Oscillatory channel flow for non-Newtonian fluid

Oscillatory flow of second grade fluid in a straight rectangular duct

Primary Cilia is appendage that extrudes from cell surface into the extracellular matrix .These organelles play a sensor role for mechanical stimulation in the cell and due to stretch ion channels in its base, play critical role in induce osteogenic differentiation of stem cells. Primary cilia deflected under fluid flow passing through the surface of the cell, which deflection causes tensile ion channels to be opened. In this study, cilia is assumed as linear elastic. The innovative aspect of this research is exerting of oscillatory fluid flow to the primary cilia and evaluating the response of cilia to the fluid flow. The results show that under conditions of exerting the oscillatory fluid flow, maximum strain occur in the base of the cilia which is experienced by tensile ion channels, is 0.5 and in the condition of steady flow is 0.3, Accordingly, mechanical stimuli are sensed by the tensile ionic channels during oscillatory flow higher than steady flow. osteogenic differentiation of stem cells, in addition, the result showed that by using the oscillatory fluid flow the mechanical stimulation better senses by cilia and It is anticipated that exerting oscillatory fluid flow facilitate osteogenic differentiation of stem cell.

Mathematical Model of Flow in a Tube with an Overlapping Constriction and Permeability

This paper aims to investigate a boundary layer flow with heat and mass transfer of a special third grade fluid over a stretchable surface in a parallel free stream. Using the similarity variables generated by the Lie group analysis, the governing nonlinear partial differential equations (PDEs) are transformed into a system of nonlinear ordinary differential equations (ODEs). The transformed equations are then solved numerically using the shooting technique. In addition, an attempt is made to carry the asymptotic solution behavior for large stretching and suction parameters, and the asymptotic results of skin friction coefficient are then compared with the direct numerical solutions, which shows a good agreement. It is observed that the similarity equations exhibit dual solutions in a certain range of shrinking strength. These two solution branches show different behavior on the skin friction coefficient, local Nusselt number, Sherwood number, velocity, and temperature profiles. Thus, emphasis has been given to carrying out a stability analysis to determine the physically reliable solution. The stability analysis shows that the upper branch solution is stable. It is observed that the suction parameter increases the range of dual solutions and the magnitude of the critical point from where the dual solutions bifurcate; however, the non-Newtonian parameter shows the opposite behavior. The momentum, thermal and concentration boundary layer thicknesses in the upper branch solution are lower than the lower branch solution.

This work investigates the unsteady magnetohydrodynamic flow of generalized second grade fluid through a porous medium with Hall effects on heat and mass transfer. The second grade fluid with a fractional derivative is used for the constitutive equation. A second-order fractional backward difference formula in the temporal direction and a spectral collocation method in the spatial direction are proposed to solve the model numerically. In the numerical implementation, a fast method is applied to decrease the memory requirement and computational cost. The velocity, temperature, and concentration profiles are discussed through graphs. The effects of various parameters on the velocity profiles, temperature field, and concentration field are shown. Results indicate that as the fractional derivative γ increases and the Hall parameter m decreases, the amplitudes of the velocity components decrease.

A numerical analysis is carried out for oscillatory flow of a viscous incompressible fluid through thin-walled elastic tubes with small curvature. A wave propagation analysis for sinusoidal input pressure disturbance yields a resulting asymmetrical flow pattern and the secondary flow pattern induced by centrifugal effects due to curvature. Essential differences between the effects of curvature on steady and oscillatory flows are obtained. A complicated quadrihelical secondary flow pattern is obtained. The flow pattern and computed wall shear in curved tubes are determined and compared with those of oscillatory flow through straight elastic tubes. Parameters in the computation are chosen to correspond to physiological flows at arterial sites of small curvature.

In this article, we have examined the effect of thermal radiation, suction/injection of the unsteady oscillatory dusty fluid flow through vertical parallel plates full of drenched porous medium with non homogeneous wall temperature. The major equations are solved by semi analytically and obtained exact solution. The effects of the various embedded parameters like Hartman number, radiation parameter, velocity profile, flow parameter on temperature, heat transfer rate and skin friction are discussed and represented graphically.

In this paper, the analytical solutions for unsteady free convection flow of rotating second grade fluid over an isothermal oscillating vertical plate are obtained. The effect of magnetohydrodynamics (MHD) flow in a porous medium is also considered. The governing equation for momentum is modelled in a rotating system such that both fluid and plate rotate in unison with uniform angular velocity. This phenomenon is modelled in the form of partial differential equations together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The corresponding non-dimensional momentum and energy equations with conditions are solved using Laplace transform technique. Expression for velocity and temperature fields are obtained and displayed graphically for different values of second grade fluid (α), rotation (b), magnetic (M) and porosity (K) parameters. Results obtained satisfied all the initial and boundary conditions.

Oscillatory fluid flow affects human marrow stromal cell proliferation and differentiation

Parameter estimation for unsteady MHD oscillatory free convective flow of generalized second grade fluid with Hall effects and thermal radiation effects

An analysis of an oscillatory magnetohydrodynamic (MHD) convective flow of a second order (viscoelastic), incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented. The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature of the plate with no-slip condition is non-uniform and oscillates periodically with time and the temperature difference of the two plates is assumed high enough to induce heat radiation. The entire system rotates in unison about the axis perpendicular to the planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters of the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of the viscoelastic parameter γ, rotation parameter Ω, suction parameter λ , Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, radiation parameter N and the frequency of oscillation ω .

BackgroundOscillatory fluid flow (OFF)-induced shear stress leads to positive bone remodeling through pro-formative and anti-resorptive effects on bone cells. In this study, the effects of high frequency OFF on expression of receptor activator of NF-κB ligand (RANKL) and osteoprotegerin (OPG), two important regulators of osteoclast differentiation, were investigated.MethodsCells were exposed to 1 Pa peak shear stress using three loading frequencies (1, 10, and 20 Hz) widely employed in cell, animal, and clinical studies of bone remodeling. Two separate experiments were performed where either the total number of cycles (3600 cycles) or the total loading time (60 min) was kept constant. Real-time RT-PCR was used to quantify mRNA levels of RANKL, OPG.Results3600 cycles of OFF at 1 Hz and 10 Hz loading decreased RANKL/OPG ratio. Interestingly, these results were due to different mechanisms where at 1 Hz the decrease was due to an increase in OPG mRNA, whereas at 10 Hz the decrease was due to a decrease in RANKL mRNA.ConclusionAlthough high frequency OFF does not appear to further enhance the decrease in the RANKL/OPG ratio, these results suggest a potential to differentially control the change in either RANKL or OPG mRNA expression by applying different loading frequencies.

Oscillatory channel flow in a rotating system is considered. The Navier–Stokes equations reduce to the Ekman equations that are solved exactly. The results show the interaction between oscillation frequency and rotation rate. Resonance occurs when the oscillation frequency is twice the rotation rate.

This study explains the transient free convection phenomenon in a vertical porous channel subject to nonlinear thermal radiation. The infinite vertical channel encloses magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid. The left channel wall possesses time-dependent velocity , while the right wall exhibits no motion. The momentum and temperature field equations are developed on the bases of momentum conservation law and Fourier’s principle of heat transfer. Laplace transformation technique and Durbin’s numerical inversion method are jointly incorporated to compute the solutions of the formulated problem. The influences of flow and material parameters on heat transfer and fluid velocity are graphically scrutinized with physical aspects. The numerical computations for skin friction and temperature gradient are tabularized to comprehensively examine the wall shear stress and heat transfer rate. Finally, velocity fields for Maxwell fluid, second grade fluid, and viscous fluid are traced out as limiting cases and their comparison is drawn with the velocity field of an Oldroyd-B fluid. Besides this, some newly published results are also deduced from the acquired solutions. It is observed that increasing the magnitude of radiation parameter Rd rapidly enhances the rate of heat transfer at the right channel wall while an inverse behavior of Nusselt number is witnessed at the left channel wall. The Maxwell fluid and second grade fluid indicate the swiftest and slowest channel flow rates respectively. The shear stress specifies dual nature for relaxation and retardation parameters subject to static and moving wall. Additionally, it is found that the flow of an Oldroyd-B fluid is retarded by a magnetic field.

To provide a quantitative description of the convection field of gas transport through the lung under both low and high-frequency ventilation conditions, volume-cycled, purely oscillatory flow has been investigated in a symmetrically bifurcating model bronchial bifurcation. Significant differences in the flow properties that developed as the Reynolds number varied from 750 to 950 and the dimensionless frequency varied from 3 to 12 are described. At low frequency, the axial velocity field was found to approximate closely that of a steady flow through a bifurcation. However, even at alpha = 3, secondary velocity fields were confined to within a few diameters of the bifurcation, with less than 10 percent of the magnitude of the axial velocity. At high frequency they were still slower and more limited. These secondary velocity observations are discussed in terms of a physical mechanism balancing inviscid centripetal acceleration with viscous retardation. As the dimensionless frequency increased but the flow amplitude decreased, the magnitude of the axial drift velocity field was found to decrease. In addition, a burst of high-frequency velocity fluctuations was detected in both the axial and secondary velocity measurements in the parent tube, in low-frequency flow, during the deceleration phase of expiration. The position and timing of this burst suggest that it derives from the free shear layer in the parent tube. Stability criteria for the flow were therefore evaluated.