MHD flow of a third grade fluid in a porous half space with plate suction or injection: An analytical approach

Aziz, Arshad; Aziz, Taha

doi:10.1016/j.amc.2012.04.006

Cited by 36 publications

(33 citation statements)

References 11 publications

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“…Half Space with Plate Suction or Injection [48]. The modelling and solution of the unsteady flow of an incompressible thirdgrade fluid over a porous plate within a porous medium were performed by A. Aziz and T. Aziz [48].…”

Section: Mhd Flow Of a Third-grade Fluid In A Porousmentioning

confidence: 99%

“…The modelling and solution of the unsteady flow of an incompressible thirdgrade fluid over a porous plate within a porous medium were performed by A. Aziz and T. Aziz [48]. Lie group theory was employed to find the symmetries of the model equation.…”

Section: Mhd Flow Of a Third-grade Fluid In A Porousmentioning

confidence: 99%

“…The method of solution employed in [1] depends on the application of a one-parameter group of transformations to the partial differential equation (48). The one-parameter group, which transforms the PDE (48) and the boundary conditions (49), is of the form [1]…”

Section: Solution Of the Rayleigh Problem For A Power-law Nonnewtoniamentioning

confidence: 99%

“…The one-parameter group, which transforms the PDE (48) and the boundary conditions (49), is of the form [1]…”

Section: Solution Of the Rayleigh Problem For A Power-law Nonnewtoniamentioning

confidence: 99%

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Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

Aziz

Mahomed

2017

Mathematical Problems in Engineering

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The present review is intended to encompass the applications of symmetry based approaches for solving non-Newtonian fluid flow problems in various physical situations. Works which deal with the fundamental science of non-Newtonian fluids that are analyzed using the Lie group method and conditional symmetries are reviewed. We provide the mathematical modelling, the symmetries deduced, and the solutions obtained for all the models considered. This survey includes, as far as possible, all the articles published until 2015. Only papers published by a process of peer review in archival journals are reviewed and are grouped together according to the specific non-Newtonian models under investigation.

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Section: Mhd Flow Of a Third-grade Fluid In A Porousmentioning

confidence: 99%

Section: Mhd Flow Of a Third-grade Fluid In A Porousmentioning

confidence: 99%

Section: Solution Of the Rayleigh Problem For A Power-law Nonnewtoniamentioning

confidence: 99%

“…The one-parameter group, which transforms the PDE (48) and the boundary conditions (49), is of the form [1]…”

Section: Solution Of the Rayleigh Problem For A Power-law Nonnewtoniamentioning

confidence: 99%

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Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

Aziz

Mahomed

2017

Mathematical Problems in Engineering

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“…18 Shahzad et al 19 studied the incompressible flow of fourth-order fluid in a porous half space; the flow was caused by the oscillations of porous plate in its own plane. Unsteady MHD flow of an incompressible third grade fluid within a porous medium was modeled and analyzed by Aziz et al 20 In addition, they have proposed the group invariant solutions for the unsteady MHD flow of third-grade fluid through a porous media. 21 Non-Newtonian fluids get more attention because of their vigorous use in industrial applications, particularly in chemical engineering processes and polymer processing.…”

Section: Introductionmentioning

confidence: 99%

On the double diffusive convection flow of Eyring-Powell fluid due to cone through a porous medium with Soret and Dufour effects

Khan

Sultan

2015

AIP Advances

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This paper devotedly study the double diffusive Darcian convection flow of Eyring-Powell fluid from a cone embedded in a homogeneous porous medium with the effects of Soret and Dufour. Arising set of non-linear partial differential equations are transformed through a suitable self-similar transformation into a set of nonlinear ordinary differential equations. Further, the numerical and the analytical solutions of the governing equations are elucidated by using numerical method as well as non-perturbation scheme. Numerical values are presented through tables for the skin friction coefficients, Nusselt number and Sherwood number. The obtained results are validated by comparing the analytical results with previously published results obtained by bvp4c for the numerical values of physical quantities. The effect of various parameters on the velocity, temperature and concentration profiles is discussed and also shown graphically.

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Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

Vasu

Dubey

Bég

2019

Heat Trans. Asian Res.

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The present study considers two-dimensional mathematical modeling of non-Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second-grade differential viscoelastic constitutive model is adopted for blood to mimic non-Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature.The governing equations are an extension of the Navier-Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid-independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (λ 1 ), thermophoresis parameter (N t ), Brownian motion parameter (N b ), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin-friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano-drugs in magnettargeted treatment of stenosed arterial disease. K E Y W O R D Sarterial stenosis, finite element method, magnetohydrodynamics, nano-drugs, non-Newtonian blood flow, thermophoresis, Vogel's model

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MHD flow of a third grade fluid in a porous half space with plate suction or injection: An analytical approach

Cited by 36 publications

References 11 publications

Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

Applications of Group Theoretical Methods to Non‐Newtonian Fluid Flow Models: Survey of Results

On the double diffusive convection flow of Eyring-Powell fluid due to cone through a porous medium with Soret and Dufour effects

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

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