Peristaltic flow of couple stress fluid through uniform porous medium

Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical anal- ysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.

Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.

Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition

This paper studies the Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of the slip boundary condition. The motion of the wall is governed by the sinusoidal wave equation. The analytical and numerical solutions for the axial velocity, the micro-polar vector, the stream function, the pressure gradient, the friction force, and the mechanical efficiency are obtained by using the lu- brication theory under the low Reynolds number and long wavelength approximations. The impacts of the emerging parameters, such as the coupling number, the micro-polar parameter, the slip parameter on pumping characteristics, the friction force, the velocity profile, the mechanical efficiency, and the trapping phenomenon are depicted graphically. The numerical results infer that large pressure is required for peristaltic pumping when the coupling number is large, while opposite behaviors are found for the micro-polar parameter and the slip parameter. The size of the trapped bolus reduces with the increase in the coupling number and the micro-polar parameter, whereas it blows up with the increase in the slip parameter.

3D radiative convective flow of ZnO-SAE50nano-lubricant in presence of varying magnetic field and heterogeneous reactions

A numerical simulation is presented to investigate the effect of an exponentially varying magnetic field on three dimensional flow of Zinc Oxide-Society of Automotive Engineers 50 nanolubricant(ZnO-SAE50nano-lubricant)past a stretching sheet.Subsequently the impact of homogenous and heterogeneous reactions on the flow of nanolubricant concerned has also taken into account.The study has been strengthened by introducing the convection mechanism and the effect of thermal radiation.Similarity transformations are employed to transform the set of partial governing equations into the set of ordinary differential equations.The suitable boundary conditions are used to obtain the numerical solution.The numerical results are simulated using Matlab bvp4c solver and validated with the existing results.The flow characteristics,thermal characteristics,nanoparticle concentration and some non-dimensional numbers are computed under the influence of the pertinent parameters.The valuable outcome of the current study is that augmented magnetic field strength is the root cause of diminishing axial as well as transverse velocities and growing trend of fluid temperature.Also,the coeffi-cients of homogenous and heterogeneous reactions are boons for ascending concentration boundary layer.

Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids

A theoretical study is conducted for magnetohydrodynamic pumping of electroconductive couple stress physiological liquids(e.g.blood)through a two-dimensional ciliated channel.A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory.A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow.A transverse static magnetic field is imposed transverse to the channel length.The Stokes’couple stress(polar)rheological model is utilized to characterize the liquid.The normalized two-dimensional conservation equations for mass,longitudinal and transverse momentum are reduced with lubrication approximations(long wavelength and low Reynolds number assumptions)and feature a fourth order linear derivative in axial velocity representing couple stress contribution.A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame.No slip conditions are imposed at the channel walls.The emerging linearized boundary value problem is solved analytically and expressions presented for axial(longitudinal)velocity,volumetric flow rate,shear stress function and pressure rise.The flow is effectively controlled by three geometric parameters,viz cilia eccentricity parameter,wave number and cilia length and two physical parameters,namely magnetohydrodynamic(MHD)body force parameter and couple stress non-Newtonian parameter.Analytical solutions are numerically evaluated with MATLAB software.Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length,couple stress and magnetic parameters,with significant flattening of profiles with the latter two parameters.Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length,in the channel core region.Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width.The pressure-flow rate relationship is confirmed to be inversely linear and pumping,free pumping and augmented pumping zones are all examined.Bolus trapping is also analyzed.The study is relevant to MHD biomimetic blood pumps.