Slip effects on the peristaltic transport of MHD fluid with variable viscosity

This Letter concerns with the peristaltic analysis of MHD viscous fluid in a two-dimensional channel with variable viscosity under the effect of slip condition. A long wavelength and low Reynolds number assumption is used in the problem formulation. An exact solution is presented for the case of hydrodynamic fluid while for magnetohydrodynamic fluid a series solution is obtained in the small power of viscosity parameter. The salient features of pumping and trapping phenomena are discussed in detail through the numerical integration. It is noted that an increase in the slip parameter decreases the peristaltic pumping region. Moreover, the size of trapped bolus decreases by increasing the slip parameter.     

Axisymmetric expanding universe with viscous fluid and heat flow

A conformally flat axisymmetric non-static metric is shown to satisfy the Einstein equations corresponding to a viscous fluid and non-zero heat flow.     

A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method

In this Letter, we considered a numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube using Adomian decomposition method and a modified form of this method. The axial velocity is obtained in a closed form. Comparison is made between the results obtained by only three terms of Adomian series with those obtained previously by perturbation technique. It is observed that only few terms of the series expansion are required to obtain the numerical solution with good accuracy.     

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.     

Nested Cartesian grid method in incompressible viscous fluid flow

In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow–structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier–Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively/accurately simulating various complex flows past different forms of immersed boundaries is extensively demonstrated, in which the nested Cartesian grid method was suitably combined together with the fractional-step algorithm to speed up the solution procedure.     

Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity

In the present study, we have analyzed the effects of variable viscosity, variable thermocapillarity on the flow and heat transfer in a thin film on a horizontal porous shrinking sheet through a porous medium. The unsteady boundary layer equations for momentum and thermal energy are simplified by using similarity transformations. The resulted, coupled nonlinear differential equations are solved by homotopy analysis method. The results are presented graphically to interpret various physical parameters appearing in the problem.     

Analytical solution of navier-stokes flow of a viscous compressible fluid

An analytical procedure is proposed to study the flow of viscous compressible continuous fluids.     

Unsteady flow of a viscous incompressible fluid past a porous plate with constant suction

An exact solution of the flow of an incompressible viscous fluid past an infinite porous plate has been derived on taking into account a step-change in suction velocity. It has been observed that the skin-friction decreases with increasingS, the suction parameter.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

Hydromagnetic flow of a variable viscosity nanofluid in a rotating permeable channel with hall effects

The flow, heat and mass transfer of water-based nanofluid are examined between two horizontal parallel plates in a rotating system. The effects of Brownian motion, thermophoresis, viscosity and Hall current parameters are considered. The governing partial differential equations are reduced to ordinary differential equations that are then solved numerically using the Runge–Kutta–Fehlberg method. Validation of numerical solution is achieved with an exact solution of primary velocity and found to be in good agreement. Results show that both surfaces experience opposite behavior regarding skin friction, Nusselt and Sherwood numbers in both primary and secondary flows. These physical quantities depend upon dimensionless parameters and numbers.     

A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity

The steady flow and heat transfer of an electrically conducting fluid with variable viscosity and electrical conductivity between two parallel plates in the presence of a transverse magnetic field is investigated. It is assumed that the flow is driven by combined action of axial pressure gradient and uniform motion of the upper plate. The governing nonlinear equations of momentum and energy transport are solved numerically using a shooting iteration technique together with a sixth-order Runge-Kutta integration algorithm. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that the combined effect of magnetic field, viscosity, exponents of variable properties, various fluid and heat transfer dimensionless quantities and the electrical conductivity variation, have significant impact on the hydromagnetic and electrical properties of the fluid.     

Magnetized nanofluid flow of ferromagnetic nanoparticles from parallel stretchable rotating disk with variable viscosity and thermal conductivity

The current work aims at studying a constructed mathematical model with an examination of heat transfer in water-based nanofluids containing ferromagnetic nanoparticles flowing between parallel stretchable spinning discs with variable viscosity influence and variable conductivity. The nonlinear coupling of the ordinary differential equations of the momentum and energy equation with the partial differential equations based on the Navier-Stokes equation employing some influential similarity transformations. The transformed system of ordinary differential equations has been solved through the Chebyshev spectral collocation procedure (CSCP). The numerical results for the velocity and temperature distributions are shown in terms of graphical presentations. The existing available literature was utilized to test for validation of the numerical findings. The outcomes demonstrate that the stretching of the lower and upper disks and spinning parameters strengthens the impetus boundary layer and diminished the temperature boundary layer, whilst the variable thermal conductivity improved the convective and conductive strength of the ferromagnetic nanoparticles considered, and the Fe₃O₄ nanofluid displays a higher thermal conductivity strength than the Mn-ZnFe₂O₄ nanofluid.     

Sonically produced heat in a fluid with bulk viscosity and shear viscosity

In a viscous fluid, sound produces heat in a spatial pattern which, in general, depends on the relative magnitudes of the shear viscosity coefficient eta and the bulk viscosity coefficient B'. It is well known that when the particle velocity components ui relative to Cartesian coordinates xi are given for an arbitrary sound field, or any field of flow, the volume rate of heat production qv can be determined from a dissipation function in the form B'T1 + eta T2. Here, T1 and T2 are quadratic functions involving derivatives of the type delta ui/delta xj. In this paper, examples are discussed for continuous monofrequency sound fields, including crossed plane waves, as well as focused and unfocused fields. In these examples, spatial distributions of the time-averaged quantity [qv] for media in which the loss mechanism is primarily bulk viscosity are compared to those for media in which shear viscosity dominates.     

Effect of viscous dissipation on temperature,viscosity, and flow parameters while filling a channel

A non-steady, non-isothermal flow while filling a channel is studied with account for dissipation of mechanical energy, dependency of viscosity on temperature, and existence of free surface. Simulation results are presented for fields of temperature, viscosity, dynamic and kinematic parameters of flow as a function of key dimensionless parameters.     

Analysis of peristaltic flow of Jeffrey six constant nano fluid in a vertical non-uniform tube

Peristaltic flow of non-Newtonian nano fluid through a non-uniform surface has been investigated in this paper. The fluid motion along the wall of the surface is caused by the sinusoidal wave traveling with constant speed. The governing equations are converted into cylindrical coordinate system and assuming low Reynolds number and long wave length partial differential equations are simplified. Analytically solutions of the problem are obtained by utilizing the homotopy perturbation method (HPM). In order to insight the impact of embedded parameters on temperature, concentration and velocity some graphs are plotted for different peristaltic waves. At the end, some observations were made from the graphical presentation that velocity, pressure rise and nano particle concentration are increasing function of thermophoresis parameter N_t while temperature and frictional forces show opposite trend.     

Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity–pressure-Lagrange multiplier algebraic system of the discrete Navier–Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5–13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.     

Bianchi type-II cosmological model with viscous fluid

A spatially homogeneous and locally rotationally symmetric Bianchi type-II cosmological model under the influence of both shear and bulk viscosity has been studied. Exact solutions are obtained with a barotropic equation of state (p=) and considering the linear relationships between, ², and ², which represent the fluid density, the expansion, and the shear scalars, respectively. Special cases with vanishing bulk viscosity coefficients and with the perfect fluid in the absence of viscosity have also been studied. The formal appearance of the solutions is the same for both the viscous as well as the perfect fluids. The difference is only in choosing a constant parameter which appears in the solutions. In the cases of either a fluid with bulk viscosity alone or a perfect fluid, the barotropic equation of state is no longer an additional assumption to be imposed; rather it follows directly from the field equations.