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We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field p. The latter has been chosen for solutions correlated explicitly with the critical maximal non-zero level of stress τs in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for two functions, p and τs. As a result, a set of new semi-analytical solutions are presented and graphically plotted. [ABSTRACT FROM AUTHOR]

Here, unsteady boundary layer flow under the action of magnetic effect over a moving stagnation surface has been investigated numerically. This study examines non-Newtonian fluid flow with respect to combined effect of magnetic field, movement of surface and time. Governing equations are dimensionless by applying nondimensional quantities. Then system of coupled ordinary differential equations are obtained by appropriate similarly transformations, in terms of the governing parameter including unsteady parameter (k) , magnetic number (M) , power-law index (n) and three-dimensional parameter (α). Thus, the obtained modelled equations are solved numerically by the shooting technique. The problem's parameters are thoroughly discussed and verified physically and graphically. The obtained results validate to literature result. The two relevant flows' velocity profile's numerical results have been examined. [ABSTRACT FROM AUTHOR]

The effect of elasticity on the peristaltic flow of a micropolar fluid containing nanoparticles in a cylindrical tube is investigated using a mathematical model. The expressions for velocity and flux flow rate are determined by using Homotopy Perturbation method, under long wave length and low Reynold's number approximations. The variation of flux is calculated by Rubinow and Keller, Muzumdar methods. Different parameters' effects on velocity and flow have been discussed. For various settings, the trapping phenomenon is demonstrated. The flux increases as the elasticity parameters, micropolar parameter, thermophoresis parameter, and coupling number increase. The flux similarly reduces as the Brownian motion parameter is increased. The obtained results are same when we apply Rubinow and Keller, Muzumdar methods. [ABSTRACT FROM AUTHOR]

The processes of hydrodynamics and heat transfer during the flow of a non-Newtonian polymeric medium in a plane channel have been investigated with boundary conditions of the first kind. Consideration was given to a steady-state nonisothermal process with low values of the Reynolds number and high values of the Péclet number, which made it possible to neglect gravity and inertial forces, and also longitudinal thermal conductivity. The Ellis model with a viscosity dependent on temperature, pressure, and the degree of chemical transformation was used as the rheological model. A high-viscosity medium was investigated. Therefore, it is the dissipative term that was taken account of in the energy equation. With the above rheological model, an expression in explicit form was obtained from the equation of motion of such a medium for the velocity profile of its flow. It has been established that the dependence of the viscosity of a medium on its temperature, pressure, and the degree of transformation has an appreciable effect on the distribution of the temperature of the medium and the velocity of its flow along the channel's length. Taking account of the temperature dependence of the viscosity of the medium leads to a decline in the role of dissipation in the process of its warmup. The dependence of the medium's viscosity on pressure, conversely, considerably enhances the dissipative effect, which appreciably accelerates the course of a chemical reaction. [ABSTRACT FROM AUTHOR]

• MHD non-Newtonian fluid flow with CNTs and heat transfer across a linearly shrinking sheet. • An exact solutions are extracted for the governing equations of the aforesaid flow. • Two types of non-Newtonian fluids like second grade fluid and Walters' liquid B. • The existence of unique and dual solutions domains are traced by physical parameters. • Dual solutions exist for second grade fluid for both slip and no-slip restrictions. The present paper focuses on electrically driven magnetohydrodynamic non-Newtonian fluid flow (viscoelastic fluid)with CNTs and heat transmission across a linearly shrinking sheet. The flow is urged with the partial slip conditions, radiation and heat source/sink. Single walled and multi walled CNTs are considered in this analysis. An exact solution is extracted for the governing equations of the aforesaid flow of two types of non-Newtonian fluids like second grade fluid and Walters' liquid B with CNTs using similarity transformations. The flow velocity is pretentious due to many physical parameters like magnetic force, visco-elasticity, slip parameter, whereas the energy profile is pretentious due to Prandtl number, Biot number, heat sink/source parameter and radiation parameter. The existence of unique and dual solutions domains are traced by combining the above parameters and velocity, energy profiles and skin friction are explained using graphs. The results reveal that the dual solutions exist for both types of viscoelastic fluids under specific flow restrictions. In particular, dual solutions exist for second grade fluid for both slip and no-slip restrictions. And similar observations are found for Walters' liquid B fluid for unique slip flow when viscoelastic parameter value increases above a definite value. Inclusion of magnetic field terminates the ambiguity of existence of solution for different λ 1 values for both viscoelastic fluids. [ABSTRACT FROM AUTHOR]

The theory of rheology of non-Newtonian fluids is based on the generalized Newtonian hypothesis of viscosity. The viscometers for non-Newtonian fluids should implement fluid flows with the known stress and strain state parameters distributions. Ideally, the distributions should be homogeneous in the flow domain. The idea of the proposed method is based on a combination of a capillary and a rotational viscometers implemented in the torus-shaped capillary viscometer. Analysis of the mathematical model of the inertial non-Newtonian fluid flow in the torus allowed to determine the conditions of homogeneity of the mechanical and thermal parameters in the flow domain and to develop method of viscosity measurement. The measured values are the shear rate on the inner surface of the capillary and the flow rate. The measurements are implemented with the computer vision system that processes data obtained from the high speed CMOS camera that records inertial flow in the transparent capillary illuminated with laser. The computer vision system is based on the application of deep convolutional neural network for laser speckle contrast imaging processing. During the experiments, the proposed viscometer was compared with the Brookfield rotational viscometer. The relative error of the proposed viscometer and method is less than 2 %. The inertial viscometer is compact, it allows to study the wide range of shear rates per one test in automatic mode, and it has low fluid capacity of approximately 1.87 ml. That makes it possible to use the viscometer as a point on care testing device in medicine to study the rheology of physiological fluids, in particular blood. [Display omitted] • Inertial flow in a torus-shape capillary is perfectly symmetrical and homogeneous. • Laser speckle-contrast imaging allows one to see flow velocity on an image. • Artificial intelligence allows computer vision to see shear rate of the fluid flow. • Inertial viscometer could be a novel point on care testing device in medicine. [ABSTRACT FROM AUTHOR]

We study the pressure driven transport of a multilayer system consisting of alternate Newtonian and non-Newtonian fluids in the narrow fluidic configuration. We consider the power law model to describe the rheology of the non-Newtonian fluid in this study. The first part of the analysis, employing the assumptions routinely conferred in the literature, constitutes for an analytical solution of the transport equation resulting in the closed-form expressions of velocity field and net throughput. We demonstrate that the rheology driven modification in the flow velocity for a given strength of the applied forcing leads to the prolific amplification in micro-pumping phenomena. In the second part, the use of artificial neural network (ANN) is implemented to present an alternative solution for the problem undertaken in this study by using the analytical results from the first part. To make the prediction using ANN, various influential transport parameters are considered and their effects on the velocity and net throughput are analyzed. It is elucidated that an appropriately trained neural network can act as a good alternative for time-consuming calculations on the multi-layered fluid flow in micro channels. The flow configuration considered in this analysis alongside the findings of our work may provide a pathway of developing novel analytical platforms for precise loading and handling of chemical samples of biological fluids in a portable fluidic environment. [Display omitted] • Transport of Multilayer system comprising of alternate Newtonian and non-Newtonian fluids. • Closed-form expressions of velocity field and net throughput. • The use of artificial neural network (ANN) implemented to present an alternative solution. • Trained neural network as a good alternative on the multi-layered fluid flow analysis. [ABSTRACT FROM AUTHOR]