska z porowatą wkładką. Porowata wkładka powiązana jest z górną nieprzepuszczalną wirującą powierzchnią, która zbliża się do dolnej nieruchomej powierzchni łożyska. Do rozwiązania równań Poissona oraz Reynoldsa wykorzystano przybliżenie Morgana-Camerona. Jako przykład rozpatrzono łożysko utworzone przez dwie kołowe tarcze.
20
Free convection effects on a perfectly conducting couple stress fluid
Ezzat M., Zakaria M., Samaan A., Abd-el Bary A.
Journal of Technical Physics
|
2006
|
Vol. 47, no 1
5-30
EN
We have introduced a magnetohydrodynamic model of boundary-layer equations for a perfectly conducting couple-stress fluid. This model is applied to study the effects of free convection currents with thermal relaxation on the flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface. The state space formulation developed in EZZAT [1] and [2j is introduced. The formulation is valid for problems with or without heat sources. The resulting formulation, together with the Laplace transform technique, are applied to a variety of problems. The solution to a thermal shock problem and to the problem of the flow in the whole space with a plane distribution of heat sources are obtained. It is also applied to a semispace problem with a plane distribution of heat sources located inside the fluid. A numerical method is employed for the inversion of the Laplace transforms. The effects of Grashof number, material parameters, Alfven velocity, relaxation time, Prandtl number and the permeability parameter on the velocity, the temperature and the angular velocity distributions are discussed. The effects of cooling and heating of a couple-stress fluid have also been discussed. Numerical results are given and illustrated graphically for the problems considered.
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