The impact of side walls on the MHD flow of a second-grade fluid through a porous medium

The magnetohydrodynamic flow through a porous medium of a second-grade fluid between two side walls induced by an infinite plate that exerts an accelerated shear stress to the fluid over an infinite plate is examined. Expressions for velocity and shear stress are determined with the help of integral transforms. In the absence of side walls, all the solutions that have been obtained are reduced to those corresponding to the motion over an infinite flat plate. The Newtonian solutions are also obtained as limiting case of the general solution. Finally, influence of magnetic and porosity parameter is graphically highlighted.

     

MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions

The flow of a radiative and electrically conducting micropolar nanofluid inside a porous channel is investigated. After implementing the similarity transformations, the partial differential equations representing the radiative flow are reduced to a system of ordinary differential equations. The subsequent equations are solved by making use of a well-known analytical method called homotopy analysis method (HAM). The expressions concerning the velocity, microrotation, temperature, and nanoparticle concentration profiles are obtained. The radiation tends to drop the temperature profile for the fluid. The formulation for local Nusselt and Sherwood numbers is also presented. Tabular and graphical results highlighting the effects of different physical parameters are presented. Rate of heat transfer at the lower wall is seen to be increasing with higher values of the radiation parameter while a drop in heat transfer rate at the upper wall is observed. Same problem has been solved by implementing the numerical procedure called the Runge–Kutta method. A comparison between the HAM, numerical and already existing results has also been made.

     

A finite element investigation of the flow of a Newtonian fluid in dilating and squeezing porous channel under the influence of nonlinear thermal radiation

The influence of nonlinear thermal radiation on the flow of a viscous fluid between two infinite parallel plates is investigated. The lower plate is solid, fixed and heated, while the upper is porous and capable of moving toward or away from the lower plate. The effects of nonlinear thermal radiation are incorporated in the energy equation by using Rosseland approximation. The similarity transformations have been used to obtain a system of ordinary differential equations. A finite element algorithm, known as Galerkin method, has been employed to obtain the solution of the resulting system of differential equations. It is observed that the radiation parameter Rd increases the temperature of the fluid in all the cases considered. Same is the case with temperature ratio parameter θ _w . The influence of the concerned parameters on the local rate of heat transfer is also displayed with the help of graphs.

     

MHD flow with heat and mass transfer of Williamson nanofluid over stretching sheet through porous medium

Microsystem Technologies - Two-dimensional hydromagnetic flow of an incompressible Williamson nanofluid over a stretching sheet in a porous media is examined during this work. Convective heat and...     

Investigation of surface roughness effects on fluid flow in passive micromixer

Surface roughness effects are dominant at microscale. In this study, microchannels are fabricated on Silicon substrate. The roughness morphology is modeled for the fabricated structure using Weierstrass-Mandelbrot function for self-similar fractals. A two dimensional model of hexagonal passive micromixer is analyzed with surface roughness present on inner walls of channels using parallel Lattice Boltzmann method, implemented on sixteen node cluster. The results are compared by simulating this micromixer structure using Navier–Stokes equations. The experimental results on the fabricated micromixers are also presented. The effects of relative roughness, fractal dimension and Reynolds number are discussed on laminar flow in hexagonal passive micromixers. The study concludes the importance of modeling surface roughness effect for better mixing efficiency.     

Exact and numerical solutions for unsteady heat and mass transfer problem of Jeffrey fluid with MHD and Newtonian heating effects

The combined heat and mass transfer of unsteady magnetohydrodynamic free convection flow of Jeffrey fluid past an oscillating vertical plate generated by thermal radiation and Newtonian heating is investigated. The incompressible fluid is electrically conducting in the presence of a uniform magnetic field which acts in a direction perpendicular to the flow. Mathematical formulation of the problem is modeled in terms of partial differential equations with some physical conditions. Some suitable non-dimensional variables are introduced to transform the system of equations. The dimensionless governing equations are solved analytically for exact solutions using the Laplace transform technique. Numerical solutions of velocity are obtained via finite difference scheme. Graphical results for velocity, temperature and concentration fields for various pertinent parameters such as material parameter of Jeffrey fluid \(\lambda_{1}\), dimensionless parameter of Jeffrey fluid \(\lambda\), Newtonian heating parameter \(\xi\), phase angle \(\omega t\), Grashof number \(Gr\), modified Grashof number \(Gm\), Hartmann number or magnetic parameter \(Ha\), Prandtl number \(Pr\), radiation parameter \(Rd\), Schimdt number \(Sc\) and dimensionless time \(t\) are displayed and discussed in detail. This study showed that the magnetic field resists the fluid flow due to the Lorentz force, whereas the thermal radiation and Newtonian heating parameters lead to the enhancement of velocity and temperature fields. Present results are also compared with the existing published work, and an excellent agreement is found.

     

Thermophoresis and MHD mixed convection three-dimensional flow of viscoelastic fluid with Soret and Dufour effects

Heat and mass transfer effects in three-dimensional mixed convection flow of viscoelastic fluid over a stretching surface with convective boundary conditions are investigated. The fluid is electrically conducting in the presence of constant applied magnetic field. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. First order chemical reaction effects are also taken into account. By using the similarity transformations, the governing boundary layer equations are reduced into the ordinary differential equations. The transformed boundary layer equations are computed for the series solutions. Dimensionless velocity, temperature, and concentration distributions are shown graphically for different values of involved parameters. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. It is found that the behaviors of viscoelastic, mixed convection, and concentration buoyancy parameters on the Nusselt and Sherwood numbers are similar. However, the Nusselt and Sherwood numbers have qualitative opposite effects for Biot number, thermophoretic parameter, and Soret-Dufour parameters.

     

Viscosity effects on flows of generalized Newtonian fluids through curved pipes

This paper is concerned with the application of finite element methods to obtain solutions for steady fully developed generalized Newtonian flows in a curved pipe of circular cross-section and arbitrary curvature ratio, under a given axial pressure gradient.     

Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium

The technique of the state space approach and the inversion of the Laplace transformation method are applied to the non-dimensional equations of an unsteady laminar free convection flow of an incompressible, viscous, electrically conducting dusty fluid through a porous medium, which is bounded by an infinite vertical plane surface of constant temperature, in the presence of a constant magnetic field. The technique is applied to the thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of the dimensionless temperature, velocity, and induced magnetic and electric field distributions are given and illustrated graphically. The effects of the material’s parameters such as the Grashof number, the Prandtl number, the permeability parameter, the mass concentration of the particle phase, the Alfven velocity, the thermal relaxation time and the relaxation time of the particle phase on the temperature, velocity and the induced magnetic and electric fields are discussed.     

Slip effects on MHD mixed convection stagnation point flow of a micropolar fluid towards a shrinking vertical sheet

In the present study, the effects of partial slip on steady boundary layer stagnation point flow of an electrically conducting micropolar fluid impinging normally towards a shrinking sheet in the presence of a uniform transverse magnetic field is investigated. A similarity transformation technique is adopted to obtain the self similar ordinary differential equations and then solved numerically using symbolic software MATHEMATICA 7.0. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed through graphs and tables. Both cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed.     

Numerical study on two-phase flow through fractured porous media

Based on the flux equivalent principle of a single fracture,the discrete fracture concept was developed,in which the macroscopic fractures are explicitly described as(n-1)dimensional geometry element.On the fundamental of this simplification,the discrete-fractured model was developed which is suitable for all types of fractured porous media.The principle of discrete-fractured model was introduced in detail,and the general mathematical model was expressed subsequently.The fully coupling discrete-fractured ma...     

Free boundary problems in the theory of fluid flow through porous media: A numerical approach

In this paper we study from the numerical point of view elliptic free boundary problems in the theory of fluid flow through porous media by a new method. Research supported by C.N.R. in the frame of the collaboration between L. A. N. of Pavia and E. R. A. 215 of C. N. R. S. and of Paris University and carried out also with the cooperation of the Division C. E. T. I. S. of C.C.R. Euratom Ispra.     

Wavelet strategy for flow and heat transfer in CNT-water based fluid with asymmetric variable rectangular porous channel

In the present work, the characteristics of physical model unsteady nanofluid flow and heat transfer in an asymmetric porous channel are analyzed numerically using wavelet collocation method. Using similarity transformation, unsteady two-dimensional flow model of nanofluid in a porous channel through expanding or contracting walls has been transformed into a system of nonlinear ordinary differential equations (ODEs). Then, the obtained nonlinear system of ODEs is solved via wavelet collocation method. The effect of various emerging parameters, such as nanoparticle volume fraction, Reynolds number (Re), and expansion ratio have been analyzed on velocity and temperature profiles. Numerical results have been presented in form of figures and tables. For some special cases, the obtained numerical results are compared with exact one and found that the results are good in agreement with exact solutions.

     

Numerical study of partial slip on the MHD flow of an Oldroyd 8-constant fluid

The steady flow of an Oldroyd 8-constant magnetohydrodynamic (MHD) fluid is considered for a cylindrical geometry when the no-slip condition between the cylinders and the fluid is no longer valid. The inclusion of the partial slip at boundaries modifies the governing boundary conditions, changing from a linear to a non-linear situation. The non-linear differential equation along with non-linear boundary conditions governing the flow has been solved numerically using a finite-difference scheme in combination with an iterative technique. The solution for the no-slip condition is a special case of the presented analysis. A critical assessment is made for the cases of partial slip and no-slip conditions.     

Adjoint-based optimization of multi-phase flow through porous media – A review

The recovery of oil from subsurface reservoirs often requires the injection of water or gas to maintain reservoir pressure and to displace the oil from injection to production wells. The design of an economically optimal recovery strategy is usually based on ’reservoir simulation’, i.e. large-scale numerical simulation of the flow of multi-phase fluids through strongly heterogeneous porous media with uncertain coefficients. Control of the recovery process is through prescribing time-varying pressures or flow rates in the wells. Efficient methods to optimize the recovery strategy make use of gradients of an economic objective function with respect to the well controls at every time step. These can be obtained efficiently with the aid of adjoint-based techniques. Constraints, in particular those that involve states (reservoir pressures or saturations) or outputs (measured well pressures or rates) require special treatment. Uncertainty in the coefficients can be incorporated through robust optimization over an ensemble of models. The limited controllability of the reservoir states offers scope for reduced-order modeling using techniques like proper orthogonal decomposition. ‘Closed-loop’ optimization can be performed through frequent repetition of the optimization during the producing life of the field in combination with updating the of the model coefficients based on production measurements. Moreover, an emerging technology is the operational use of model-based optimization which requires a combination of long-term and short-term objectives through multi-level optimization strategies.     

A new analytical study of MHD stagnation-point flow in porous media with heat transfer

The similarity solution for the MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium gives a system of nonlinear partial differential equations. These equations are solved analytically by using a novel analytical method (DTM-Padé technique which is a combination of the differential transform method and the Padé approximation). This method is applied to give solutions of nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the Prandtl number, permeability parameter, Hartmann number and suction/blowing parameter on the velocity and temperature profiles.     

Numerical analysis of non Newtonian fluid flow in a low voltage cascade electroosmotic micropump

In microfluidic devices, many fluids have non-Newtonian behaviors, especially biofluids. The viscosity of these fluids mostly depends on the shear rate. Sometimes the non-Newtonian fluids should be transferred by micropumps in lab-on-chip devices. Previous researchers investigated the flow rate in simple electroosmotic flow micropumps which have a simple channel geometry. In the present study, the effects of non-Newtonian properties of fluid in a low voltage cascade electroosmotic micropump are numerically investigated using the power law model. The micropump is modeled in two dimensional with one symmetric step and has a more complex geometry than previous studies. The numerical results show that, the non-Newtonian behavior of fluid affects flow rate in the micropump. The flow rate decreases if the fluid is dilatant. Also, it increases if the fluid is pseudoplastic. Moreover, the pressure which is needed to stop the electroosmotic flow rate in the micropump is calculated. Results show that, the back pressure has a slight change as the fluid has non-Newtonian behavior.