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.     

Soret and MHD effects on bioconvection wall jet flow of nanofluid containing gyrotactic microorganisms

Various applications of bioconvection phenomena in the field of medicine and biotechnology boost us to present the study of laminar wall jet flow in this specific direction. For the purpose, we have considered nanofluid containing gyrotactic microorganisms in the presence of normally applied magnetohydrodynamic forces along with Soret effects. Boundary layer approximation and similarity transformation are utilized to convert governing equations into ordinary differential equations. Influence of different emerging parameters on velocity, temperature and concentration profiles of solute, nanoparticle and motile microorganisms has been investigated. The role of physical quantities like Nusselt number, Sherwood number and density number of microorganisms is also highlighted. Increase in Nusselt number and density number of motile microorganism is observed for incremental values of bioconvection Peclet number. Soret number reflects increasing effect on Nusselt number and decreasing effect on Sherwood number because solute diffusion faces resistance due to higher values of Soret number and in return decreases rate of mass transfer. Also bioconvection Rayleigh number imposes decreasing effect on density number of the motile microorganisms.

     

Thermal convection of viscoelastic fluid with Biot boundary conduction

Two-dimensional unsteady natural convection of a non-linear fluid represented by Criminale–Erickson–Filbey (CEF) fluid model in a square cavity is studied in the fluid for Rayleigh–Benard convection case. The governing vorticity and energy transport equations are solved numerically either simple explicit and ADI methods, respectively. The two-dimensional convective motion is generated by buoyancy forces on the fluid in a square cavity, when the vertical walls are either perfectly insulated or conducted with Biot boundary conduction condition. The contributions of the elastic and shear dependent characteristics of the liquid to the non-Newtonian behaviour are investigated on the temperature distribution and heat transfer. The effect of the Weissenberg (which is a measure of the elasticity of the fluid), Rayleigh and Biot numbers on the temperature and streamline profiles are delineated and this has been documented first time for the viscoelastic fluid.     

Falkner–Skan wedge flow of a power-law fluid with mixed convection and porous medium

This article describes the mixed convection flow of a non-Newtonian fluid past a wedge. An incompressible power-law fluid occupies the porous space. The arising mathematical problem has been solved by homotopy analysis method (HAM). Convergence of the derived solution is checked. The local skin friction coefficient and Nusselt number are also discussed.     

Thermal convection of MHD Blasius and Sakiadis flow with thermal convective conditions and variable properties

Microsystem Technologies - A theoretical study on the effect of magnetohydrodynamic field on the classical Blasius and Sakiadis flows of heat transfer characteristics with variable conditions and...     

Finite-element approximation of viscoelastic fluid flow with slip boundary condition

We present a theoretical study of a creeping, steady-state, isothermal flow of a viscoelastic fluid obeying an Oldroyd-type constitutive law with slip boundary condition. The slip boundary condition is appropriate for problems that involve free boundaries and other examples where the usual no-slip condition u = 0 is not valid, such as fiber spinning and microfluidics.First, we study the Newtonian problem with slip boundary condition where the viscoelastic stress is added into the list of unknowns. In addition, the normal viscoelastic stress component associated with the slip boundary condition is introduced. In order to balance its effects, a second inf-sup condition is proven.To treat the discrete case, we assume that the continuous solution of the non-Newtonian problem exists and is small and smooth. Approximating the extra stress, velocity, pressure, and normal viscoelastic stress component via P₁ discontinuous, P₂ continuous, P₁ continuous, and P₀ discontinuous elements, respectively, yields a stable finite-element scheme. Finally, via a fixed point argument, we establish the existence of an approximate solution and derive error estimates.     

Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators

The magnetohydrodynamic (MHD) flow has been concerned widely for its widespread adoption in the field of astrophysics, electronics and many other industries over the years. The purpose of this article is to introduce the variable and distributed order space fractional models to characterize the MHD flow and heat transfer of heterogeneous viscoelastic fluids in a parallel plates. Based on the central difference approximation of Riesz space fractional derivative, the Crank–Nicolson difference scheme for the governing equations is established, and the effectiveness of the algorithm is verified by two numerical examples. We examine the effects of fractional-order model parameters on the velocity and temperature, our investigation indicates that for the constant fractional model, the larger the fractional order parameter, the smaller the velocity and temperature. The variable space fractional method can be used to describe dynamic behavior with time and space dependence, while the distributed space fractional model can describe various phenomena in which the number of differential orders varies over a certain range, characterizing their complex processes over space, and it is also more suitable for simulating the fluid flow and thermal behavior of complex viscoelastic magnetic fluid.     

Investigation of MHD effects on micropolar–Newtonian fluid flow through composite porous channel

Microfluidics and Nanofluidics - We discuss the rotational force-induced flow dynamics of a viscoplastic fluid in a polymeric layer grafted soft microfluidic channel. In this analysis, the...     

Lie-group similarity solution and analysis for fractional viscoelastic MHD fluid over a stretching sheet

Lie-group is introduced for studying boundary layer flow and heat transfer of fractional viscoelastic MHD fluid over a stretching sheet. Fractional boundary layer equations, based on Riemann–Liouville operators, are reduced and solved numerically by Grünwald scheme approximation. Results show that the skin friction and thermal conductivity are strongly affected by magnetic field parameter, fractional derivative and wall stretching exponent. The bigger of the fractional order derivative leads to the faster velocity of viscoelastic fluids near the plate but not to hold near the outer flow. Skin friction increases with increase of magnetic field parameter $M$, while the heat transfer decreases. For wall stretching exponent parameter $\beta =1.0$, the velocity profile decreases with the increase of similarity variable $\eta$. However, for $\beta =?1.5$, the velocity profile increases initially and then decreases afterwards with the biggest velocity at the interior of boundary layer.     

Magnetohydrodynamic three-dimensional nonlinear convective flow of viscoelastic nanofluid with heat and mass flux conditions

The present research focuses on three-dimensional nonlinear convective flow of viscoelastic nanofluid. Here, the flow is generated due to stretching of a impermeable surface. The phenomenon of heat transport is analyzed by considering thermal radiation and prescribed heat flux condition. Nanofluid model comprises of Brownian motion and thermophoresis. An electrically conducting fluid is accounted due to consideration of an applied magnetic field. The dimensionless variables are introduced for the conversion of partial differential equations into sets of ordinary differential systems. The transformed expressions are explored through homotopic algorithm. Behavior of different dimensionless parameters on the non-dimensional velocities, temperature and concentration are scrutinized graphically. The values of skin friction coefficients, Nusselt and Sherwood numbers are also calculated and elaborated. It is visualized that the heat transfer rate increases with Prandtl number and radiation parameter is higher.

     

Simulation of three-dimensional nonideal MHD flow at high magnetic Reynolds number

A conservative TVD scheme is adopted to solve the equations governing the three-dimensional flow of a nonideal compressible conducting fluid in a magnetic field.The eight-wave equations for magnetohydrodynamics(MHD) are proved to be a non-strict hyperbolic system,therefore it is difficult to develop its eigenstructure.Powell developed a new set of equations which cannot be numerically simulated by conservative TVD scheme directly due to its non-conservative form.A conservative TVD scheme augmented with a ne...     

Approximation of time-dependent,multi-component,viscoelastic fluid flow

In this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow. The Oldroyd B constitutive equation is used to model the viscoelastic stress. For the discretization, time derivatives are replaced by backward difference quotients, and the non-linear terms are linearized by lagging appropriate factors. The modeling equations for the individual fluids are combined into a single system of equations using a continuum surface model. The numerical approximation is stabilized by using an SUPG approximation for the constitutive equation. Under a small data assumption on the true solution, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of the mesh parameter h, the time discretization parameter Δt, and the SUPG coefficient ν are also derived. Numerical simulations of viscoelastic fluid flow involving two immiscible fluids are also presented.     

Rotating flow of viscoelastic fluid with nonlinear thermal radiation: a numerical study

This work is concerned with the numerical solution for rotating viscoelastic flow developed by an exponentially stretching impermeable surface. Temperature at the sheet is also assumed to vary exponentially. Energy equation involves the novel nonlinear radiation heat flux term. Suitable transformations are utilized to nondimensionalize the relevant boundary layer equations. Numerical solutions are developed by means of standard shooting approach. The results demonstrate that both rotation and viscoelasticity serve to reduce the hydrodynamic boundary layer thickness. Temperature function has a special S-shaped profile when the difference between wall and ambient temperatures is sufficiently large. Heat transfer coefficient at the surface diminishes when rotation parameter is increased. Current numerical computations are consistent with those of the existing studies in the literature.

     

Mixed finite element method for analysis of viscoelastic fluid flow

In the present paper, numerical analysis of incompressible viscoelastic fluid flow is discussed using mixed finite element Galerkin method. Because Maxwellian viscoelasticity is assumed as the constitutive equation, stress components could not be eliminated from the governing equation system. Because of this, mixed finite element method is utilized to discretize the basic equations. For the solution procedures to solve discretized equation system, Newton-Raphson method for steady flow and perturbation method for unsteady flow is employed. As the numerical examples, comparison was made on the finite element computational results between by direct method and by mixed method. Effects of the viscoelasticity is analyzed for the flows at Reynold's numbers 30, 50 and 70.     

Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls: Some applications to haemodynamics

Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter’s liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agreement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.     

Velocity and temperature slip effects on squeezing flow of nanofluid between parallel disks in the presence of mixed convection

Velocity and temperature slip effects on squeezing flow of nanofluid between parallel disks in the presence of mixed convection is considered. Equations that govern the flow are transformed into a set of differential equations with the help of transformations. For the purpose of solution, homotopy analysis method is used. The BVPh2.0 package is utilized for the said purpose. Deviations in the velocity, temperature and the concentration profiles are depicted graphically. Mathematical expressions for skin friction coefficient, Nusselt and the Sherwood numbers are derived and the variations in these numbers are portrayed graphically. From the results obtained, we observed that the coefficient of skin friction increases with increase in Hartmann number M for the suction flow (A > 0), while in the blowing flow (A < 0) a fall is seen with increasing M. However, for rising values of velocity parameter β the effect of skin friction coefficient is opposite to that accounted for M. Variations in thermophoresis parameter N _T and thermal slip parameter γ give rise in Nusselt number for both the suction and injection at wall. For both the suction and injection at wall, Sherwood number gets a rise with growing values of Brownian motion parameter N _B, while a drop is seen in Sherwood number for increasing values of thermophoresis parameter N _T. For the sake of comparison, the same problem is also solved by employing a numerical scheme called Runge–Kutta–Fehlberg (RKF) method. Results thus obtained are compared with existing ones and are found to be in agreement.

     

Vortex instability of MHD natural convection flow over a horizontal plate in a porous medium

The present work investigates the vortex instability of a horizontal MHD natural convection boundary layer flow in a saturated porous medium including the radiation effect. The numerical results are solves by Keller-Box method incorporated with linear stability theory. The velocity and temperature profiles, local Nusselt number, as well as instability parameters for magnetic parameter M ranging from 0 to 2 and radiation parameter R ranging from 0 to 0.03 are presented. Numerical results showed that, as magnetic parameter M increases or radiation parameter R decreases, the heat transfer rate decrease. In addition, the magnetic effect destabilizes the flow to vortex mode of disturbance, while the radiation effect stabilizes it.