3 research outputs found

    Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia

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    In this paper, we present an analytical study of pressure-driven flow of micropolar non-Newtonian physiological fluids through a channel comprising two parallel oscillating walls. The cilia are arranged at equal intervals and protrude normally from both walls of the infinitely long channel. A metachronal wave is generated due to natural beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. Appropriate expressions are presented for deformation via longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The conservation equations for mass, longitudinal and transverse (linear) momentum and angular momentum are reduced in accordance with the long wavelength and creeping Stokesian flow approximations and then normalized with appropriate transformations. The resulting non-linear moving boundary value problem is solved analytically for constant micro-inertia density, subject to physically realistic boundary conditions. Closed-form expressions are derived for axial velocity, angular velocity, volumetric flow rate and pressure rise. The transport phenomena are shown to be dictated by several non-Newtonian parameters, including micropolar material parameter and Eringen coupling parameter, and also several geometric parameters, viz eccentricity parameter, wave number and cilia length. The influence of these parameters on streamline profiles (with a view to addressing trapping features via bolus formation and evolution), pressure gradient and other characteristics are evaluated graphically. Both axial and angular velocities are observed to be substantially modified with both micropolar rheological parameters and furthermore are significantly altered with increasing volumetric flow rate. Free pumping is also examined. An inverse relationship between pressure rise and flow rate is computed which is similar to that observed in Newtonian fluids. The study is relevant to hemodynamics in narrow capillaries and also bio-inspired micro-fluidic devices

    Finite element study of biomagnetic fluid flow in a symmetrically stenosed channel

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    The two-dimensional unsteady, laminar flow of a viscous, Newtonian, incompressible and electrically conducting biofluid in a channel with a stenosis, under the influence of a spatially varying magnetic field, is considered. The mathematical modeling of the problem results in a coupled nonlinear system of equations and is given in stream function-vorticity-temperature formulation for the numerical treatment. These equations together with their appropriate boundary conditions are solved iteratively using the finite element method for the spatial discretization, and an unconditionally stable backward difference scheme is employed for the time integration. The numerical results obtained are illustrated using streamlines, vorticity and temperature contours. The behavior of the biofluid along the thin channel is investigated for a symmetric stenosis of degrees 40% and 60%, with a magnetic source placed below the lower plate. The results indicate that the flow is appreciably affected by the presence of stenosis and the magnetic source in terms of vortices. The lengths of the vortices and the temperature increase with increase in the intensity of the magnetic field and the degree of the constriction
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