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Purpose: Cilia serves numerous biological functions in the human body. Malfunctioning of nonmotile or motile cilia will have different kinds of consequences for human health. More specifically, the directed and rhythmic beat of motile cilia facilitates the unidirectional flow of fluids that are crucial in both homeostasis and the development of ciliated tissues. In cilia-dependent hydrodynamic flows, tapering geometries look a lot like the structure of biological pathways and vessels, like airways and lymphatic vessels. In this paper, the Carreau fluid model through the cilia-assisted tapered channel (asymmetric) under the influence of induced magnetic field and convective heat transfer is investigated. Design/methodology/approach: Lubrication theory is a key player in the mathematical formulation of momentum, magnetic field and energy equations. The formulated nonlinear and coupled differential equations are solved with the aid of the homotopy perturbation method (HPM). The graphical results are illustrated with the help of the computational software "Mathematica." Findings: The impact of diverse emerging physical parameters on velocity, induced magnetic field, pressure rise, current density and temperature profiles is presented graphically. It is observed that the cilia length parameter supported the velocity and current density profiles, while the Hartman number and Weissenberg number were opposed. A promising effect of emerging parameters on streamlines is also perceived. Originality/value: The study provides novel aspects of cilia-driven induced magnetohydrodynamics flow of Carreau fluid under the influence of induced magnetic field and convective heat transfer through the asymmetric tapered channel. [ABSTRACT FROM AUTHOR]

Forced convective heat transfer and boundary layer flow of non-Newtonian fluid over a moving wedge is numerically studied. The non-Newtonian fluid is represented by Carreau fluid which is inelastic and characterizes shear-thinning and shear-thickening fluid. The thermal conductivity of fluid is no longer constant during heat transfer but is a function of temperature. The motion of the wedge surface is considered in the direction of mainstream or opposite. Both wedge and mainstream flows are assumed as a power of distance from the origin. Upon using similarity transformations, resultant equations are analyzed numerically using Chebyshev collocation and shooting methods for simulations of solutions. Most of the general features of solutions are identical to Newtonian fluid, the effects of Carreau fluid are to increase the velocity and heat transfer rate, and decrease the thicknesses. The present results of Carreau fluid and heat transfer unveil single and double solutions for the same system parameters and are shown to be a continuation of the Newtonian fluid. Also, the non-uniqueness of the solutions for the same set of parameters is classified as first and second solutions. Thus, there is a critical point beyond which no solution exists to model. In order to identify which of these solutions can be simulated practically, we perform linear stability analysis on velocity and temperature solutions. The eigenvalue analysis shows that the first solutions are always stable and the second solutions are amplified in time. Other interesting flows and heat transfer features are discussed in detail. [Display omitted] • We study boundary layer flow and forced convective heat transfer in Carreau fluid. • We also include generalized thermal conductivity and viscous dissipation in model. • Governing equations are solved using Chebyshev collocation and shooting technique. • We experience the non-uniqueness of the model which produces the dual solutions. • Stability of dual solutions is analyzed using an eigenvalue approach. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model of the blade coating of the viscoelastic Carreau fluid which passes through the gap between the fixed blade and the moving substrate is constructed. The governing equations in the light of LAT (Lubrication Approximation Theory) are nondimensionalized and the solutions for the velocity, volumetric flow rate and the pressure gradient are calculated using Adomian decomposition method and numerical method. Numerical results for the velocity distribution using shooting method have also been studied by taking the full lubrication equation without taking the binomial expansion. Some important quantities from the industrial point of view like pressure, shear stress, Nusselt number and skin friction coefficient are also calculated. The important results are graphically shown at the end. With exponential blade coater, we have calculated velocity profiles, pressure, coating thickness and blade loading. Some of these results are shown graphically while other are presented in the tabulated form. [ABSTRACT FROM AUTHOR]

The unsteady flow characteristics of blood in a catheterized overlapping stenosed artery are analyzed in presence of body acceleration and magnetic field. The stenosed arterial segment is modeled as a rigid constricted tube. An improved shape of stenosis in the realm of the formulation of the arterial narrowing caused by atheroma is integrated in the present study. The catheter inside the artery is approximated by a thin rigid tube of small radius while the streaming blood in the artery is characterized by the Carreau model. Employing mild stenosis condition, the governing equation of the flow is derived which is then solving numerically using finite difference scheme. The variation of axial velocity, flow rate, resistance impendence and wall shear stress is shown graphically for various parameters of interest. The flow patterns illustrating the global behavior of blood are also presented. [ABSTRACT FROM AUTHOR]

Abstract: The effect of an induced magnetic field on peristaltic flow of an incompressible Carreau fluid in an asymmetric channel is analyzed. Perturbation solution to equations under long wavelength approximation is derived in terms of small Weissenberg number. Expressions have been constructed for the stream function, the axial induced magnetic field, the magnetic force function, the current density distribution and the temperature. Trapping phenomenon is examined with respect to emerging parameters of interest. [Copyright &y& Elsevier]

Abstract: Magnetohydrodynamic (MHD) peristaltic flow of a Carreau fluid in a channel with different wave forms are analyzed in this investigation. The flow analysis is conducted in the presence of an induced magnetic field. Long wavelength approach is adopted. Mathematical expressions of stream function, magnetic force function and an axial induced magnetic field are constructed. Pressure rise and pumping phenomena are described. [Copyright &y& Elsevier]

In this paper a problem of a hydraulic fracture driven by a non-Newtonian shear-thinning fluid is analysed. For the PKN fracture geometry three different rheological models of fluid are considered: (i) the Carreau fluid, (ii) the truncated power-law fluid, (iii) the power-law fluid. For each of these models a number of simulations are performed. The results are post-processed and compared with each other in order to find decisive factors for similarities/dissimilarities. It is shown that under certain conditions even the basic power-law rheology can be a good substitute for the Carreau characteristics. Although for a particular fluid such a conclusion cannot be made a priori, post-processing based on average values of the fluid shear rates is a very good tool to verify credibility of the results obtained for simplified rheological models. The truncated power-law rheology is a good alternative for the Carreau model. It always produces results that are very similar to those obtained with the equivalent Carreau fluid and simultaneously provides a relative ease of numerical implementation. [ABSTRACT FROM AUTHOR]